2012 SIAM Conference on Uncertainty Quantification 1 Final Program and Abstracts

This conference is being held in cooperation with the American Statistical Association (ASA), the Statistical and Applied Mathematical Sciences Institute (SAMSI), and the United States Association for Computational Mechanics (USACM).

Sponsored by the SIAM Activity Group on Uncertainty Quantification (SIAG/UQ)

The SIAM Activity Group on Uncertainty Quantification (SIAG/UQ) fosters activity and collaboration on all aspects of the effects of uncertainty and error on mathematical descriptions of real phenomena. It seeks to promote the development of theory and methods to describe quantitatively the origin, propagation, and interplay of different sources of error and uncertainty in analysis and predictions of the behavior of complex systems, including biological, chemical, engineering, financial, geophysical, physical and social/political systems. The SIAG/UQ serves to support interactions among mathematicians, statisticians, engineers, and scientists working in the interface of computation, analysis, statistics, and probability.

Society for Industrial and Applied Mathematics 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215-386-7999 Conference E-mail: [email protected] Conference Web: www.siam.org/meetings/ Membership and Customer Service: (800) 447-7426 (US & Canada) or +1-215-382-9800 (worldwide)

www.siam.org/meetings/uq12 2 2012 SIAM Conference on Uncertainty Quantification

Table of Contents Philip Stark Hotel Check-in University of California, Berkeley, USA and Check-out Times Christian Soize Program-at-a-Glance...... Fold out section Check-in time is 4:00 PM and check-out Université Paris-Est Marne-la-Vallée, France General Information...... 2 time is 12:00 PM. Get-togethers...... 4 Dongbin Xiu Purdue University, USA Invited Plenary Presentations ...... 8 Minitutorials...... 5 Child Care Poster Session...... 11 SIAM Registration Desk For local child care options, please Program Schedule...... 10 The SIAM registration desk is located in contact the concierge at the Raleigh Abstracts...... 61 the Chancellor Room and Pre-Function Marriott City Center Hotel Speaker and Organizer Index...... 143 Area. It is open during the following (+1-919-833-1120). Conference Budget...... Inside Back cover times: Hotel Meeting Room Map...... Back cover Sunday, April 1 5:00 PM - 8:00 PM Corporate Members and Affiliates SIAM corporate members provide Organizing Committee Co-Chairs Monday, April 2 their employees with knowledge about, Don Estep 7:00 AM - 5:00 PM access to, and contacts in the applied Colorado State University, USA mathematics and computational sciences Dave Higdon community through their membership Tuesday, April 3 Los Alamos National Laboratory, USA benefits. Corporate membership is more (ASA Representative) 7:45 AM - 5:00 PM than just a bundle of tangible products Habib Najm and services; it is an expression of Sandia National Laboratories, USA Wednesday, April 4 support for SIAM and its programs. SIAM is pleased to acknowledge its 7:45 AM - 5:00 PM Organizing Committee corporate members and sponsors. In recognition of their support, non- Susie Bayarri member attendees who are employed by University of Valencia, Spain Thursday, April 5 the following organizations are entitled 7:45 AM - 1:30 PM Jim Berger to the SIAM member registration rate. Duke University, USA Roger Ghanem University of Southern California, Los Angeles, Hotel Address Corporate Institutional USA (USACM Representative) Raleigh Marriott City Center Hotel Members Albert Gilg 500 Fayetteville Street The Aerospace Corporation Siemens, Germany Raleigh, North Carolina 27601 USA Air Force Office of Scientific Research Pierre Gremaud Statistical and Applied Mathematical Sciences Telephone: + 1-919-833-1120 AT&T Laboratories - Research Institute, USA (SAMSI Representative) Reservations: + 1-888-236-2427 Bechtel Marine Propulsion Laboratory Max Gunzburger Fax: +1- 919-833-8912 The Boeing Company Florida State University, USA CEA/DAM Gardar Johannesson Lawrence Livermore National Laboratory, USA Hotel Telephone Number DSTO- Defence Science and Laura Lurati To reach an attendee or to leave a Technology Organisation Boeing Inc., USA message, call + 1-919-833-1120. The Hewlett-Packard Youssef Marzouk hotel operator can either connect you IBM Corporation Massachusetts Institute of Technology, USA with the SIAM registration desk or to IDA Center for Communications the attendee’s room. Messages taken Anthony O’Hagan Research, La Jolla University of Sheffield, United Kingdom at the SIAM registration desk will be posted to the message board located in IDA Center for Communications Stephan Sain the registration area. Research, Princeton National Center for Atmospheric Research, USA 2012 SIAM Conference on Uncertainty Quantification 3

Institute for Defense Analyses, Center Leading the applied Fax: +1-215-386-7999 for Computing Sciences mathematics community . . . E-mail: [email protected] Lawrence Berkeley National Laboratory Join SIAM and save! Postal mail: Lockheed Martin Society for Industrial and Applied SIAM members save up to $130 on full Mathematics, Mathematical Sciences Research registration for the SIAM Conference Institute 3600 Market Street, 6th floor, on Uncertainty Quantification (UQ12)! Philadelphia, PA 19104-2688 USA Max-Planck-Institute for Dynamics of Join your peers in supporting the Complex Technical Systems premier professional society for applied Mentor Graphics mathematicians and computational scientists. SIAM members receive Standard Audio/Visual The MITRE Corporation subscriptions to SIAM Review and Set-Up in Meeting Rooms National Institute of Standards and SIAM News and enjoy substantial SIAM does not provide computers for Technology (NIST) discounts on SIAM books, journal any speaker. When giving an electronic National Security Agency (DIRNSA) subscriptions, and conference presentation, speakers must provide their Naval Surface Warfare Center, Dahlgren registrations. own computers. SIAM is not responsible Division If you are not a SIAM member and paid for the safety and security of speakers’ computers. NEC Laboratories America, Inc. the Non-Member or Non-Member Mini Speaker/Organizer rate to attend the The Plenary Session Room will have two Oak Ridge National Laboratory, conference, you can apply the difference (2) overhead projectors, two (2) screens managed by UT-Battelle for the between what you paid and what a and one (1) data projector. Cables or Department of Energy member would have paid ($130 for a adaptors for Apple computers are not PETROLEO BRASILEIRO S.A. – Non-Member and $65 for a Non-Member supplied, as they vary for each model. PETROBRAS Mini Speaker/Organizer) towards a Please bring your own cable/adaptor if Philips Research SIAM membership. Contact SIAM using a Mac computer. Customer Service for details or join at Sandia National Laboratories All other concurrent/breakout rooms the conference registration desk. will have one (1) screen and one (1) data Schlumberger-Doll Research If you are a SIAM member, it only costs projector. Cables or adaptors for Apple Tech X Corporation $10 to join the SIAM Activity Group computers are not supplied, as they vary Texas Instruments Incorporated on Uncertainty Quantification (SIAG/ for each model. Please bring your own UQ). As a SIAG/UQ member, you are cable/adaptor if using a Mac computer. U.S. Army Corps of Engineers, Engineer eligible for an additional $10 discount Overhead projectors will be provided Research and Development Center on this conference, so if you paid only when requested. United States Department of Energy the SIAM member rate to attend the If you have questions regarding conference, you might be eligible for a availability of equipment in the meeting *List current February 2012 free SIAG/UQ membership. Check at room of your presentation, or to request the registration desk. an overhead projector for your session, Free Student Memberships are available please see a SIAM staff member at the to students who attend an institution that registration desk. Funding Agency is an Academic Member of SIAM, are SIAM and the Conference Organizing members of Student Chapters of SIAM, Committee wish to extend their thanks or are nominated by a Regular Member E-mail Access and appreciation to the U.S. National of SIAM. Complimentary wireless Internet will Science Foundation and the Department Join onsite at the registration desk, go to be available to SIAM attendees booked of Energy (DOE) for their support of this www.siam.org/joinsiam to join online or within the SIAM room block in guest conference. download an application form, or contact rooms, hotel lobby and bar area. Guests SIAM Customer Service will need to accept charges upon Telephone: +1-215-382-9800 accessing the Internet. The fees will be (worldwide); or 800-447-7426 (U.S. and reversed upon-check out. Canada only) SIAM will also provide a limited number of email stations. 4 2012 SIAM Conference on Uncertainty Quantification

Registration Fee Includes Table Top Displays Social Media • Admission to all technical sessions Princeton University Press SIAM is promoting the use of social • Business Meeting (open to SIAG/UQ SIAM media, such as Facebook and Twitter, members) in order to enhance scientific discussion Springer at its meetings and enable attendees • Coffee breaks daily to connect with each other prior to, • Room set-ups and audio/visual during and after conferences. If you equipment Name Badges are tweeting about a conference, please • Welcome Reception and Poster A space for emergency contact use the designated hashtag to enable Session information is provided on the back of other attendees to keep up with the your name badge. Help us help you in Twitter conversation and to allow better the event of an emergency! archiving of our conference discussions. Job Postings The hashtag for this meeting is #SIAMUQ12. Please check with the SIAM registration desk regarding the availability of job Comments? postings or visit http://jobs.siam.org. Comments about SIAM meetings are encouraged! Please send to: Sven Leyffer, SIAM Vice President for Important Notice Programs ([email protected]) to Poster Presenters The poster session is scheduled for Sunday, April 1 from 6:00 PM – 8:00 Get-togethers PM. Poster presenters are requested • Sunday, April 1, 6:00 PM to set up their poster material on the Welcome Reception provided 4’ x 8’ poster boards in State and Poster Session DEF between the hours of 2:00 PM and • Monday, April 2, 8:00 PM 6:00 PM. All materials must be posted Business Meeting by Sunday, April 1 at 6:00 PM, official (open to SIAG/UQ members) start time of the session. Posters will remain on display through 8:00 PM. Complimentary beer and wine will be Poster displays must be removed by served. 8:00 PM on Sunday, April 1. Posters remaining after this time will be discarded. SIAM is not responsible for Please Note discarded posters. SIAM is not responsible for the safety and security of attendees’ computers. Do not leave your laptop computers SIAM Books and Journals unattended. Please remember to turn Display copies of books and off your cell phones, pagers, etc. during complimentary copies of journals are sessions. available on site. SIAM books are available at a discounted price during Recording of Presentations the conference. If a SIAM books Audio and video recording of representative is not available, completed presentations at SIAM meetings is order forms and payment (credit cards prohibited without the written are preferred) may be taken to the SIAM permission of the presenter and SIAM. registration desk. The books table will close at 9:30 AM on Thursday, April 5.

2012 SIAM Conference on Uncertainty Quantification 5

Minitutorials ** All Minitutorials will take place in State C**

Analysis of SPDEs and Numerical Methods Emulation, Elicitation and Calibration for Uncertainty Quantification This minitutorial concerns statistical approaches to UQ based This tutorial explores numerical and functional analysis on Bayesian statistics and the use of emulators. It is organised techniques for solving PDEs with random input data, such as three 2-hour sessions. The first begins with an overview as model coefficients, forcing terms, initial and boundary of UQ tasks (uncertainty propagation, sensitivity analysis, conditions, material properties, source and interaction terms or calibration, validation) and of how emulation (a non-intrusive geometry. The resulting stochastic systems will be investigated technique) tackles those tasks efficiently. It continues with an for well-posedness and regularity. We will present detailed introduction to elicitation, a key component of input uncertainty convergence analysis of several intrusive and non-intrusive quantification in practice. The second session presents the basic methods for quantifying the uncertainties associated with ideas of emulation and illustrates its power for uncertainty input information onto desired quantities of interest, forward propagation, etc. The third session is about calibration, and inverse UQ approaches, and necessary theoretical results including the importance of model discrepancy and history from stochastic processes and random fields, error analysis, matching. anisotropy, adaptive methods, high-dimensional approximation, random sampling and sparse grids. MT2 Part I: Monday, April 2, 2:00 PM - 4:00 PM MT5 Part II: Tuesday, April 3, 2:00 PM - 4:00 PM MT8 Part III: Wednesday, April 4, 2:00 PM - 4:00 PM MT1 Part I: Monday, April 2, 9:30 AM - 12:30 PM MT4 Part II: Tuesday, April 3, 9:30 AM - 12:30 PM Organizer: Organizer: Anthony O’Hagan, University of Sheffield, United Kingdom Clayton G. Webster, Oak Ridge National Laboratory, USA Co-author: Speakers: Max Gunzburger, Florida State University, USA Peter Challenor, National Oceanography Centre, Southampton, United Kingdom Anthony O’Hagan, University of Sheffield, United Kingdom Speakers: Ian Vernon, University of Durham, United Kingdom John Burkardt, Florida State University, USA Clayton G. Webster, Oak Ridge National Laboratory, USA 6 2012 SIAM Conference on Uncertainty Quantification

SIAM Activity Group on Uncertainty Quantification (SIAG/UQ) www.siam.org/activity/uq

A GREAT WAY TO GET invOlvEd! Collaborate and interact with mathematicians and applied scientists whose work involves uncertainty quantification.

ACTIVITES INCLUDE: • Special sessions at SIAM Annual Meetings • Biennial conference • Website

BENEFITS OF SIAG/UQ mEmBErShIp: • Listing in the SIAG’s online-only membership directory • Additional $10 discount on registration at the SIAM Conference on Uncertainty Quantification(excludes student) • Electronic communications about recent developments in your specialty • Eligibility for candidacy for SIAG/UQ office • Participation in the selection of SIAG/UQ officers

ELIGIBILITY: • Be a current SIAM member

COST: • $10 per year • Student SIAM members can join 2 activity groups for free!

2011-2012 SIAG/UQ OFFICErS: • Chair: Donald Estep, Colorado State University • Vice Chair: Max Gunzburger, Florida State University • Program Director: Roger Ghanem, University of Southern California • Secretary: Habib Najm, Sandia National Laboratories

TO JOIN: SIAG/UQ: my.siam.org/forms/join_siag.htm SIAm: www.siam.org/joinsiam 2012 SIAM Conference on Uncertainty Quantification 7

Minitutorials * *All minitutorials will take place in State C**

Uncertainty Quantification: Foundations and Introduction to Statistical Analysis of Capabilities for Model-Based Simulations Extremes The minitutorial will present the physical motivation and This minitutorial will introduce the ideas and techniques mathematical foundations necessary for the formulation involved in the analysis of both univariate and multivariate of well-posed UQ problems in computational science and extremes. Statistical practice relies on fitting distributions engineering. In particular, the minitutorial will cover 1) aspects suggested by asymptotic theory to a subset of data considered of probabilistic modeling and analysis, 2) polynomial chaos to be extreme. The minitutorial will introduce the fundamental representations, 3) stochastic processes and Karhunen-Loeve asymptotic results which underlie extremes analysis via expansions, 4) forward UQ including sampling, sparse-grid, demonstrations and examples. Both block maximum and stochastic Galerkin and collocation, 5) inverse problems in UQ, threshold exceedance approaches will be presented for both the 6) overview of software resources, 7) summary of advanced univariate and multivariate cases. The multivariate portion of the topics. course will largely focus on how dependence is described for extremes: via an angular measure rather than via correlation.

MT3 Part I: Monday, April 2, 4:30 PM - 6:30 PM MT6 Part II: Tuesday, April 3, 4:30 PM - 6:30 PM MT7 Wednesday, April 4, 9:30 AM - 12:30 PM MT9 Part III: Wednesday, April 4, 4:30 PM - 6:30 PM Organizer and Speaker: Organizer: Dan Cooley, Colorado State University, USA Roger Ghanem, University of Southern California, USA

Speakers: Roger Ghanem, University of Southern California, USA A Tutorial on Uncertainty Quantification and Bert Debusschere, Sandia National Laboratories, USA Data Analysis for Inverse Problems We will start with a brief overview of ill-posed inverse problems and regularization that includes a quick review of the necessary results from functional analysis. We then focus on uncertainty quantification for a particular class of regularization procedures using frequentist and Bayesian frameworks. We describe basic methods to assess uncertainty in each of these frameworks. This will include a review of the basic statistics and probability tools needed. We end with an introduction to exploratory data analysis methods that can be used for model validation.

MT10 Thursday, April 5, 9:30 AM - 12:30 PM

Organizer and Speaker: Luis Tenorio, Colorado School of Mines, USA 8 2012 SIAM Conference on Uncertainty Quantification

Invited Plenary Speakers * *All Invited Plenary Presentations will take place in State C/D **

Monday, April 2

8:15 AM - 9:00 AM IP1 Sparse Tensor Algorithms in Uncertainty Quantification Christoph Schwab, ETH Zürich, Switzerland

1:00 PM - 1:45 PM IP2 Integrating Data from Multiple Simulation Models - Prediction and Tuning Derek Bingham, Simon Fraser University, Canada

Tuesday, April 3

8:15 AM - 9:00 AM IP3 Polynomial Chaos Approaches to Multiscale and Data Intensive Computations Omar M. Knio, Duke University, USA 2012 SIAM Conference on Uncertainty Quantification 9

Invited Plenary Speakers

Wednesday, April 4

8:15 AM - 9:00 AM IP4 Large Deviation Methods for Quantifying Uncertainty George C. Papanicolaou, Stanford University, USA

1:00 PM - 1:45 PM IP5 Model Reduction for Uncertainty Quantification of Large-scale Systems Karen E. Willcox, Massachusetts Institute of Technology, USA

Thursday, April 5

8:15 AM - 9:00 AM IP6 Statistical Approaches to Combining Models and Observations Mark Berliner, Ohio State University, USA 10 2012 SIAM Conference on Uncertainty Quantification

UQ12 Program 2012 SIAM Conference on Uncertainty Quantification 11

Sunday, April 1 Multiple Precision, Spatio-Temporal Sunday, April 1 Computer Model Validation using PP1 Predictive Processes Matthew J. Heaton, Stephan Sain, William Welcome Reception Kleiber, and Michael Wiltberger, National Registration and Poster Session Center for Atmospheric Research, USA; 5:00 PM-8:00 PM Derek Bingham, Simon Fraser University, 6:00 PM-8:00 PM Canada; Shane Reese, Brigham Young Room:Chancellor and Pre-Function Area Room:State DEF University, USA A Statistical Decision-Theoretic Variance Based Sensitivity Analysis of Approach to Dynamic Resource Epidemic Size to Network Structure Allocation for a Self-Aware Kyle S. Hickmann, Tulane University, Unmanned Aerial Vehicle USA; James (Mac) Hyman, Los Alamos Doug Allaire and Karen E. Willcox, National Laboratory, USA; John E. Massachusetts Institute of Technology, Ortmann, Tulane University, USA USA Autoregressive Model for Real-Time Computational Reductions in Weather Prediction and Detecting Stochastically Driven Neuronal Climate Sensitivity Models with Adaptation Currents Emily L. Kang, University of Cincinnati, Victor Barranca and Gregor Kovacic, USA; John Harlim, North Carolina State Rensselaer Polytechnic Institute, USA; University, USA David Cai, New York University, USA A Split Step Adams Moulton Milstein A Predictive Model for Geographic Method for Stiff Stochastic Differential Statistical Data Equations Jorge Diaz-Castro, University of Puerto Abdul M. Khaliq, Middle Tennessee State Rico, Puerto Rico University, USA; David A. Voss, Western Illinois University, USA A Stochastic Collocation Method Combined with a Reduced Basis Computer Model Calibration with Method to Compute Uncertainties in High and Low Resolution Model the Sar Induced by a Mobile Phone Output for Spatio-Temporal Data Mohammed Amine Drissaoui, Laboratoire William Kleiber, Stephan Sain, and AMPERE, France Michael Wiltberger, National Center for Atmospheric Research, USA; Derek Random and Regular Dynamics Bingham, Simon Fraser University, of Stochastically Driven Neuronal Canada; Shane Reese, Brigham Young Networks University, USA Pamela B. Fuller, Rensselaer Polytechnic Institute, USA Propagating Arbitrary Uncertainties Through Models Via the Probabilistic Calibration of Computer Models for Collocation Method Radiative Shock Experiments Matthew Cherry, University of Dayton, Jean Giorla, Commissariat à l’Energie USA; Jeremy Knopp, Air Force Research Atomique, France; E. Falize, CEA/ Laboratory, USA DAM/DIF, F-91297, Arpajon, France; C. Busschaert and B. Loupias, CEA, Goal-Oriented Statistical Inference DAM, DIF-Bruyeres, France; M. Koenig, Chad E. Lieberman and Karen E. Willcox, A. Ravasio, and A. Dizière, Ecole Massachusetts Institute of Technology, Polytechnique, Palaiseau, France; Josselin USA Garnier, Université Paris VII, France; C. Uncertainty in Model Selection in Michaut, Observatoire de Paris, Meudon, Remote Sensing France Anu Määttä, Marko Laine, and Johanna Regional Climate Model Ensembles Tamminen, Finnish Meteorological and Uncertainty Quantification Institute, Helsinki, Finland Tamara A. Greasby, National Center for Multifidelity Approach to Variance Atmospheric Research, USA Reduction in Monte Carlo Simulation Leo Ng, and Karen E. Willcox, Massachusetts Institute of Technology, USA 12 2012 SIAM Conference on Uncertainty Quantification

Local Sensitivity Analysis of Stochastic Monday, April 2 Systems with Few Samples Monday, April 2 John E. Ortmann, Tulane University, USA; IP1 James (Mac) Hyman, Los Alamos National Laboratory, USA; Kyle S. Hickmann, Sparse Tensor Algorithms in Tulane University, USA Registration Uncertainty Quantification Worst Case Scenario Analysis Applied 7:00 AM-5:00 PM 8:15 AM-9:00 AM to Uncertainty Quantification in Room:Chancellor and Pre-Function Area Room:State C/D Electromagnetic Simulations Ulrich Roemer, Stephan Koch, and Thomas Chair: Olivier P. Le Maitre, LIMSI-CNRS, Weiland, Technical University Darmstadt, France Germany Opening Remarks We survey recent mathematical and Constructive and Destructive 8:00 AM-8:15 AM computational results on sparse tensor Correlation Dynamics in Simple discretizations of Partial Differential Room:State C/D Stochastic Swimmer Models Equations (PDEs) with random inputs. Kajetan Sikorski, Rensselaer Polytechnic The sparse Tensor discretizations allow, Institute, USA as a rule, to overcome the curse of Preserving Positivity in Pc dimensionality in approximating infinite Approximations Via Weighted Pc dimensional problems. Results and Expansions Methods surveyed include a) regularity Faidra Stavropoulou and Josef Obermaier, and N-term gpc approximation results Helmholtz Zentrum München, Germany and algorithms for elliptic and parabolic Visualization of Uncertainty: Standard PDEs with random coefficients [joint Deviation and Pdf’s work with A. Cohen, R. DeVore and Richard A. Strelitz, Los Alamos National V.H.Hoang] and b) existence and Laboratory, USA regularity results for solutions of How Typical Is Solar Energy? A 6 Year classes of certain hyperbolic PDEs Evaluation of Typical Meteorological from conservation and balance laws. Year Data (TMY3) Multi-Level Monte-Carlo (MLMC) Matthew K. Williams and Shawn Kerrigan, Locus Energy, USA [joint with A. Barth] and Multi-Level Quasi-Monte-Carlo (MLQMC) [joint Second-Order Probability for Error with I. Graham, R. Scheichl, F.Y.Kuo Analysis in Numerical Computation and I.M. Sloan] methods can be viewed Hua Chen, Yingyan Wu, Shudao Zhang, Haibing Zhou, and Jun Xiong, Institute as particular classes of sparse tensor of Applied Physics and Computational discretizations. Numerical MLMC and Mathematics, China MLQMC results for elliptic PDEs with random coefficients and for nonlinear Uncertainty Quantification for Hydromechanical Coupling in Three systems of hyperbolic conservation laws Dimensional Discrete Fracture Network are presented [joint work with S. Mishra Souheil M. Ezzedine, and Frederick Ryerson, and J. Sukys (ETH)]. We compare the Lawrence Livermore National Laboratory, performance of these methods with USA that of adaptive generalized polynomial chaos discretizations. Christoph Schwab ETH Zürich, Switzerland

Coffee Break 9:00 AM-9:30 AM Room:Pre-Function Area 2012 SIAM Conference on Uncertainty Quantification 13

Monday, April 2 Monday, April 2 Monday, April 2 MT1 MS1 MS2 Analysis of SPDEs and Frontiers in Emulation Stochastic Uncertainty: Numerical Methods for 9:30 AM-11:30 AM Modeling, Forward Uncertainty Quantification - Room:State D Propagation, and Inverse Part I of II The area of computer models is an Problems - Part I of V 9:30 AM - 12:30 PM emerging and highly topical field of 9:30 AM-11:30 AM statistical research, with many challenges For Part 2 see MT4 Room:State A and an enormous range of applications. Room: State C For Part 2 see MS11 This tutorial explores numerical and Full uncertainty quantification regarding the complex physical system centres Uncertainty quantification in functional analysis techniques for solving computational science and engineering PDEs with random input data, such around the use of an emulator: a fast stochastic function which replaces the has two main components: (i) modeling as model coefficients, forcing terms, of the uncertainty in the input initial and boundary conditions, material complex and expensive physical model. Despite their successes, emulators parameters, consistent with available properties, source and interaction terms information, physical constraints, or geometry. The resulting stochastic still face several challenges both in terms of their construction and their and prior knowledge; (ii) the forward systems will be investigated for well- propagation of input uncertainty to the posedness and regularity. We will present use in various applications. Here, recent developments at the frontiers of output quantities used in engineering detailed convergence analysis of several design and regulatory requirements. This intrusive and non-intrusive methods for emulation methodology are discussed including efficient calibration techniques, minisymposium focuses on the stochastic quantifying the uncertainties associated approach to uncertainty quantification in with input information onto desired super-parameterisation and solutions to ill-conditioning. Applications in Oceanic, computational science and engineering; quantities of interest, forward and it aims to showcase emerging inverse UQ approaches, and necessary Galaxy formation and Natural History models will be discussed. methodologies for building parametric theoretical results from stochastic and nonparametric stochastic models for processes and random fields, error Organizer: Ian Vernon uncertain input parameters, eventually analysis, anisotropy, adaptive methods, University of Durham, United Kingdom involving the solution of stochastic high-dimensional approximation, random 9:30-9:55 History Matching: An inverse problems, as well as innovative sampling and sparse grids. alternative to Calibration for a Galaxy techniques for propagating input Formation Simulation Organizer: stochasticity through complex differential Ian Vernon, University of Durham, United models and computing statistics of the Clayton G. Webster, Oak Ridge National Kingdom output quantities of interest. Laboratory, USA 10:00-10:25 Emulation of Count Data in Healthcare Models Organizer: Youssef M. Marzouk Ben Youngman, University of Sheffield, Massachusetts Institute of Technology, USA Speakers: United Kingdom Organizer: Olivier LeMaitre John Burkardt, Florida State University, 10:30-10:55 Effective and Efficient LIMSI-CNRS, France USA Handling of Ill-Conditioned Correlation Organizer: Fabio Nobile Clayton Webster, Oak Ridge National Matrices in Kriging and Gradient EPFL, Switzerland Enhanced Kriging Emulators through Laboratory, USA 9:30-9:55 Bayesian Inference with Pivoted Cholesky Factorization Optimal Maps Keith Dalbey, Sandia National Laboratories, Tarek El Moselhy and Youssef M. Marzouk, USA Massachusetts Institute of Technology, 11:00-11:25 Super-parameterisation USA of Oceanic Deep Convection using 10:00-10:25 Nonparametric Bayesian Emulators Inference for Inverse Problems Yiannis Andrianakis, University of Andrew Stuart, University of Warwick, United Southampton, United Kingdom Kingdom 10:30-10:55 Sample-based UQ via Computational Linear Algebra (Not MCMC) Colin Fox, University of Otago, New Zealand

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Monday, April 2 Monday, April 2 Monday, April 2 MS2 MS3 MS4 Stochastic Uncertainty: Stochastic Sensitivity Analysis Kriging-based Surrogate Modeling, Forward for Correlated Inputs Models for Expensive Propagation, and Inverse 9:30 AM-11:30 AM Computer Codes Problems - Part I of V Room:State B 9:30 AM-11:30 AM continued Many mathematical models use a large Room:State E 11:00-11:25 Toward Extreme-scale number of poorly-known parameters Kriging-based surrogate models have Stochastic Inversion as inputs. Quantifying the influence of been widely developed in computer Tan Bui, University of Texas at Austin, each of these parameters is one of the experiments. The objective of this USA; Carsten Burstedde, Universitaet aims of sensitivity analysis. Stochastical mini-symposium is to present recent Bonn, Germany; Omar Ghattas, James R. approaches in the case of independent advances in kriging to perform Martin, Georg Stadler, and Lucas Wilcox, inputs have been widely developed. This optimization, statistical prediction, and University of Texas at Austin, USA session focus on the recent results derived risk analysis. In particular, the case of in the more realistic case where input codes with tunable precision and their parameters may be correlated. The main exploitation – with stochastic simulators difficulty is then to take into account the and partial converged simulations – are joint inputs distribution which is often presented. To conclude the symposium, unknown in practice. Various measures a presentation describing a problem with and computation tools will be described complex inputs is given. It will be the in the four next talks. opportunity to exchange on different Organizer: Clémentine Prieur methodologies and to consider how they Université Joseph Fourier and INRIA, France can benefit mutually. 9:30-9:55 Sensitivity Indices Based on a Organizer: Loic Le Gratiet Generalized Functional ANOVA Université Paris VII, France Clémentine Prieur, Université Joseph Fourier 9:30-9:55 Sampling Strategy and INRIA, France; Gaelle Chastiang, for Stochastic Simulators with INRIA, France; Fabrice Gamboa, University Heterogeneous Noise of Toulouse, France Loic Le Gratiet and Josselin Garnier, 10:00-10:25 Global Sensitivity Analysis Université Paris VII, France for Systems with Independent and/or 10:00-10:25 Optimization of Expensive Correlated Inputs Computer Experiments Using Partially Herschel Rabitz and Genyuan Li, Princeton Converged Simulations and Space- University, USA time Gaussian Processes 10:30-10:55 Variance-based Sensitivity Victor Picheny, CERFACS, France Indices for Models with Correlated 10:30-10:55 Quantifying and Inputs Using Polynomial Chaos Reducing Uncertainties on a Set of Expansions Failure Using Random Set Theory and Bruno Sudret, Université Paris-Est, France; Kriging Yann Caniou and Alexandre Micol, Chevalier Clément, IRSN and UNIBE, Phimeca, France France; David Ginsbourger, University 11:00-11:25 Global Sensitivity Analysis of Berne, Switzerland; Julien Bect, with Correlated Inputs: Numerical SUPELEC, France; Ilya Molchanov, Aspects in Distribution-Based Sensitivity University of Berne, Switzerland Measures 11:00-11:25 Models with Complex Emanuele Borgonovo, Bocconi University, Uncertain Inputs Italy David M. Steinberg, Tel Aviv University, Israel 2012 SIAM Conference on Uncertainty Quantification 15

Monday, April 2 Monday, April 2 Monday, April 2 MS5 MS6 MS7 A Posteriori Error Estimation Data Analysis and Inference Scalable Methods for for Reliable Uncertainty in Functional Spaces; Uncertainty Quantification Quantification - Part I of II Statistical and Numerical 9:30 AM-11:30 AM 9:30 AM-11:30 AM Approaches to Uncertainty Room:Congressional B Room:State F Estimation - Part I of II Uncertainty Quantification (UQ) in For Part 2 see MS14 9:30 AM-11:30 AM complex dynamic networks is essential A posteriori error estimation has Room:Congressional A for robust operation of commercial and defense systems. This session presents a rich history in the analysis of For Part 2 see MS15 recent advances in fast UQ methods for partial differential equations and is This minisymposium considers models high dimensional dynamical systems a standard verification technique for at the interplay between statistics that arise in industry. In particular we deterministic models. The extension and numerical analysis, dealing with will present a new iterative scheme for of error estimation techniques to uncertainty quantification and variability scalable propagation of uncertainty stochastic models has been the subject estimation in functional space settings. through networks of switching of increasing interest in recent years. The analysis of complex and high- systems and methods for uncertainty Themes of this minisymposium include dimensional data and problems (images, quantification utilizing sensitivity theoretical and numerical analysis of functional signals and dynamics, shapes, analysis and model reduction. We will errors in the propagation of uncertainty etc) calls in fact for the merging of also demonstrate how scalable UQ through computational models resulting advanced statistical and numerical can be used to design energy efficient from discretization, the use of surrogate expertise. The minisymposium aims building systems and discuss recent models/emulators, and sampling. in particular at showcasing recent and advances in wide usability of non- Both forward and inverse/inference innovative techniques for functional data intrusive polynomial chaos methods for problems may be considered. The intent analysis, including penalized smoothing high dimensional problems. of this minisymposium is to bring with differential regularizations, together researchers to report on recent statistical inference and functional Organizer: Tuhin Sahai developments and to facilitate discussion parameter estimation in differential United Technologies Research Center, USA and collaboration. models. 9:30-9:55 Global Sensitivity and Reduction of Very High-Dimensional Organizer: Tim Wildey Organizer: Fabio Nobile Models with Correlated Inputs Sandia National Laboratories, USA EPFL, Switzerland Vladimir Fonoberov, AIMdyn, Inc., USA; Organizer: Troy Butler Organizer: Laura M. Sangalli Igor Mezic, University of California, University of Texas at Austin, USA Politecnico di Milano, Italy Santa Barbara, USA 9:30-9:55 A Posteriori Error Analysis Organizer: Piercesare Secchi 10:00-10:25 NIPC: A MATLAB GUI and Adaptive Sampling for Politecnico di Milano, Italy for Wider Usability of Nonintrusive Probabilities using Surrogate Models Polynomial Chaos Tim Wildey, Sandia National Laboratories, 9:30-9:55 Spatial Spline Regression Kanali Togawa and Antonello Monti, RWTH USA; Troy Butler, University of Texas at Models Aachen University, Germany Austin, USA Laura M. Sangalli, Politecnico di Milano, Italy; Laura Azzimonti, Politecnico di 10:30-10:55 Iterative Methods for 10:00-10:25 Approximation and Milano, Italy; James O. Ramsay, McGill Propagating Uncertainty through Error Estimation in High Dimensional University, Canada; Piercesare Secchi, Networks of Switching Dynamical Stochastic Collocation Methods on Politecnico di Milano, Italy Systems Arbitrary Sparse Samples Tuhin Sahai, United Technologies Research Rick Archibald, Oak Ridge National 10:00-10:25 Sparse Grids for Center, USA Laboratory, USA Regression Jochen Garcke, University of Bonn, Germany 11:00-11:25 Uncertainty 10:30-10:55 Spatially Varying Quantification in Energy Efficient Stochastic Expansions for Embedded 10:30-10:55 Heat Kernel Smoothing Building Retrofit Design Uncertainty Quantification on an Arbitrary Manifold Using the Slaven Peles, United Technologies Research Eric C. Cyr, Sandia National Laboratories, Laplace-Beltrami Eigenfunctions Center, USA USA Moo Chung, University of Wisconsin, Madison, USA 11:00-11:25 Simultaneous Local and Dimension Adaptive Sparse Grids for 11:00-11:25 Second-Order Uncertainty Quantification Comparison of Random Functions John D. Jakeman, Sandia National Victor M. Panaretos, EPFL, Switzerland Laboratories, USA; Stephen G. Roberts, Australian National University, Australia 16 2012 SIAM Conference on Uncertainty Quantification

Monday, April 2 Monday, April 2 Monday, April 2 MS8 MS9 Lunch Break Sensitivity Analysis for Hybrid Uncertainty 11:30 AM-1:00 PM Investigating Uncertainty in Quantification Methods for Attendees on their own Model Predictions Multi-physics Application 9:30 AM-11:30 AM 9:30 AM-11:30 AM Room:University A Room:University B IP2 In most computer model predictions, Uncertainty quantification (UQ) for Integrating Data from there will be two sources of uncertainty: multi-physics applications is challenging Multiple Simulation Models - uncertainty in the choice of model input for both intrusive and non-intrusive Prediction and Tuning parameters, and uncertainty in how methods. A question naturally arises: well the computer model represents “Can we take the best of both worlds to 1:00 PM-1:45 PM reality (“model discrepancy”). We introduce a ‘hybrid’ UQ methodology Room:State C/D consider using sensitivity analysis for multi-physics applications?” Chair: James Berger, Duke University, USA tools to investigate both sources of This minisymposium brings together Simulation of complex systems has uncertainty. Such analyses can be used to researchers who are exploring hybrid UQ become commonplace in most areas understand how best to reduce prediction methods. In particular, we emphasize of science. In some settings, several uncertainty, either by learning more techniques that propagate global simulators are available to explore about particular input parameters, or by uncertainties yet allow individual physics the system, each with varying levels improving the structure of the model components to use their local intrusive of fidelity. In this talk, Bayesian to better represent reality. Tools for or non-intrusive UQ methods. Relevant methodology for integrating outputs computationally expensive models are issues for discussions are: hybrid from multi-fidelity computer models, presented, and applications are given uncertainty propagation algorithms, and field observations, to build a in aerosol modelling, infectious disease dimension reduction, Bayesian data predictive model of a physical system is modelling, and health economics. fusion techniques, design of hybrid presented. The problem is complicated computational framework, and scalable Organizer: Jeremy Oakley because inputs to the computer models algorithms for hybrid UQ. University of Sheffield, United Kingdom are not all the same and the simulators 9:30-9:55 Sensitivity Analysis for Organizer: Charles Tong have inputs (tuning parameters) that Complex Computer Models Lawrence Livermore National Laboratory, must be estimated from data. The Jeremy Oakley, University of Sheffield, USA methodology is demonstrated on an United Kingdom Organizer: Gianluca Iaccarino application from the University of 10:00-10:25 Sensitivity Analysis of a Stanford University, USA Michigan’s Center for Radiative Shock Global Aerosol Model to Quantify the 9:30-9:55 A High Performance Hybrid Hydrodynamics. Effect of Uncertain Model Parameters pce Framework for High Dimensional Lindsay Lee and Kenneth Carslaw, University Derek Bingham UQ Problems Simon Fraser University, Canada of Leeds, United Kingdom Akshay Mittal, Stanford University, USA 10:30-10:55 Speeding up 10:00-10:25 Hybrid UQ Method for the Sensitivity Analysis of an Multi-Species Reactive Transport Epidemiological Model Xiao Chen, Brenda Ng, Yunwei Sun, and Intermission John Paul Gosling, University of Leeds, Charles Tong, Lawrence Livermore 1:45 PM-2:00 PM United Kingdom National Laboratory, USA 11:00-11:25 Managing Model 10:30-10:55 Stochastic Dimension Uncertainty in Health Economic Reduction Techniques for Uncertainty Decision Models Quantification of Multiphysics Systems Mark Strong and Jeremy Oakley, University Eric Phipps, Sandia National Laboratories, of Sheffield, United Kingdom USA; Maarten Arnst, Université de Liege, Belgium; Paul Constantine, Stanford University, USA; Roger Ghanem, University of Southern California, USA; John Red-Horse and Tim Wildey, Sandia National Laboratories, USA 11:00-11:25 Preconditioners/Multigrid for Stochastic Polynomial Chaos Formulations of the Diffusion Equation Barry Lee, Pacific Northwest National Laboratory, USA 2012 SIAM Conference on Uncertainty Quantification 17

Monday, April 2 Monday, April 2 Monday, April 2 MT2 CP1 CP2 Emulation, Elicitation and UQ in Material Science Model Validation & Calibration - Part I of III 2:00 PM-4:00 PM Discrepancy 2:00 PM - 4:00 PM Room:University A 2:00 PM-4:00 PM For Part 2 see MT5 Chair: Sourish Chakravarty, State University Room:University B Room: State C of New York at Buffalo, USA Chair: Ajaykumar Rajasekharan, Seagate This minitutorial concerns statistical 2:00-2:15 Capturing Signatures Technology International, USA approaches to UQ based on Bayesian of microcracks from macrolevel 2:00-2:15 Quantifying Uncertainty statistics and the use of emulators. It Responses and Accounting Model Discrepancy is organised as three 2-hour sessions. Sonjoy Das and Sourish Chakravarty, State in Slider Air Bearing Simulations for The first begins with an overview of University of New York at Buffalo, USA Calibration and Prediction UQ tasks (uncertainty propagation, 2:20-2:35 Uncertainty Quantification in Ajaykumar Rajasekharan and Paul J Sonda, sensitivity analysis, calibration, Image Processing Seagate Technology International, USA validation) and of how emulation Torben Pätz, University of Bremen, Germany; 2:20-2:35 Model Inadequacy (a non-intrusive technique) tackles Michael Kirby, University of Utah, USA; Quantification for Simulations of those tasks efficiently. It continues Tobias Preusser, University of Bremen, Structures Using Bayesian Inference with an introduction to elicitation, a Germany Richard Dwight and Hester Bijl, Delft key component of input uncertainty 2:40-2:55 Identification of Uncertain University of Technology, Netherlands quantification in practice. The second Time-Dependent Material Behavior 2:40-2:55 Model Discrepancy and session presents the basic ideas of with Artificial Neural Networks Uncertainty Quantification emulation and illustrates its power for Steffen Freitag and Rafi L. Muhanna, Georgia Jenny Brynjarsdottir, Statistical and Applied Institute of Technology, USA uncertainty propagation, etc. The third Mathematical Sciences Institute, USA; Anthony O’Hagan, University of Sheffield, session is about calibration, including 3:00-3:15 Statistics of Mesoscale United Kingdom the importance of model discrepancy Conductivities and Resistivities in and history matching. Polycrystalline Graphite 3:00-3:15 Quantitative Model Shivakumar I. Ranganathan, American Validation Techniques: New Insights Organizer: University of Sharjah, United Arab You Ling and Sankaran Mahadevan, Vanderbilt Anthony O’Hagan, University of Emirates; Martin Ostoja-Starzewski, University, USA University of Illinois at Urbana-Champaign, Sheffield, United Kingdom 3:20-3:35 Integration of Verification, USA Validation, and Calibration Activities 3:20-3:35 Random Fields for Stochastic for Overall Uncertainty Quantification Speakers: Mechanics of Materials Shankar Sankararaman and Sankaran Peter Challenor, National Oceanography Martin Ostoja-Starzewski, University of Mahadevan, Vanderbilt University, USA Illinois at Urbana-Champaign, USA; Luis Centre, Southampton, United Kingdom 3:40-3:55 Dynamic Model Validation of Costa, US Army ARL-ARDEC, USA; a 160 Mw Steam Turbine Lp Last Stage Anthony O’Hagan, University of Emilio Porcu, Georg-August-Universität (L-0) Blade Sheffield, United Kingdom Göttingen, Germany Sadegh Rahrovani and Thomas Abrahamsson, Ian Vernon, University of Durham, 3:40-3:55 Uncertainty Quantification Chalmers University of Technology, Sweden United Kingdom of Discrete Element Micro-Parameters Conditioned on Sample Preparation of Homogeneous Particle Materials Patrick R. Noble, Tam Doung, and Zenon Medina-Cetina, Texas A&M University, USA 18 2012 SIAM Conference on Uncertainty Quantification

Monday, April 2 Monday, April 2 3:00-3:25 Identification of Polynomial Chaos Representations in High MS10 MS11 Dimension Guillaume Perrin, Christian Soize, and Denis Numerical Methods for High- Stochastic Uncertainty: Duhamel, Université Paris-Est, France; Dimensional Uncertainty Modeling, Forward Christine Funfschilling, SNCF, France Quantification - Part I of V Propagation, and Inverse 3:30-3:55 Inverse Problems for Problems - Part II of V Nonlinear Systems via Bayesian 2:00 PM-4:00 PM Parameter Identification Room:State D 2:00 PM-4:00 PM Bojana V. Rosic, Oliver Pajonk, Alexander Litvinenko, and Hermann G. Matthies, For Part 2 see MS17 Room:State A Technical University Braunschweig, There has been a growing interest For Part 1 see MS2 Germany; Anna Kucerova and Jan Sykora, in developing scalable numerical For Part 3 see MS18 Czech Technical University, Prague, Czech methods for stochastic computation Uncertainty quantification in Republic in the presence of high-dimensional computational science and engineering random inputs. This is motivated by has two main components: (i) modeling the need to reduce the issue of curse- of the uncertainty in the input of-dimensionality, i.e., exponential parameters, consistent with available increase of computational complexity, information, physical constraints, in predictive simulation of physical and prior knowledge; (ii) the forward systems where accurate description of propagation of input uncertainty to the uncertainties entails a large number of output quantities used in engineering random variables. To this end, several design and regulatory requirements. novel approaches based on multi-level, This minisymposium focuses on the reduced order, sparse, and low-rank stochastic approach to uncertainty approximations have been recently quantification in computational science developed. This minisymposium presents and engineering; it aims to showcase state-of-the-art in such developments emerging methodologies for building for various aspects of high-dimensional parametric and nonparametric stochastic stochastic computation, including models for uncertain input parameters, analysis, algorithms, implementation, and eventually involving the solution of applications. stochastic inverse problems, as well as Organizer: Dongbin Xiu innovative techniques for propagating Purdue University, USA input stochasticity through complex differential models and computing Organizer: Alireza Doostan University of Colorado at Boulder, USA statistics of the output quantities of interest. 2:00-2:25 Stochastic Collocation Methods in Unstructured Grids Organizer: Youssef M. Marzouk Akil Narayan and Dongbin Xiu, Purdue Massachusetts Institute of Technology, USA University, USA Organizer: Olivier LeMaitre 2:30-2:55 First Order k-th Moment LIMSI-CNRS, France Finite Element Analysis of Nonlinear Organizer: Fabio Nobile Operator Equations with Stochastic EPFL, Switzerland Data Alexey Chernov, University of Bonn, 2:00-2:25 Data Analysis Methods for Germany; Christoph Schwab, ETH Zürich, Inverse Problems Switzerland Luis Tenorio, Colorado School of Mines, USA 3:00-3:25 An Adaptive Iterative Method for High-dimensional 2:30-2:55 A Dynamic Programming Stochastic PDEs Approach to Sequential and Tarek El Moselhy and Youssef M. Marzouk, Nonlinear Bayesian Experimental Massachusetts Institute of Technology, Design USA Xun Huan, and Youssef M. Marzouk, Massachusetts Institute of Technology, 3:30-3:55 Adjoint Enhancement Within USA Global Stochastic Methods Michael S. Eldred, Eric Phipps, and Keith continued in next column Dalbey, Sandia National Laboratories, USA 2012 SIAM Conference on Uncertainty Quantification 19

Monday, April 2 3:00-3:25 Least-Squares Estimation Monday, April 2 of Distributed Random Diffusion MS12 Coefficients MS13 Hans-Werner van Wyk and Jeff Borggaard, Optimization Methods for Virginia Polytechnic Institute & State UQ for Model Calibration, Stochastic Inverse Problems University, USA Validation and Predictions - - Part I of II 3:30-3:55 Stochastic Inverse Problems Part I of II via Probabilistic Graphical Model 2:00 PM-4:00 PM Techniques 2:00 PM-4:00 PM Room:State B Nicholas Zabaras and Peng Chen, Cornell Room:State E University, USA For Part 2 see MS19 For Part 2 see MS20 A stochastic inverse problem is a The ultimate purpose of computational general framework used to convert models is to predict quantities of uncertainties in observed measurements interest (QoIs) to decision makers. into useful information about a physical The incorporation of uncertainty in system of interest. The transformation computational models is key for predicting from statistical data to random model QoIs more realistically, improving the parameters is a result of the interaction chances for more informed and better of a physical system with the object decisions. The whole prediction process that we wish to infer properties about. might involve not only the forward As such, this minisymposium focuses propagation of uncertainties, but also on optimization methods for stochastic model calibration, data assessment (which identification/control of input random data is more informative?), and model data constrained by systems partial ranking (which models are “better”?). differential equations. The optimization This minisymposium targets scientists approaches presented in this session that develop and use UQ for model allow for the optimal identification of calibration, validation and predictions. statistical moments or even the whole The participation of a wide variety of probability distribution of the input algorithms and applications is encouraged. random fields, given the probability Organizer: Gabriel A. Terejanu distribution of some responses of the University of Texas at Austin, USA system. Organizer: Ernesto E. Prudencio Organizer: Clayton G. Webster Institute for Computational Engineering and Oak Ridge National Laboratory, USA Sciences, USA Organizer: Max Gunzburger 2:00-2:25 Challenges on Incorporating Florida State University, USA Uncertainty in Computational Model Organizer: Hyung-Chun Lee Predictions Ernesto E. Prudencio, Institute for Ajou University, South Korea Computational Engineering and Sciences, 2:00-2:25 Analysis and Finite Element USA; Gabriel A. Terejanu, University of Approximations of Optimal Control Texas at Austin, USA Problems for Stochastic PDEs Hyung-Chun Lee, Ajou University, South 2:30-2:55 A Randomized Iterative Korea Proper Orthogonal Decomposition (RI-POD) Technique for Model 2:30-2:55 Generalized Methodology Identification for Inverse Modeling Constrained by Dan Yu and Suman Chakravorty, Texas A&M SPDEs University, USA Catalin S. Trenchea, University of Pittsburgh, USA; Max Gunzburger, Florida State 3:00-3:25 Sparse Bayesian Techniques University, USA; Clayton G. Webster, Oak for Surrogate Creation and Uncertainty Ridge National Laboratory, USA Quantification Nicholas Zabaras and Ilias Bilionis, Cornell continued in next column University, USA 3:30-3:55 A Stochastic Collocation Approach to Constrained Optimization for Random Data Estimation Problems Max Gunzburger, Florida State University, USA; Catalin S. Trenchea, University of Pittsburgh, USA; Clayton G. Webster, Oak Ridge National Laboratory, USA 20 2012 SIAM Conference on Uncertainty Quantification

Monday, April 2 Monday, April 2 3:00-3:25 Computation of Posterior Distribution in Ordinary Differential MS14 MS15 Equations with Transport Partial Differential Equations A Posteriori Error Estimation Data Analysis and Inference Nicolas J-B Brunel and Vincent Torri, for Reliable Uncertainty in Functional Spaces; Université Evry Val d’Essonne, France Quantification - Part II of II Statistical and Numerical 3:30-3:55 A Statistical Approach to Approaches to Uncertainty Data Assimilation for Hemodynamics 2:00 PM-3:30 PM Alessandro Veneziani, Emory University, Room:State F Estimation - Part II of II USA; Marta D’Elia, Emory University, For Part 1 see MS5 2:00 PM-4:00 PM USA A posteriori error estimation has a Room:Congressional A rich history in the analysis of partial For Part 1 see MS6 differential equations and is a standard This minisymposium considers models verification technique for deterministic at the interplay between statistics models. The extension of error estimation and numerical analysis, dealing with techniques to stochastic models has been uncertainty quantification and variability the subject of increasing interest in recent estimation in functional space settings. years. Themes of this minisymposium The analysis of complex and high- include theoretical and numerical analysis dimensional data and problems (images, of errors in the propagation of uncertainty functional signals and dynamics, shapes, through computational models resulting etc) calls in fact for the merging of from discretization, the use of surrogate advanced statistical and numerical models/emulators, and sampling. expertise. The minisymposium aims Both forward and inverse/inference in particular at showcasing recent and problems may be considered. The intent innovative techniques for functional data of this minisymposium is to bring analysis, including penalized smoothing together researchers to report on recent with differential regularizations, developments and to facilitate discussion statistical inference and functional and collaboration. parameter estimation in differential Organizer: Tim Wildey models. Sandia National Laboratories, USA Organizer: Fabio Nobile Organizer: Troy Butler EPFL, Switzerland University of Texas at Austin, USA Organizer: Laura M. Sangalli 2:00-2:25 Estimating and Bounding Politecnico di Milano, Italy Errors in Distributions Propagated via Organizer: Piercesare Secchi Surrogate Models Politecnico di Milano, Italy Troy Butler and Clint Dawson, University of Texas at Austin, USA; Tim Wildey, Sandia 2:00-2:25 Nonparametric Estimation National Laboratories, USA of Diffusions: A Differential Equations Approach 2:30-2:55 An Adjoint Error Estimation Omiros Papaspiliopoulos, Universitat Pompeu Technique Using Finite Volume Fabra, Spain; Yvo Pokern, University Methods for Hyperbolic Equations College, London, United Kingdom; Gareth Jeffrey M. Connors, University of Pittsburgh, O. Roberts, Warwick University, United USA; Jeffrey W. Banks, Lawrence Kingdom; Andrew M. Stuart, University of Livermore National Laboratory, USA; Warwick, United Kingdom Jeffrey A. Hittinger and Carol S. Woodward, Lawrence Livermore National 2:30-2:55 Large-scale Seismic Laboratory, USA Inversion: Elastic-acoustic Coupling, DG Discretization, and Uncertainty 3:00-3:25 Application of Goal-Oriented Quantification Error Estimation Methods to Statistical Tan Bui, University of Texas at Austin, USA; Quantities of Interest Carsten Burstedde, Universitaet Bonn, Corey Bryant and Serge Prudhomme, Germany; Omar Ghattas, Georg Stadler, University of Texas at Austin, USA James R. Martin, and Lucas Wilcox, University of Texas, Austin, USA continued in next column 2012 SIAM Conference on Uncertainty Quantification 21

Monday, April 2 Monday, April 2 Monday, April 2 MS16 Coffee Break CP3 Statistical Surrogates and 4:00 PM-4:30 PM Multi-fidelity UQ Functional Output Room:Pre-Function Area 4:30 PM-6:10 PM 2:00 PM-4:00 PM Room:Congressional B Room:Congressional B Chair: Matthew Parno, Massachusetts Institute of Technology, USA UQ of large complex computer MT3 models requires use of fast surrogates Uncertainty Quantification: 4:30-4:45 Contour Estimation Via Two or approximations, which are fitted Fidelity Computer Simulators under Foundations and Limited Resources with relatively few runs of the Capabilities for Model- Ray-Bing Chen, National Cheng Kung model. Statistical surrogates provide Based Simulations - University, Taiwan; Ying-Chao Hung, a distribution for the prediction of National Chengchi University, Taiwan; model output at each input; this full Part I of III Weichung Wang and Sung-Wei Yen, distribution is useful in complex 4:30 PM - 6:30 PM National Taiwan University, Taiwan UQ tasks that require combination For Part 2 see MT6 4:50-5:05 Dimension Reduction and of all sources of uncertainty, since Measure Transformation in Stochastic Room: State C the distributions can be coherently Multiphysics Modeling combined through probability theory. The minitutorial will present the physical Maarten Arnst, Université de Liege, Belgium; The most used statistical emulators for motivation and mathematical foundations Roger Ghanem, University of Southern UQ are Gaussian Processes (GPs). This necessary for the formulation of well- California, USA; Eric Phipps and John session presents recent perspectives on posed UQ problems in computational Red-Horse, Sandia National Laboratories, USA GPs, suggests improved methods of science and engineering. In particular, fitting GPs, and addresses propagation the minitutorial will cover 1) aspects 5:10-5:25 Improvement in Multifidelity through the dynamics of the model. of probabilistic modeling and analysis, Modeling Using Gaussian Processes 2) polynomial chaos representations, Celine Helbert and Federico Zertuche, Organizer: M.J. Bayarri 3) stochastic processes and Karhunen- Université de Grenoble I, France University of Valencia, Spain Loeve expansions, 4) forward UQ 5:30-5:45 A Multiscale Framework for Organizer: James Berger including sampling, sparse-grid, Bayesian Inference in Elliptic Problems Duke University, USA stochastic Galerkin and collocation, 5) Matthew Parno and Youssef M. Marzouk, 2:00-2:25 Statistical Approximation inverse problems in UQ, 6) overview Massachusetts Institute of Technology, of Computer Model Output aka of software resources, 7) summary of USA Emulation of Simulation advanced topics. 5:50-6:05 An Uncertainty Jerry Sacks, National Institute of Statistical Organizer: Quantification Approach to Assess Sciences, USA Geometry-Optimization Research 2:30-2:55 Improving Gaussian Roger Ghanem, University of Southern Spaces through Karhunen-Loève Stochastic Process Emulators California, USA Expansion Danilo Lopes, SAMSI, USA Matteo Diez, CNR-INSEAN, Italy; Daniele Peri, INSEAN, Italy; Frederick Stern, 3:00-3:25 Emulating Dynamic Speakers: University of Iowa, USA; Emilio Campana, Models: An Overview of Suggested INSEAN, Italy Approaches Roger Ghanem, University of Southern Peter Reichert, Swiss Federal Institute California, USA of Aquatic Science and Technology, Bert Debusschere, Sandia National Switzerland Laboratories, USA 3:30-3:55 Toward Improving Statistical Components of Multi- scale Simulation Schemes Peter R. Kramer, Rensselaer Polytechnic Institute, USA; Sorin Mitran, University of North Carolina at Chapel Hill, USA; Sunli Tang, Rensselaer Polytechnic Institute, USA; M.J. Bayarri, University of Valencia, Spain; James Berger, Duke University, USA; Murali Haran, Pennsylvania State University, USA; Hans Rudolf Kuensch, ETH Zürich, Switzerland 22 2012 SIAM Conference on Uncertainty Quantification

Monday, April 2 Monday, April 2 Monday, April 2 CP4 CP5 MS17 UQ & Computation Emulation Numerical Methods for High- 4:30 PM-6:30 PM 4:30 PM-6:30 PM Dimensional Uncertainty Room:University A Room:University B Quantification - Part II of V Chair: Jeroen Witteveen, Stanford University, Chair: Alex A. Gorodetsky, Massachusetts 4:30 PM-6:30 PM USA Institute of Technology, USA Room:State D 4:30-4:45 Efficient Evaluation of 4:30-4:45 A Learning Method for For Part 1 see MS10 Integral Quantities in Rdo by the Approximation of Discontinuous For Part 3 see MS23 Sequential Quadrature Formulas Functions in High Dimensions There has been a growing interest in Daniele Peri, INSEAN, Italy; Matteo Diez, Alex A. Gorodetsky and Youssef M. Marzouk, CNR-INSEAN, Italy Massachusetts Institute of Technology, USA developing scalable numerical methods for stochastic computation in the presence of 4:50-5:05 Robust Approximation of 4:50-5:05 Svr Regression with high-dimensional random inputs. This is Stochastic Discontinuities Polynomial Kernel and Monotonicity motivated by the need to reduce the issue Jeroen Witteveen and Gianluca Iaccarino, Constraints Stanford University, USA Francois Wahl, IFPEN, USA of curse-of-dimensionality, i.e., exponential increase of computational complexity, in 5:10-5:25 Super Intrusive Polynomial 5:10-5:25 Constrained Gaussian predictive simulation of physical systems Chaos for An Elliptic Pde for Heat Process Modeling where accurate description of uncertainties Transfer Sebastien Da Veiga, IFP, France; Amandine Andrew Barnes, GE Global Research, USA; Marrel, CEA, France entails a large number of random variables. Jose Cordova, General Electric Global To this end, several novel approaches Research Center, USA 5:30-5:45 Shape Invariant Model based on multi-level, reduced order, Approach to Functional Outputs sparse, and low-rank approximations 5:30-5:45 Adjoint Error Estimation for Modelling Stochastic Collocation Methods Ekaterina Sergienko and Fabrice Gamboa, have been recently developed. This Bettina Schieche, and Jens Lang, Technical University of Toulouse, France; Daniel minisymposium presents state-of-the-art in University Darmstadt, Germany Busby, IFP Energies Nouvelles, France such developments for various aspects of high-dimensional stochastic computation, 5:50-6:05 A Library for Large Scale 5:50-6:05 Reduced Basis Surrogate Parallel Modeling and Simulation of Models and Sensitivity Analysis including analysis, algorithms, Spatial Random Fields Alexandre Janon, Maelle Nodet, and implementation, and applications. Brian Carnes and John Red-Horse, Sandia Clémentine Prieur, Université Joseph Organizer: Alireza Doostan National Laboratories, USA Fourier and INRIA, France University of Colorado at Boulder, USA 6:10-6:25 Application of a Novel 6:10-6:25 Improvement of the Organizer: Dongbin Xiu Adaptive Finite Difference Solution Accuracy of the Prediction Variance Purdue University, USA of The Fokker-Planck Equation for Using Bayesian Kriging: Application to 4:30-4:55 A Compressive Sampling Uncertainty Quantification Three Industrial Case Studies Approach for the Solution of High- Mani Razi, Peter Attar, and Prakash Vedula, Celine Helbert, Université de Grenoble I, dimensional Stochastic PDEs University of Oklahoma, USA France Alireza Doostan, University of Colorado at Boulder, USA 5:00-5:25 PDE with Random Coefficient as a Problem in Infinite-dimensional Numerical Integration Ian H. Sloan, University of New South Wales, Australia 5:30-5:55 Adaptive Sparse Grids for Stochastic Collocation on Hybrid Architectures Rick Archibald, Oak Ridge National Laboratory, USA 6:00-6:25 Tensor-based Methods for Uncertainty Propagation: Alternative Definitions and Algorithms Anthony Nouy, Billaud Marie, Mathilde Chevreuil, Rai Prashant, and Zahm Olivier, Université de Nantes, France 2012 SIAM Conference on Uncertainty Quantification 23

Monday, April 2 5:00-5:25 A Multiscale Domain Monday, April 2 Decomposition Method for the Solution MS18 of Stochastic Partial Differential MS19 Equations with Localized Uncertainties Stochastic Uncertainty: Mathilde Chevreuil, and Anthony Nouy, Optimization Methods for Modeling, Forward Université de Nantes, France; Safatly Elias, Stochastic Inverse Problems Propagation, and Inverse Ecole Centrale de Nantes, France - Part II of II Problems - Part III of V 5:30-5:55 Solving Saddle Point Problems with Random Data 4:30 PM-6:30 PM 4:30 PM-6:30 PM Catherine Powell, University of Manchester, Room:State B United Kingdom Room:State A For Part 1 see MS12 For Part 2 see MS11 6:00-6:25 Greedy Algorithms for Non A stochastic inverse problem is a general For Part 4 see MS24 Symmetric Linear Problems with framework used to convert uncertainties Uncertainty quantification in Uncertainty in observed measurements into useful Virginie Ehrlacher, CERMICS, France computational science and engineering information about a physical system of has two main components: (i) modeling interest. The transformation from statistical of the uncertainty in the input data to random model parameters is a parameters, consistent with available result of the interaction of a physical information, physical constraints, system with the object that we wish and prior knowledge; (ii) the forward to infer properties about. As such, this propagation of input uncertainty to the minisymposium focuses on optimization output quantities used in engineering methods for stochastic identification/ design and regulatory requirements. control of input random data constrained This minisymposium focuses on the by systems partial differential equations. stochastic approach to uncertainty The optimization approaches presented quantification in computational science in this session allow for the optimal and engineering; it aims to showcase identification of statistical moments or emerging methodologies for building even the whole probability distribution parametric and nonparametric stochastic of the input random fields, given the models for uncertain input parameters, probability distribution of some responses eventually involving the solution of of the system. stochastic inverse problems, as well as Organizer: Clayton G. Webster innovative techniques for propagating Oak Ridge National Laboratory, USA input stochasticity through complex Organizer: Max Gunzburger differential models and computing Florida State University, USA statistics of the output quantities of interest. Organizer: Hyung-Chun Lee Ajou University, South Korea Organizer: Youssef M. Marzouk 4:30-4:55 Optimization and Model Massachusetts Institute of Technology, USA Reduction for Parabolic PDEs with Organizer: Olivier LeMaitre Uncertainties LIMSI-CNRS, France Matthias Heinkenschloss, Rice University, USA Organizer: Fabio Nobile 5:00-5:25 An Efficient Sparse-Grid- EPFL, Switzerland Based Method for Bayesian Uncertainty 4:30-4:55 Optimized Polynomial Analysis Approximations of PDEs with Random Guannan Zhang, Max Gunzburger, and Ming Coefficients Ye, Florida State University, USA Joakim Beck, KAUST Supercomputing 5:30-5:55 Optimal Control of Stochastic Laboratory, Saudi Arabia; Fabio Nobile, Flow Using Reduced-order Modeling EPFL, Switzerland; Lorenzo Tamellini, Ju Ming and Max Gunzburger, Florida State Politecnico di Milano, Italy; Raul F. University, USA Tempone, King Abdullah University of 6:00-6:25 A Stochastic Galerkin Method Science & Technology (KAUST), Saudi for Stochastic Control Problems Arabia Jangwoon Lee, University of Mary Washington, continued in next column USA; Hyung-Chun Lee, Ajou University, South Korea 24 2012 SIAM Conference on Uncertainty Quantification

Monday, April 2 Monday, April 2 Monday, April 2 MS20 MS21 MS22 UQ for Model Calibration, Statistical Design and Simulation Informatics: Validation and Predictions - Modeling of Computer Applying Machine Learning Part II of II Experiments- Part I of II Techniques To Simulation 4:30 PM-6:30 PM 4:30 PM-6:30 PM Databases Room:State E Room:State F 4:30 PM-6:30 PM For Part 1 see MS13 For Part 2 see MS27 Room:Congressional A The ultimate purpose of computational Computer models are now used As computing power for simulation-based models is to predict quantities of ubiquitously in sciences and engineering. analysis approaches the exascale, the interest (QoIs) to decision makers. This minisymposium aims to showcase need will arise for practical, efficient, and The incorporation of uncertainty in recent methodological advances in robust exascale data management. Modern computational models is key for predicting the statistical design and modeling of physical simulations produce prodigious QoIs more realistically, improving the computer experiments and illustrate amounts of data that must be compared chances for more informed and better them with diverse applications. The to experiments, theory, and other decisions. The whole prediction process minisymposium invites eight speakers simulations. Moreover, simulation results might involve not only the forward from various universities and national contain uncertainties that typically require propagation of uncertainties, but also labs. Topics to be discussed include new an ensemble of runs to characterize. In model calibration, data assessment (which classes of space-filling and sequential this minisymposium, we will explore the data is more informative?), and model designs, alternatives to Gaussian process application of scalable informatics and ranking (which models are “better”?). models, modeling computer experiments machine learning methods to the outputs This minisymposium targets scientists with nonstationary output or massive of physical simulations, where theoretical that develop and use UQ for model data, statistical model-reduction and insights from the physical models calibration, validation and predictions. variable selection for large-scale inform the choice of learning methods. The participation of a wide variety of problems and the interplay between These methods will be used to quantify algorithms and applications is encouraged. design and modeling in computer the uncertainty associated with model experiments. Organizer: Gabriel A. Terejanu predictions. University of Texas at Austin, USA Organizer: Peter Qian Organizer: Paul Constantine University of Wisconsin, Madison, USA Organizer: Ernesto E. Prudencio Stanford University, USA Institute for Computational Engineering and Organizer: Jeff Wu Organizer: David F. Gleich Georgia Institute of Technology, USA Sciences, USA Purdue University, USA 4:30-4:55 A Matrix-Free Approach 4:30-4:55 Physics-based Auto- and 4:30-4:55 Simulation Informatics for Gaussian Process Maximum Cross-Covariance Models for Gaussian David F. Gleich, Purdue University, USA Process Regression Likelihood Calculations Emil M. Constantinescu, and Mihai Anitescu, Jie Chen, Argonne National Laboratory, USA 5:00-5:25 Extracting Non-conventional Information in Simulation of Chaotic Argonne National Laboratory, USA 5:00-5:25 Sequential Optimization of a Dynamical Systems Computer Model: What’s So Special 5:00-5:25 Covariance Approximation Qiqi Wang, Massachusetts Institute of about Gaussian Processes Anyway? Techniques in Bayesian Non-stationary Technology, USA Gaussian Process Models Hugh Chipman and Pritam Ranjan, Acadia Bledar Konomi and Guang Lin, Pacific University, Canada 5:30-5:55 Machine Learning to Recognize Phenomena in Large Scale Northwest National Laboratory, USA 5:30-5:55 Extracting Key Features of Simulations Physical Systems for Emulation and 5:30-5:55 Fundamental Limitations Barnabas Poczos, Carnegie Mellon University, Calibration of Polynomial Chaos Expansions for USA Uncertainty Quantification in Systems Nicolas Hengartner, Los Alamos National 6:00-6:25 Scientific Data Mining with Intermittent Instabilities Laboratory, USA Techniques for Extracting Information Michal Branicki, New York University, 6:00-6:25 Sliced Cross-validation for from Simulations USA; Andrew Majda, Courant Institute of Surrogate Models Chandrika Kamath, Lawrence Livermore Mathematical Sciences, New York University, Peter Qian, and Qiong Zhang, University of National Laboratory, USA USA Wisconsin, Madison, USA 6:00-6:25 Inertial Manifold Dimensionality & Finite-time Instabilities in Fluid Flows Themistoklis Sapsis, New York University, USA 2012 SIAM Conference on Uncertainty Quantification 25

Monday, April 2 Tuesday, April 3 Tuesday, April 3 Dinner Break MT4 6:30 PM-8:00 PM Analysis of Spdes and Registration Attendees on their own Numerical Methods for 7:45 AM-5:00 PM Uncertainty Quantification - Room:Chancellor and Pre-Function Area SIAG/UQ Business Meeting Part II of II 8:00 PM-8:45 PM 9:30 AM - 12:30 PM Room:State C/D For Part 1 see MT1 Remarks Room: State C Complimentary beer and wine will be served. 8:10 AM-8:15 AM This tutorial explores numerical and Room:State C/D functional analysis techniques for solving PDEs with random input data, such as model coefficients, forcing terms, initial and boundary conditions, material IP3 properties, source and interaction terms Polynomial Chaos or geometry. The resulting stochastic systems will be investigated for well- Approaches to Multiscale posedness and regularity. We will present and Data Intensive detailed convergence analysis of several Computations intrusive and non-intrusive methods for 8:15 AM-9:00 AM quantifying the uncertainties associated with input information onto desired Room:State C/D quantities of interest, forward and inverse Chair: Nicholas Zabaras, Cornell University, UQ approaches, and necessary theoretical USA results from stochastic processes and Prediction of multiscale systems is random fields, error analysis, anisotropy, increasingly being based on complex adaptive methods, high-dimensional physical models that depend on large approximation, random sampling and uncertain data sets. In this talk, we sparse grids. will outline recent developments in polynomial chaos (PC) methods for Organizer: uncertainty quantification in such systems. Implementations will be Clayton G. Webster, Oak Ridge National illustrated in light of applications to Laboratory, USA chemical kinetics, and geophysical flows. Conclusions are in particular drawn Speakers: concerning the potential of parallel databases in providing a platform for John Burkardt, Florida State University, discovery, assessing prediction fidelity, USA and decision support. Clayton Webster, Oak Ridge National Omar M. Knio Laboratory, USA Duke University, USA

Coffee Break 9:00 AM-9:30 AM Room:Pre-Function Area 26 2012 SIAM Conference on Uncertainty Quantification

Tuesday, April 3 Tuesday, April 3 Tuesday, April 3 CP6 CP7 MS23 Design and Control Dynamic Systems Numerical Methods for High- 9:30 AM-10:50 AM 9:30 AM-11:10 AM Dimensional Uncertainty Room:University A Room:University B Quantification - Part III of V Chair: Khanh D. Pham, Air Force Chair: Mircea Grigoriu, Cornell University, 9:30 AM-11:30 AM Research Laboratory, USA USA Room:State D 9:30-9:45 Risk-Averse Control of 9:30-9:45 A Method for Solving For Part 2 see MS17 Linear Stochastic Systems with Low Stochastic Equations by Reduced For Part 4 see MS31 Sensitivity: An Output-Feedback Order Models There has been a growing interest in Paradigm Mircea Grigoriu, Cornell University, USA developing scalable numerical methods Khanh D. Pham, Air Force Research 9:50-10:05 Effect of Limited for stochastic computation in the presence Laboratory, USA Measurement Data on State and of high-dimensional random inputs. This 9:50-10:05 Path Variability Due To Parameters Estimation in Dynamic is motivated by the need to reduce the Sensor Geometry Systems issue of curse-of-dimensionality, i.e., Timothy Hall, PQI Consulting, USA Sonjoy Das, and Reza Madankan, and Puneet exponential increase of computational 10:10-10:25 Quantification of Singla, State University of New York, Buffalo, USA complexity, in predictive simulation Uncertainty of Low Fidelity Models of physical systems where accurate and Application to Robust Design 10:10-10:25 Managing Uncertainty in description of uncertainties entails a large Jessie Birman, Airbus Operation S.A.S., Complex Dynamic Models number of random variables. To this end, France Ufuk Topcu, California Institute of Technology, USA; Peter Seiler, University several novel approaches based on multi- 10:30-10:45 An Information-Based of Minnesota, USA; Michael Frenklach, level, reduced order, sparse, and low- Sampling Scheme with Applications University of California, Berkeley, USA; rank approximations have been recently to Reduced-Order Modeling Gary Balas, University of Minnesota, USA; Raphael Sternfels and Christopher J. Earls, developed. This minisymposium presents Andrew Packard, University of California, Cornell University, USA state-of-the-art in such developments Berkeley, USA for various aspects of high-dimensional 10:30-10:45 On-Line Parameter stochastic computation, including Estimation and Control of Systems with analysis, algorithms, implementation, and Uncertainties applications. Faidra Stavropoulou, Helmholtz Zentrum Organizer: Dongbin Xiu München, Germany; Johannes Mueller, TU Purdue University, USA München, Germany 10:50-11:05 Estimation and Verification Organizer: Alireza Doostan of Curved Railway Track Geometry University of Colorado at Boulder, USA Using Monte Carlo Particle Filters 9:30-9:55 Stochastic Basis Reduction Akiyoshi Yoshimura, Tokyo University of by QoI Adaptation Technology, Japan Roger Ghanem and Ramakrishna Tippireddy, University of Southern California, USA 10:00-10:25 Distinguishing and Integrating Aleatoric and Epistemic Variation in UQ Kenny Chowdhary and Jan S. Hesthaven, Brown University, USA 10:30-10:55 Adaptive Basis Selection and Dimensionality Reduction with Bayesian Compressive Sensing Khachik Sargsyan, Cosmin Safta, Robert D. Berry, Bert J. Debusschere, and Habib N. Najm, Sandia National Laboratories, USA; Daniel Ricciuto and Peter Thornton, Oak Ridge National Laboratory, USA 11:00-11:25 Stochastic Collocation Methods for Stochastic Differential Equations Driven by White Noise Zhongqiang Zhang, George E. Karniadakis, and Boris Rozovsky, Brown University, USA 2012 SIAM Conference on Uncertainty Quantification 27

Tuesday, April 3 10:00-10:25 Computation of the Tuesday, April 3 Second Order Wave Equation with MS24 Random Discontinuous Coefficients MS25 Mohammad Motamed, King Abdullah Stochastic Uncertainty: University of Science & Technology Uncertainty Quantification Modeling, Forward (KAUST), Saudi Arabia; Fabio Nobile, Techniques and EPFL, Switzerland; Raul F. Tempone, Propagation, and Inverse King Abdullah University of Science & Applications for Engineering Problems - Part IV of V Technology (KAUST), Saudi Arabia Problems in the Geosphere 9:30 AM-11:30 AM 10:30-10:55 Probabilistic UQ for PDEs - Part I of II with Random Data: A Case Study Room:State A 9:30 AM-11:30 AM Oliver G. Ernst, TU Bergakademie Freiberg, For Part 3 see MS18 Germany Room:State B For Part 5 see MS32 For Part 2 see MS33 Uncertainty quantification in 11:00-11:25 A Predictor-corrector Method for Fluid Flow Exhibiting Geologic experience and data along computational science and engineering Uncertain Periodic Dynamics with geophysical models are often used has two main components: (i) modeling Michael Schick and Vincent Heuveline, as input to engineering designs. Limited of the uncertainty in the input Karlsruhe Institute of Technology, sampling of geologic properties and the parameters, consistent with available Germany; Olivier LeMaitre, LIMSI- potentially large discrepancy in temporal information, physical constraints, CNRS, France and spatial scales between different and prior knowledge; (ii) the forward types of information often serves as propagation of input uncertainty to the sources of uncertainty in predicting the output quantities used in engineering performance of the engineered system. design and regulatory requirements. Probabilistic techniques can be used to This minisymposium focuses on the estimate unknown model parameters stochastic approach to uncertainty conditional on varying initial and quantification in computational science boundary conditions, constitutive and and engineering; it aims to showcase even intrinsic numerical parameters. emerging methodologies for building These serve as the basis for predicting parametric and nonparametric stochastic performance of the engineered system. models for uncertain input parameters, This minisymposium aims at discussing eventually involving the solution of research developments to engineered stochastic inverse problems, as well as systems that interface with the innovative techniques for propagating geosphere. input stochasticity through complex differential models and computing Organizer: Zenon Medina-Cetina Texas A&M University, USA statistics of the output quantities of interest. Organizer: Sean A McKenna Sandia National Laboratories, USA Organizer: Youssef M. Marzouk Massachusetts Institute of Technology, USA 9:30-9:55 Quantifying and Reducing Uncertainty through Sampling Design Organizer: Olivier LeMaitre Sean A McKenna, Jaideep Ray, and Bart G. LIMSI-CNRS, France Van Bloemen Waanders, Sandia National Organizer: Fabio Nobile Laboratories, USA EPFL, Switzerland 10:00-10:25 Uncertainty Analysis in 9:30-9:55 Proper Generalized the Florida Public Hurricane Loss Decomposition for Stochastic Navier- Model Stokes Equations Sneh Gulati, Shahid S. Hamid, and Golam Olivier LeMaitre, LIMSI-CNRS, France Kibria, Florida International University, USA; Steven Cocke, Florida State University, USA; Mark D. Powell, continued in next column National Oceanic and Atmospheric Administration, USA; Jean-Paul Pinelli, Florida Institute of Technology, USA; Kurtis R. Gurley, University of Florida, USA; Shu-Ching Chen, Florida International University, USA

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Tuesday, April 3 Tuesday, April 3 10:30-10:55 Random Fluctuations in Homogenization Theory; How MS25 MS26 Stochasticity Propagates Through Scales Uncertainty Quantification Predictive Fidelity in Guillaume Bal, Columbia University, USA Techniques and Multiscale Simulations - 11:00-11:25 Uncertainty Applications for Engineering Part I of III Quantification in Multi-Scale, Multi-Physics MEMS Performance Problems in the Geosphere 9:30 AM-11:30 AM Prediction - Part I of II Room:State E Sankaran Mahadevan, You Ling, Joshua Mullins, and Shankar Sankararaman, 9:30 AM-11:30 AM For Part 2 see MS41 Vanderbilt University, USA continued In many applications, the overall system dynamics are affected by coupled physical phenomena, occurring over a 10:30-10:55 Uncertainty wide range of time and length scales. Quantification of Shallow Multiscale physics simulations employ Groundwater Impacts due to CO2 the requisite models that represent the Sequestration relevant physics on each time and length Daniel M. Tartakovsky, University of scale level, and couple the various California, San Diego, USA; Hari models across the scales in order to Viswanathan, Elizabeth Keating, Zhenxue Dai, and Rajesh Pawar, Los Alamos resolve the overall system behavior. National Laboratory, USA Assessing the predictive fidelity of multiscale simulations requires careful 11:00-11:25 Toward Transparency quantification and propagation of and Refutability in Environmental Modeling uncertainties on all scales, as well as Mary Hill, U.S. Geological Survey, USA; in the coupling between scales. This Dmitri Kavetski, University of Newcastle, minisymposium covers research topics Australia; Martyn Clark, University in this general area. of Colorado, Boulder, USA; Ming Ye, Organizer: Bert J. Debusschere Florida State University, USA; Mazdak Sandia National Laboratories, USA Arabi, Colorado State University, USA; Laura Foglia, University of California, Organizer: Habib N. Najm Davis, USA; Steffen Mehl, California Sandia National Laboratories, USA State University, Chico, USA Organizer: Allen C. Robinson Sandia National Laboratories, USA 9:30-9:55 Quantifying Sampling Noise and Parametric Uncertainty in Coupled Atomistic-Continuum Simulations Maher Salloum, Khachik Sargsyan, Reese Jones, Bert J. Debusschere, Habib N. Najm, and Helgi Adalsteinsson, Sandia National Laboratories, USA 10:00-10:25 UQ in MD Simulations: Forward Propagation and Parameter Inference Francesco Rizzi, Johns Hopkins University, USA; Omar M. Knio, Duke University, USA; Habib N. Najm, Bert J. Debusschere, Khachik Sargsyan, Maher Salloum, and Helgi Adalsteinsson, Sandia National Laboratories, USA

continued in next column 2012 SIAM Conference on Uncertainty Quantification 29

Tuesday, April 3 Tuesday, April 3 Tuesday, April 3 MS27 MS28 MS29 Statistical Design and Efficiency in an Uncertain Implicit Sampling: Theory Modeling of Computer World, UQ in High and Application to Data Experiments - Part II of II Performance Buildings Assimilation 9:30 AM-11:30 AM 9:30 AM-12:00 PM 9:30 AM-11:30 AM Room:State F Room:Congressional A Room:Congressional B For Part 1 see MS21 Buildings are the largest single source of The effective sampling of Computer models are now used energy consumption and pollution in the multidimensional probability densities is ubiquitously in sciences and US, and because of this, efficient design one of the key problems in computational engineering. This minisymposium aims and operation of buildings is needed for science. The difficulty lies in the fact that to showcase recent methodological energy security, economic prosperity, and there are too many states to be listed, and advances in the statistical design and environmental stability. The objective the fraction of states that has a significant modeling of computer experiments of this symposium is to bring together probability is too small for standard and illustrate them with diverse experts and practitioners to share state- sampling methods. Implicit sampling applications. The minisymposium of-the-art methods in UQ with focus on is a new methodology for finding high invites eight speakers from various the underlying mathematics, simulation probability samples by solving a random universities and national labs. Topics methods and the characteristics of UQ equation. This minisymposium focuses on to be discussed include new classes of analysis for buildings. The intent is to the theory of implicit sampling applied to space-filling and sequential designs, articulate problems in building design data assimilation. Two of the talks have a alternatives to Gaussian process models, and operation that require UQ capability, theoretic emphasis; the other two present modeling computer experiments with the current barriers to deploying applications of implicit sampling to data nonstationary output or massive data, UQ analysis at scale, and benefits of assimilation in geophysics. statistical model-reduction and variable deploying such capabilities. Organizer: Matthias Morzfeld selection for large-scale problems Organizer: Bryan Eisenhower Lawrence Berkeley National Laboratory, USA and the interplay between design and University of California, Santa Barbara, 9:30-9:55 A Tutorial on Implicit Particle modeling in computer experiments. USA Filtering for Data Assimilation Organizer: Peter Qian Organizer: Satish Narayanan Xuemin Tu, University of Kansas, USA University of Wisconsin, Madison, USA United Technologies Research Center, USA 10:00-10:25 Implicit Particle Filtering for Organizer: Jeff Wu Organizer: Clas Jacobson Geomagnetic Data Assimilation Georgia Institute of Technology, USA United Technologies Research Center, USA Matthias Morzfeld, Lawrence Berkeley National Laboratory, USA 9:30-9:55 Evaluation of Mixed 9:30-9:55 An Integrated Approach Continuous-Discrete Surrogate to Design and Operation of High 10:30-10:55 Application of the Implicit Approaches Performance Buildings in the Particle Filter to a Model of Nearshore Patricia D. Hough, Sandia National Presence of Uncertainty Circulation Laboratories, USA Bryan Eisenhower, University of California, Robert Miller, Oregon State University, USA 10:00-10:25 Large-scale Surrogate Santa Barbara, USA 11:00-11:25 An Application of Rare Models 10:00-10:25 Sensitivity of Building Event Tools to a Bimodal Ocean Matthew Pratola, Los Alamos National Parameters with Building Type, Current Model Laboratory, USA Climate, and Efficiency Level Jonathan Weare, University of Chicago, USA; 10:30-10:55 High Performance John Kennedy, Autodesk, Inc., USA Eric Vanden-Eijnden, Courant Institute Bayesian Assessment of Earthquake of Mathematical Sciences, New York 10:30-10:55 Uncertainty University, USA Source Models for Ground Motion Quantification Methods for Multi- Simulations physics Applications Ernesto E. Prudencio, Institute for Charles Tong, Lawrence Livermore National Computational Engineering and Sciences, Laboratory, USA USA Lunch Break 11:00-11:25 Uncertainty 11:30 AM-2:00 PM 11:00-11:25 Use of Gaussian Process Quantification of Building Energy Modeling to Improve the Perez Model Models Attendees on their own in the Study of Surface Irradiance of Godfried Augenbroe, Georgia Institute of Buildings Technology, USA Heng Su, Georgia Institute of Technology, USA 11:30-11:55 UQ for Better Commercial Buildings: From Design to Operation Gregor Henze, University of Colorado at Boulder, USA 30 2012 SIAM Conference on Uncertainty Quantification

Tuesday, April 3 Tuesday, April 3 Tuesday, April 3 MS30: Cancelled MT5 CP8 1:00 PM-1:45 PM Emulation, Elicitation and Sensitivity Analysis I Calibration - Part II of III 2:00 PM-3:40 PM 2:00 PM - 4:00 PM Room:University A For Part 1 see MT2 Chair: Kyle S. Hickmann, Tulane University, For Part 3 see MT8 USA Room: State C 2:00-2:15 Global Sensitivity Analysis for This minitutorial concerns statistical Disease and Population Models approaches to UQ based on Bayesian Kyle S. Hickmann, Tulane University, USA; statistics and the use of emulators. It James (Mac) Hyman, Los Alamos National is organised as three 2-hour sessions. Laboratory, USA; John E. Ortmann, Tulane The first begins with an overview of University, USA UQ tasks (uncertainty propagation, 2:20-2:35 Locality Aware Uncertainty sensitivity analysis, calibration, Quantification and Sensitivity validation) and of how emulation Algorithms (a non-intrusive technique) tackles Steven F. Wojtkiewicz, University of those tasks efficiently. It continues Minnesota, USA; Erik A. Johnson, with an introduction to elicitation, a University of Southern California, USA key component of input uncertainty 2:40-2:55 Fast and Rbd Revisited quantification in practice. The second Jean-Yves Tissot, Université de Grenoble session presents the basic ideas of I, France; Clémentine Prieur, Université emulation and illustrates its power for Joseph Fourier and INRIA, France uncertainty propagation, etc. The third 3:00-3:15 A Global Sensitivity Analysis session is about calibration, including Method for Reliability Based Upon the importance of model discrepancy Density Modification and history matching. Paul Lemaître, INRIA Bordeaux Sud-Ouest, France; Ekaterina Sergienko and Fabrice Organizer: Gamboa, University of Toulouse, France; Anthony O’Hagan, University of Bertrand Iooss, Institut Mathématique de Sheffield, United Kingdom Toulouse, France 3:20-3:35 Investigations on Sensitivity Analysis of Complex Final Repository Speakers: Models Peter Challenor, National Oceanography Dirk-Alexander Becker, Gesellschaft für Centre, Southampton, United Kingdom Anlagen- und Reaktorsicherheit mbH, Germany Anthony O’Hagan, University of Sheffield, United Kingdom Ian Vernon, University of Durham, United Kingdom 2012 SIAM Conference on Uncertainty Quantification 31

Tuesday, April 3 Tuesday, April 3 2:30-2:55 Multiple Computer Experiments: Design and Modeling CP9 MS31 Youngdeok Hwang, Xu He, and Peter Qian, University of Wisconsin, Madison, USA Dynamical Systems & EnKF Numerical Methods 3:00-3:25 Uncertainty Quantification 2:00 PM-3:40 PM for High-Dimensional for Overcomplete Basis Representation in Computer Experiments Room:University B Uncertainty Quantification - Part IV of V Jeff Wu, Georgia Institute of Technology, Chair: Yuefeng Wu, University of California, USA Santa Cruz, USA 2:00 PM-4:00 PM 3:30-3:55 Efficient Analysis of High 2:00-2:15 Collocation Inference Room:State D Dimensional Data in Tensor Formats for Nonlinear Stochastic Dynamic For Part 3 see MS23 Alexander Litvinenko, TU Braunschweig, Systems with Noisy Observations Germany Yuefeng Wu, University of California, For Part 5 see MS38 Santa Cruz, USA; Giles Hooker, Cornell There has been a growing interest University, USA in developing scalable numerical methods for stochastic computation 2:20-2:35 Uncertainty Quantification in the Ensemble Kalman Filter in the presence of high-dimensional Jon Saetrom, Statoil ASA, Norway; Henning random inputs. This is motivated by Omre, Norwegian University of Science the need to reduce the issue of curse- and Technology, Norway of-dimensionality, i.e., exponential 2:40-2:55 A Spectral Approach to increase of computational complexity, Linear Bayesian Updating in predictive simulation of physical Oliver Pajonk, Technische Universität systems where accurate description Braunschweig, Germany; Bojana V. of uncertainties entails a large Rosic and Alexander Litvinenko, TU number of random variables. To Braunschweig, Germany; Hermann this end, several novel approaches G. Matthies, Technical University based on multi-level, reduced order, Braunschweig, Germany sparse, and low-rank approximations 3:00-3:15 Multi-Modal Oil Reservoir have been recently developed. This History Matching Using Clustered minisymposium presents state-of-the- Ensemble Kalman Filter art in such developments for various Ahmed H. ElSheikh, Imperial College aspects of high-dimensional stochastic London, United Kingdom computation, including analysis, 3:20-3:35 Emulating Dynamic Models algorithms, implementation, and –- Numerical Challenge applications. Carlo Albert, Eawag, Switzerland Organizer: Alireza Doostan University of Colorado at Boulder, USA Organizer: Dongbin Xiu Purdue University, USA 2:00-2:25 An Adaptive Sparse Grid Generalized Stochastic Collocation Method for High-dimensional Stochastic Simulations Clayton G. Webster, Oak Ridge National Laboratory, USA; Max Gunzburger, Florida State University, USA; Fabio Nobile, EPFL, Switzerland; Raul F. Tempone, King Abdullah University of Science & Technology (KAUST), Saudi Arabia

continued in next column 32 2012 SIAM Conference on Uncertainty Quantification

Tuesday, April 3 2:30-2:55 Efficient Algorithm for Tuesday, April 3 Computing Rare Failure Probability MS32 Jing Li and Dongbin Xiu, Purdue University, MS33 USA Stochastic Uncertainty: Uncertainty Quantification 3:00-3:25 Pink and 1/fα Noise Inputs Modeling, Forward in Stochastic PDEs Techniques and Propagation, and Inverse John Burkardt, Max Gunzburger, and Applications for Engineering Problems - Part V of V Miroslav Stoyanov, Florida State Problems in the Geosphere University, USA - Part II of II 2:00 PM-4:00 PM 3:30-3:55 Computational Nonlinear Room:State A Stochastic Homogenization Using a 2:00 PM-4:00 PM Non-concurrent multiscale Approach For Part 4 see MS24 Room:State B for Hyperelastic Heterogeneous Uncertainty quantification in Microstructures Analysis For Part 1 see MS25 computational science and engineering Alexandre Clément and Christian Soize, Geologic experience and data along has two main components: (i) modeling Université Paris-Est, France with geophysical models are often used of the uncertainty in the input as input to engineering designs. Limited parameters, consistent with available sampling of geologic properties and the information, physical constraints, potentially large discrepancy in temporal and prior knowledge; (ii) the forward and spatial scales between different propagation of input uncertainty to the types of information often serves as output quantities used in engineering sources of uncertainty in predicting the design and regulatory requirements. performance of the engineered system. This minisymposium focuses on the Probabilistic techniques can be used to stochastic approach to uncertainty estimate unknown model parameters quantification in computational science conditional on varying initial and and engineering; it aims to showcase boundary conditions, constitutive and emerging methodologies for building even intrinsic numerical parameters. parametric and nonparametric stochastic These serve as the basis for predicting models for uncertain input parameters, performance of the engineered system. eventually involving the solution of This minisymposium aims at discussing stochastic inverse problems, as well as research developments to engineered innovative techniques for propagating systems that interface with the input stochasticity through complex geosphere. differential models and computing Organizer: Zenon Medina-Cetina statistics of the output quantities of Texas A&M University, USA interest. Organizer: Sean A McKenna Organizer: Youssef M. Marzouk Sandia National Laboratories, USA Massachusetts Institute of Technology, USA 2:00-2:25 Causality and Stochastic Organizer: Olivier LeMaitre Processes with Varying Evidence LIMSI-CNRS, France Conditions Organizer: Fabio Nobile Zenon Medina-Cetina, Texas A&M EPFL, Switzerland University, USA 2:00-2:25 Hierarchical Multi-output 2:30-2:55 Uncertainty in Geotechnical Gaussian Process Regression for Engineering Uncertainty Quantification with Gabriel Auvinet-Guichard, Universidad Arbitrary Input Probability Distributions Nacional Autonoma de Mexico, Mexico Ilias Bilionis and Nicholas Zabaras, Cornell 3:00-3:25 Modelling Uncertainty in University, USA Risk Assessment for Natural Hazards Farrokh Nadim, Norwegian Geotechnical continued in next column Institute, Norway 3:30-3:55 Estimation of Multiscale Fields Representing Anthropogenic CO2 Emissions from Sparse Observations Jaideep Ray, Bart G. Van Bloemen Waanders, and Sean A McKenna, Sandia National Laboratories, USA 2012 SIAM Conference on Uncertainty Quantification 33

Tuesday, April 3 Tuesday, April 3 Tuesday, April 3 MS34 MS35 MS36 Code Verification: Practices UQ Solutions for Design Data Assimilation in Large- and Problem Development and Manufacturing Process scale Weather and Climate - Part I of II Engineering - Part I of II Models 2:00 PM-4:00 PM 2:00 PM-4:00 PM 2:00 PM-4:00 PM Room:Congressional B Room:State F Room:Congressional A For Part 2 see MS39 For Part 2 see MS42 Data assimilation is concerned with For scientific simulation codes, rigorous This minisymposium convenes leaders quantifying the uncertainty in state code verification is essential to provide of several concurrent development estimates used for initializing large confidence in code correctness and as efforts in uncertainty quantification models. An emerging technique to the a foundation for subsequent validation (UQ) methodologies, techniques, and challenge of refining large models is and uncertainty quantification activities. tools for design and manufacturing using low-dimensional solutions in While a consensus theory of code process engineering. The emphasis data assimilation methods. Approaches verification has emerged, many issues is on practical methodologies and such as local low dimensionality and remain in its practice. In Session I techniques that are effectively the Local Ensemble Transform Kalman speakers will address considerations implemented by mathematically Filter are promising for improving such as criteria of completeness, rigorous, computationally efficient, and existing data assimilation schemes effective conveyance of results, engineer-friendly tools. The solutions for difficult computational problems. and use of verification to improve should advance systems engineering This minisymposium will survey code development. Furthermore, the and/or concurrent engineering how current ensemble, variational, availability of effective test problems approaches. The target audience is and hybrid data assimilation methods is critical to success of any code engineering practitioners who would quantify uncertainty in weather and verification effort, and speakers in like to better solve their UQ problems, climate models, from low-dimensional Session II will discuss informative as well as researchers who would theoretical models to large-scale test problems developed for their like to understand the scope of, and operational models. Talks will applications. relationship between, existing state- examine both analytical and numerical Organizer: Carol S. Woodward of-the-art UQ solutions in design and approaches in such models. Lawrence Livermore National Laboratory, manufacturing process engineering. Organizer: Lewis Mitchell USA Organizer: Mark Campanelli University of Vermont, USA Organizer: V. Gregory Weirs National Institute of Standards and Organizer: Thomas Bellsky Technology, USA Sandia National Laboratories, USA Arizona State University, USA 2:00-2:25 Exact Calculations for 2:00-2:25 Code Verification: Practices 2:00-2:25 Local-Low Dimensionality of Random Variables in Uncertainty and Perils Complex Atmospheric Flows Quantification Using a Computer Carol S. Woodward, Lawrence Livermore Thomas Bellsky, Arizona State University, Algebra System National Laboratory, USA USA Lawrence Leemis, College of William & 2:30-2:55 Challenges in Devising Mary, USA 2:30-2:55 Uncertainty Quantification Manufactured Solutions for PDE and Data Assimilation in Multiscale 2:30-2:55 HPD Liberates Applied Applications Systems Using Stochastic Probability AND Enables Patrick M. Knupp, Sandia National Homogenization Comprehensively Tackling Design Laboratories, USA Lewis Mitchell, University of Vermont, USA; Engineering Georg A. Gottwald, University of Sydney, 3:00-3:25 Tools and Techniques Jean Parks and Chun Li, Variability Australia for Code Verification using Associates, USA Manufactured Solutions 3:00-3:25 Assimilation of 3:00-3:25 Practical UQ for Engineering Nicholas Malaya, Roy Stogner, and Robert Thermodynamic Profiler Retrievals Applications with DAKOTA D. Moser, University of Texas at Austin, in the Boundary Layer: Comparison Brian M. Adams, Laura Swiler, and Michael USA of Methods and Observational Error S. Eldred, Sandia National Laboratories, Specifications 3:30-3:55 The Requirements and USA Challenges for Code Verification Sean Crowell and Dave Turner, National Needed to Support the Use of 3:30-3:55 Open TURNS: Open source Severe Storms Laboratory, USA Treatment of Uncertainty, Risk ‘N Computational Fluid Dynamics for 3:30-3:55 Lagrangian Data Statistics Nuclear Reactor Design and Safety Assimilation and Control: Hide and Anne-Laure Popelin, EDF, France; Anne Applications Seek Dutfoy, EDF, Clamart, France; Paul Hyung B. Lee, Bettis Laboratory, USA Damon Mcdougall, University of Warwick, Lemaître, INRIA Bordeaux Sud-Ouest, United Kingdom France 34 2012 SIAM Conference on Uncertainty Quantification

Tuesday, April 3 Tuesday, April 3 Tuesday, April 3 MS37 MT6 CP10 Uncertainty Quantification Uncertainty Quantification: Inverse Problems I for Volcanic Hazard Foundations and 4:30 PM-6:30 PM Assessment Capabilities for Model- Room:University A 2:00 PM-4:00 PM Based Simulations - Chair: Cranos M. Williams, North Carolina Room:State E Part II of III State University, USA Large granular volcanic events -- 4:30 PM - 6:30 PM 4:30-4:45 Langevin Based Inversion of Pressure Transient Testing Data pyroclastic flows -- are rare yet potentially For Part 1 see MT3 Richard Booth and Kirsty Morton, devastating for communities situated For Part 3 see MT9 Schlumberger Brazil Research and near volcanoes. Proper assessment of Room: State C Geoengineering Center, Brazil; Mustafa such hazards must include scenarios The minitutorial will present Onur, Istanbul Technical University, that are larger in volume than any the physical motivation and Turkey; Fikri Kuchuk, Schlumberger previous events. This task inherently mathematical foundations necessary Riboud Product Center, France requires a combination of physical and for the formulation of well-posed UQ 4:50-5:05 Inverse Problem: Information statistical modeling as well as large problems in computational science Extraction from Electromagnetic scale computations. Accounting for and engineering. In particular, the Scattering Measurement these multiple sources of uncertainty is minitutorial will cover 1) aspects of Pierre Minvielle-Larrousse, Marc Sancandi, crucial in the hazard assessment process. probabilistic modeling and analysis, Francois Giraud, and Pierre Bonnemason, Furthermore, one must carefully handle 2) polynomial chaos representations, CEA/CESTA, France the rare nature of the most dangerous 3) stochastic processes and Karhunen- 5:10-5:25 Bayesian Acoustic Wave- events to keep probability calculations Loeve expansions, 4) forward UQ Field Inversion of a 1D Heterogeneous computationally feasible. To this end, including sampling, sparse-grid, Media model surrogates prove a useful powerful stochastic Galerkin and collocation, 5) Saba S. Esmailzadeh and Zenon Medina- Cetina, Texas A&M University, USA; Jun tool in developing probabilistic hazard inverse problems in UQ, 6) overview Won Kang, New Mexico State University, maps. of software resources, 7) summary of USA; Loukas F. Kallivokas, University of Organizer: Elaine Spiller advanced topics. Texas at Austin, USA Marquette University, USA Organizer: 5:30-5:45 Some Inverse Problems for 2:00-2:25 Overview of Volcanic Hazard Roger Ghanem, University of Southern Groundwater Assessment California, USA Nicholas Dudley Ward, Otago Computational M.J. Bayarri, University of Valencia, Spain Modelling Group, New Zealand; Tiangang Cui, University of Auckland, New 2:30-2:55 Modeling Large Scale Zealand; Jari P Kaipio, University of Geophysical Flows: Physics and Speakers: Eastern Finland, Finland and University of Uncertainty Roger Ghanem, University of Southern Auckland, New Zealand E. Bruce Pitman, State University of New California, USA York, Buffalo, USA; M.J. Bayarri, 5:50-6:05 Set-Based Parameter University of Valencia, Spain; James Bert Debusschere, Sandia National and State Estimation in Nonlinear Berger, Duke University, USA; Eliza Laboratories, USA Differential Equations Using Sparse Calder, University of Buffalo, USA; Abani Discrete Measurements K. Patra, State University of New York, Cranos M. Williams and Skylar Marvel, North Buffalo, USA; Elaine Spiller, Marquette Carolina State University, USA University, USA; Robert Wolpert, Duke 6:10-6:25 Probabilistic Solution of University, USA Inverse Problems under Varying 3:00-3:25 Design and Use of Surrogates Evidence Conditions in Hazard Assessment Zenon Medina –Cetina and Negin Yousefpour, Elaine Spiller, Marquette University, USA Texas A&M University, USA; Hans Petter 3:30-3:55 Combining Deterministic Langtangen, Are Magnus Bruaset, and and Stochastic Models For Hazard Stuart Clark, Simula Research Laboratory, Assessment Norway Robert Wolpert, Duke University, USA; Elaine Spiller, Marquette University, USA

Coffee Break 4:00 PM-4:30 PM Room:Pre-Function Area 2012 SIAM Conference on Uncertainty Quantification 35

Tuesday, April 3 Tuesday, April 3 Tuesday, April 3 CP11 MS38 MS39 Inverse Problems II Numerical Methods Code Verification: Practices 4:30 PM-6:10 PM for High-Dimensional and Problem Development Uncertainty Quantification - - Part II of II Room:University B Part V of V Chair: Nikhil Galagali, Massachusetts 4:30 PM-6:30 PM Institute of Technology, USA 4:30 PM-6:30 PM Room:Congressional B 4:30-4:45 Chemical Reaction Room:State D For Part 1 see MS34 Mechanism Generation Using For Part 4 see MS31 For scientific simulation codes, rigorous Bayesian Variable Selection There has been a growing interest in code verification is essential to provide Nikhil Galagali and Youssef M. Marzouk, confidence in code correctness and as Massachusetts Institute of Technology, developing scalable numerical methods a foundation for subsequent validation USA for stochastic computation in the presence of high-dimensional random inputs. This and uncertainty quantification activities. 4:50-5:05 Inferring Bottom Bathymetry is motivated by the need to reduce the While a consensus theory of code from Free-Surface Flow Features verification has emerged, many issues Sergey Koltakov, Gianluca Iaccarino, and issue of curse-of-dimensionality, i.e., remain in its practice. In Session I Oliver Fringer, Stanford University, USA exponential increase of computational complexity, in predictive simulation speakers will address considerations 5:10-5:25 Bayesian Updating of of physical systems where accurate such as criteria of completeness, Uncertainty in the Description of effective conveyance of results, Transport Processes in Heterogeneous description of uncertainties entails a large and use of verification to improve Materials number of random variables. To this end, Jan Sykora and Anna Kucerova, Czech several novel approaches based on multi- code development. Furthermore, the Technical University, Prague, Czech level, reduced order, sparse, and low- availability of effective test problems Republic; Bojana V. Rosic, and Hermann rank approximations have been recently is critical to success of any code G. Matthies, Technical University developed. This minisymposium presents verification effort, and speakers in Braunschweig, Germany state-of-the-art in such developments Session II will discuss informative 5:30-5:45 Adaptive Error Modelling for various aspects of high-dimensional test problems developed for their in Mcmc Sampling for Large Scale stochastic computation, including applications. Inverse Problems analysis, algorithms, implementation, and Organizer: Carol S. Woodward Tiangang Cui, University of Auckland, applications. Lawrence Livermore National Laboratory, New Zealand; Nicholas Dudley Ward, USA Otago Computational Modelling Group, Organizer: Alireza Doostan New Zealand; Colin Fox, University of University of Colorado at Boulder, USA Organizer: V. Gregory Weirs Otago, New Zealand; Mike O’Sullivan, Organizer: Dongbin Xiu Sandia National Laboratories, USA University of Auckland, New Zealand Purdue University, USA 4:30-4:55 Several Interesting 5:50-6:05 Scalable Methods for 4:30-4:55 Numerical Strategies for Parabolic Test Problems Large-Scale Statistical Inverse Epistemic Uncertainty Analysis Jeffrey A. Hittinger, and Jeffrey W. Banks, Problems, with Applications to Xiaoxiao Chen, Purdue University, USA; Lawrence Livermore National Laboratory, Subsurface Flow Eun-Jae Park, Yonsei University, South USA; Jeffrey M. Connors, University of H. Pearl Flath, Tan Bui-Thanh, and Omar Korea; Dongbin Xiu, Purdue University, Pittsburgh, USA; Carol S. Woodward, Ghattas, University of Texas at Austin, USA Lawrence Livermore National Laboratory, USA USA 5:00-5:25 Uncertainty Quantification with High Dimensional, Experimentally 5:00-5:25 Exact Error Behavior of Measured Inputs Simple Numerical Problems Ilias Bilionis and Nicholas Zabaras, Cornell Daniel Israel, Los Alamos National University, USA Laboratory, USA 5:30-5:55 Stochastic Integration 5:30-5:55 Verification and Validation Methods and their Application to in Solid Mechanics Reliability Analysis Krishna Kamojjala and Rebecca Brannon, Utz Wever and Albert B. Gilg, Siemens University of Utah, USA AG Corporate Technology, Germany; 6:00-6:25 Cross-Application of Meinhard Paffra, Siemens AG, Germany Uncertainty Quantification and Code 6:00-6:25 A Localized Strategy for Verification Techniques Generalized Polynomial Chaos V. Gregory Weirs, Sandia National Methods Laboratories, USA Yi Chen and Dongbin Xiu, Purdue University, USA 36 2012 SIAM Conference on Uncertainty Quantification

Tuesday, April 3 5:30-5:55 Recovery from Modeling Tuesday, April 3 Errors in Non-stationary Inverse MS40 Problems: Application to Process MS41 Tomography Methods for Uncertainty Aku Seppanen, and Antti Lipponen, Predictive Fidelity in Quantification in Inverse University of Eastern Finland, Finland; Multiscale Simulations - Jari P. Kaipio, University of Eastern Problems and Data Finland, Finland and University of Part II of III Assimilation - Part I of II Auckland, New Zealand 4:30 PM-6:30 PM 4:30 PM-6:30 PM 6:00-6:25 Variational Approximations Room:State E in Large-scale Data Assimilation: Room:State B For Part 1 see MS26 Experiments with a Quasi- For Part 3 see MS48 For Part 2 see MS47 Geostrophic Model In many applications, the overall system In an inverse problem, estimates of Antti Solonen, Lappeenranta University of unknown parameters in a physical Technology, Finland dynamics are affected by coupled model are sought from measured physical phenomena, occurring over a data assumed to have been output wide range of time and length scales. from the model. Due to random Multiscale physics simulations employ noise in the measurement process, the requisite models that represent the parameter estimates are also random, relevant physics on each time and length and hence quantifying uncertainty in scale level, and couple the various estimators is an important task. In this models across the scales in order to minisymposium, we focus on techniques resolve the overall system behavior. for uncertainty quantification in inverse Assessing the predictive fidelity of problems. The inverse problems multiscale simulations requires careful considered range from classical high- quantification and propagation of dimensional applications in image uncertainties on all scales, as well as deblurring and tomography, to time in the coupling between scales. This varying data assimilation problems minisymposium covers research topics in weather prediction and process in this general area. tomography, to lower-dimensional Organizer: Bert J. Debusschere parameter estimation problems in Sandia National Laboratories, USA climate modeling, biology, and Organizer: Habib N. Najm chemistry. Sandia National Laboratories, USA Organizer: Johnathan M. Bardsley Organizer: Allen C. Robinson University of Montana, USA Sandia National Laboratories, USA 4:30-4:55 Sampling and Inference for 4:30-4:55 A Spectral Uncertainty Large-scale Inverse Problems Using Quantification Approach in Ocean an Optimization-based Approach General Circulation Modeling Johnathan M. Bardsley, University of Alen Alexanderian, Johns Hopkins Montana, USA University, USA; Justin Winokur and Ihab 5:00-5:25 Approximate Sraj, Johns Hopkins University, USA; Marginalization of Uninteresting Ashwanth Srinivasan, and Mohamed Distributed Parameters in Inverse Iskandarani, University of Miami, USA; Problems WilliamCarlisle Thacker, National Oceanic Ville P. Kolehmainen, University of Kuopio, and Atmospheric Administration, USA; Finland; Jari P Kaipio, University of Omar M. Knio, Duke University, USA Eastern Finland, Finland and University of 5:00-5:25 Uncertainty Quantification Auckland, New Zealand; Tanja Tarvainen, of Equation-of-state Closures and University of Eastern Finland, Finland; Shock Hydrodynamics Simon Arridge, University College Allen C. Robinson, Robert D. Berry, John H. London, United Kingdom Carpenter, Bert J. Debusschere, Richard continued in next column R. Drake, Ann E. Mattsson, and William J. Rider, Sandia National Laboratories, USA

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5:30-5:55 Optimal Uncertainty Tuesday, April 3 Tuesday, April 3 Quantification and (Non-) Propagation of Uncertainties Across MS42 MS43 Scales Tim Sullivan, Michael McKerns, Michael UQ Solutions for Design Random Media: Models, Ortiz, and Houman Owhadi, California and Manufacturing Process Simulations, and Institute of Technology, USA; Clint Engineering - Part II of II Applications Scovel, Los Alamos National Laboratory, USA; Florian Theil, University of 4:30 PM-6:00 PM 4:30 PM-7:00 PM Warwick, United Kingdom Room:State F Room:Congressional A 6:00-6:25 Coarse Graining with For Part 1 see MS35 The understanding of uncertainty Uncertainty: A Relative Entropy This minisymposium convenes leaders Framework quantitfication is a current thrust in Nicholas Zabaras and Ilias Bilionis, Cornell of several concurrent development many applied sciences, in particular University, USA efforts in uncertainty quantification geosciences. A crucial component is (UQ) methodologies, techniques, and the construction of stochastic models tools for design and manufacturing of uncertainty and the understanding process engineering. The emphasis of subsequent properties. Questions is on practical methodologies and abound: What distributional properties techniques that are effectively are desired? How should parameters be implemented by mathematically selected? How well does the behavior rigorous, computationally efficient, and of subsequent models reflect physical engineer-friendly tools. The solutions reality? Is numerical simulation should advance systems engineering feasible? The ensemble of talks in this and/or concurrent engineering session give some insight in model approaches. The target audience is selection, simulation, and evaluation engineering practitioners who would in the context of modeling physical like to better solve their UQ problems, processes in random media. as well as researchers who would Organizer: Mina E. Ossiander like to understand the scope of, and Oregon State University, USA relationship between, existing state- of-the-art UQ solutions in design and Organizer: Malgorzata Peszynska Oregon State University, USA manufacturing process engineering. Organizer: Nathan L. Gibson Organizer: Mark Campanelli Oregon State University, USA National Institute of Standards and Technology, USA 4:30-4:55 Stochastic Models, Simulation and Analysis in Subsurface 4:30-4:55 UQ Practices and Standards Flow and Transport for Design and Manufacturing Mina E. Ossiander, Malgorzata Peszynska, Process Engineering and Veronika S. Vasylkivska, Oregon State Mark Campanelli, National Institute of University, USA Standards and Technology, USA 5:00-5:25 Macroscopic Properties of 5:00-5:25 Systematic Integration Isotropic and Anisotropic Fracture of Multiple Uncertainty Sources in Networks from the Percolation Design Process Threshold to Very Large Densities Sankaran Mahadevan, Vanderbilt University, Pierre Adler, Université Pierre et Marie USA Curie, France; Jean Francois Thovert and 5:30-5:55 Generalized Chapman- Valeri Mourzenko, PPRIME, France Kolmogorov Equation for Multiscale 5:30-5:55 A Comparative Study on System Analysis Reservoir Characterization using Two Yan Wang, Georgia Institute of Technology, Phase Flow Model USA Victor E. Ginting, Felipe Pereira, and Arunasalam Rahunanthan, University of Wyoming, USA

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Tuesday, April 3 Tuesday, April 3 Tuesday, April 3 MS43 MS44 PD1 Random Media: Models, Spatial UQ Forward Looking Panel Simulations, and 4:30 PM-6:30 PM Discussion Applications Room:State A 8:00 PM-9:00 PM 4:30 PM-7:00 PM This session is devoted to computer Room:State C/D continued models in which the spatial dimension Chair: James Berger, Duke University, USA is key to the uncertainty quantification. The Committee on Mathematical 6:00-6:25 Uncertainty Quantification Open questions are: (1) Where should Foundations of Verification, Validation, Methods for Unsaturated Flow in we collect information to efficiently Porous Media and Uncertainty Quantification was calibrate parameterizations? (2) What formed by the National Research David A. Barajas-Solano, University of spatial covariance should we employ California, San Diego, USA Council with several charges, to model the spatial uncertainty of the including (i) identifying mathematical 6:30-6:55 Adaptive AMG for Diffusion outputs in emulators? (3) What levels sciences research needed to establish Equations with Stochastic Coefficients of spatial resolution will achieve low Christian Ketelsen and Panayot Vassilevski, a foundation for building a science of predictive uncertainty? Various Bayesian V&V and for improving the practice Lawrence Livermore National Laboratory, formulations are developed to address USA of VVUQ, and (ii) recommending these issues. Applications presented in educational changes needed in the this symposium are: geophysical model mathematical sciences community and for pressure wave attenuation; spatial mathematical sciences education needed distribution of fish species; air pollution by other scientific communities to most on streets; energy consumption by effectively use VVUQ. The report of the buildings in cities. committee will just have been released Organizer: Ruchi Choudhary by the time of the conference, and the University of Cambridge, United Kingdom co-chairs of the committee will open the 4:30-4:55 Spatial Analysis of Energy forward looking session by summarizing Consumption by Non-Domestic relevant aspects of the report. Buildings in Greater London Ruchi Choudhary and Wei Tian, University Panelists: of Cambridge, United Kingdom Marvin Adams 5:00-5:25 Adding Spatial Texas A&M University, USA Dependence Constraints to a David Higdon Geophysical Inverse Problem Los Alamos National Laboratory, USA Eugene Morgan, Duke University, USA 5:30-5:55 Spatial Statistical Calibration of a Turbulence Model Nina Glover, Serge Guillas, and Liora Malki-Epshtein, University College London, United Kingdom 6:00-6:25 Asessing the Spatial Distribution of Fish Species Using Bayesian Latent Gaussian Models Facundo Muñoz, University of Valencia, Spain; María Pennino, Spanish Institute of Oceanography, Spain; David Conesa and Antonio López-Quílez, University of Valencia, Spain

Dinner Break 6:30 PM-8:00 PM Attendees on their own 2012 SIAM Conference on Uncertainty Quantification 39

Wednesday, Wednesday, April 4 Wednesday, April 4 April 4 MT7 CP12 Introduction to Statistical Calibration & Inverse Analysis of Extremes Problems Registration 9:30 AM - 12:30 PM 9:30 AM-10:50 AM 7:45 AM-5:00 PM Room: State C Room:University A Room:Chancellor and Pre-Function Area This minitutorial will introduce the ideas Chair: Benjamin P. Smarslok, Air Force and techniques involved in the analy- Research Laboratory, USA sis of both univariate and multivariate 9:30-9:45 Bayesian Models for the Remarks extremes. Statistical practice relies on Quantification of Model Errors in Pde- fitting distributions suggested by asymp- Based Systems 8:10 AM-8:15 PM totic theory to a subset of data consid- Phaedon S. Koutsourelakis, Heriot-Watt Room:State C/D ered to be extreme. The minitutorial will University, Scotland introduce the fundamental asymptotic 9:50-10:05 Investigating Uncertainty results which underlie extremes analysis in Aerothermal Model Predictions for via demonstrations and examples. Both Hypersonic Aircraft Structures IP4 block maximum and threshold exceed- Benjamin P. Smarslok, Air Force Research ance approaches will be presented for Laboratory, USA; Sankaran Mahadevan, Large Deviation Methods for Vanderbilt University, USA both the univariate and multivariate cas- Quantifying Uncertainty es. The multivariate portion of the course 10:10-10:25 Predictive Simulation for 8:15 AM-9:00 AM will largely focus on how dependence is CO2 Sequestration in Saline Aquifers described for extremes: via an angular Victor E. Ginting, Marcos Mendes, Felipe Room:State C/D Pereira, and Arunasalam Rahunanthan, measure rather than via correlation. Chair: Andrew Stuart, University of University of Wyoming, USA Warwick, United Kingdom Organizer and Speaker: 10:30-10:45 The Effect of Prediction Large deviation methods have been Dan Cooley, Colorado State University, Error Correlation on Bayesian Model Updating particularly successful in assessing USA small probabilities of rare events, which Ellen Simoen, K.U. Leuven, Belgium; Costas Papadimitriou, University of Thessaly, are difficult to compute. They are Greece; Guido De Roeck and Geert also at the center of many importance Lombaert, K.U. Leuven, Belgium sampling methods that aim to estimate probabilities of rare events by Monte Carlo methods. Since probabilities of rare events are an important part of the emerging field of uncertainty quantification in complex scientific problems, the question arises as to how effective they are. This is because the results of large deviation theory depend sensitively on details of the probabilistic model used, and such details may not be available or may themselves be subject to uncertainty. I will address these issues with some examples using mean-field models and conservation laws and attempt to draw some broader conclusions. George C. Papanicolaou Stanford University, USA

Coffee Break 9:00 AM-9:30 AM Room:Pre-Function Area 40 2012 SIAM Conference on Uncertainty Quantification

Wednesday, April 4 Wednesday, April 4 Zanna, University of Oxford, United Kingdom; Andrew M. Moore, University MS45 of California, Santa Cruz, USA; Eli CP13 Tziperman, Harvard University, USA Climate Uncertainty Propagation & Estimation 10:30-10:55 Uncertainty 9:30 AM-11:30 AM Quantification - Part I of IV Quantification for Large Multivariate Spatial Computer Model Output with Room:University B 9:30 AM-11:30 AM Climate Applications Chair: Patrick R. Conrad, Massachusetts Room:State D K. Sham Bhat, Los Alamos National Institute of Technology, USA For Part 2 see MS52 Laboratory, USA 9:30-9:45 Multilevel Monte Carlo Uncertainty quantification of climate 11:00-11:25 Quantifying Uncertainty for Uncertainty Quantification in predictions is challenging. Climate for Climate Change Predictions with Subsurface Flow models used for making predictions Model Error in non-Gaussian Systems Robert Scheichl, University of Bath, United contain not only many aleatoric with Intermittency Kingdom; Andrew Cliffe, University of sources of uncertainty, many of their Michal Branicki, New York University, Nottingham, United Kingdom; Michael epistemological aspects are not well USA; Andrew Majda, Courant Institute B. Giles, University of Oxford, United of Mathematical Sciences, New York defined. How can we test model Kingdom; Minho Park, University of University, USA Nottingham, United Kingdom; Aretha responses to a forcing for which we Teckentrup and Elisabeth Ullmann, do not have observations? How do University of Bath, United Kingdom we separate observations used to 9:50-10:05 Comparison of Stochastic drive model development from those Methods for Bayesian Updating used for model evaluation? Climate of Uncertainty in Parameters of models simulate non-linear processes Nonlinear Models that interact on many time and space Anna Kucerova and Jan Sykora, Czech scales, so representing, sampling, Technical University, Prague, Czech and computing aleatoric uncertainties Republic; Bojana V. Rosic, TU alone is a major challenge. We Braunschweig, Germany; Hermann welcome contributions that address G. Matthies, Technical University any challenges in climate uncertainty Braunschweig, Germany quantification. 10:10-10:25 Adaptive Smolyak Pseudospectral Expansions Organizer: Guang Lin Patrick R. Conrad and Youssef M. Marzouk, Pacific Northwest National Laboratory, USA Massachusetts Institute of Technology, Organizer: Charles Jackson USA University of Texas at Austin, USA 10:30-10:45 Reservoir Uncertainty Organizer: Donald D. Lucas Quantification Using Clustering Lawrence Livermore National Laboratory, Methods USA Asaad Abdollahzadeh, Heriot-Watt 9:30-9:55 Quantifying Uncertainties in University, Scotland; Mike Christie and Fully Coupled Climate Models David W. Corne, Heriot-Watt University, Donald D. Lucas, Scott Brandon, Curt United Kingdom Covey, Davlid Domyancic, Gardar 10:50-11:05 Stochastic Anova- Johannesson, Stephen Klein, John Galerkin Projection Schemes Tannahill, and Yuying Zhang, Lawrence Prasanth B. Nair, University of Toronto, Livermore National Laboratory, USA Canada; Christophe Audouze, Université 10:00-10:25 Upper Ocean Singular Paris-Sud, France Vectors of the North Atlantic: 11:10-11:25 Uncertainty and Implications for Linear Predictability Differences in Global Climate Models and Observational Requirement Joshua P. French, University of Colorado, Patrick Heimbach, Massachusetts Denver, USA; Stephan Sain, National Institute of Technology, USA; Laure Center for Atmospheric Research, USA continued in next column 2012 SIAM Conference on Uncertainty Quantification 41

Wednesday, April 4 Wednesday, April 4 Wednesday, April 4 MS46 MS47 MS48 Recent Advances in Methods for Uncertainty Predictive Fidelity in Numerical SPDES - Part I of II Quantification in Inverse Multiscale Simulations - 9:30 AM-11:30 AM Problems and Data Part III of III Room:State A Assimilation - Part II of II 9:30 AM-11:00 AM For Part 2 see MS53 9:30 AM-11:30 AM Room:State E It is well understood that effective Room:State B For Part 2 see MS41 numerical methods for stochastic partial For Part 1 see MS40 In many applications, the overall system differential equations (SPDES) are In an inverse problem, estimates of dynamics are affected by coupled essential for uncertainty quantification. unknown parameters in a physical physical phenomena, occurring over a In the last decade much progress has model are sought from measured data wide range of time and length scales. been made in the construction numerical assumed to have been output from Multiscale physics simulations employ algorithms to efficiently solve SPDES the model. Due to random noise in the requisite models that represent the with random coefficients and white the measurement process, parameter relevant physics on each time and length noise perturbations. However, high estimates are also random, and hence scale level, and couple the various dimensionality and low regularity quantifying uncertainty in estimators models across the scales in order to is still the bottleneck in solving real is an important task. In this mini- resolve the overall system behavior. world applicable SPDES with efficient symposium, we focus on techniques Assessing the predictive fidelity of numerical methods. This mini-symposium for uncertainty quantification in inverse multiscale simulations requires careful is intended to address the mathematical problems. The inverse problems quantification and propagation of aspects of numerical approximations considered range from classical high- uncertainties on all scales, as well as of SPDES, including error analysis dimensional applications in image in the coupling between scales. This and complexity analysis and deblurring and tomography, to time minisymposium covers research topics development of new efficient numerical varying data assimilation problems in this general area. algorithms. in weather prediction and process Organizer: Bert J. Debusschere Organizer: Yanzhao Cao tomography, to lower-dimensional Sandia National Laboratories, USA Auburn University, USA parameter estimation problems in Organizer: Habib N. Najm Organizer: Clayton G. Webster climate modeling, biology, and Sandia National Laboratories, USA chemistry. Oak Ridge National Laboratory, USA Organizer: Allen C. Robinson 9:30-9:55 Efficient Nonlinear Filtering Organizer: Johnathan M. Bardsley Sandia National Laboratories, USA of a Singularly Perturbed Stochastic University of Montana, USA 9:30-9:55 Heterogeneous Deformation Hybrid System 9:30-9:55 Putting Computational of Polycrystalline Metals and Extreme Boris Rozovski, Brown University, USA Inference into an FPGA Value Events 10:00-10:25 Efficient Spectral Garlerkin Colin Fox, University of Otago, New Curt Bronkhorst, Los Alamos National Method with Orthgonal Polynomials for Zealand Laboratory, USA SPDES 10:00-10:25 Model Reductions by 10:00-10:25 Coupled Chemical Yanzhao Cao, Auburn University, USA MCMC Master Equation - Fokker Planck 10:30-10:55 Two Stochastic Modeling Heikki Haario, Lappeenranta University of Solver for Stochastic Reaction Strategies for Elliptic Problems Technology, Finland Networks Xiaoliang Wan, Louisiana State University, 10:30-10:55 Advanced Uncertainty Khachik Sargsyan, Cosmin Safta, Bert J. USA Evaluation of Climate Models by Debusschere, and Habib N. Najm, Sandia 11:00-11:25 Adaptive Methods for Monte Carlo Methods National Laboratories, USA Elliptic Partial Differential Equations Marko Laine, Finnish Meteorological 10:30-10:55 A New Approach for with Random Operators Institute, Helsinki, Finland Solving Multiscale SPDEs using Claude Gittelson, Purdue University, USA 11:00-11:25 Covariance Estimation Probabilistic Graphical Models Using Chi-squared Tests Nicholas Zabaras and Jiang Wan, Cornell Jodi Mead, Boise State University, USA University, USA 42 2012 SIAM Conference on Uncertainty Quantification

Wednesday, April 4 Wednesday, April 4 Wednesday, April 4 MS49 MS50 MS62 UQ in Engineering Uncertainty Quantification Recent Advances and Applications - Part I of III and Prediction with Applications of Stochastic 9:30 AM-11:30 AM Applications in Geoscience Partial Differential Equations- Room:State F 9:30 AM-11:30 AM Part I of III For Part 2 see MS56 Room:Congressional A 9:30 AM-11:30 AM Uncertainty quantification plays a critical Characterization of the uncertainties Room:Congressional B role in model validation and system for high-dimensional parameter spaces For Part 2 see MS69 design, reducing risks associated with and expensive forward simulations Stochastic partial differential equations computations in engineering practice. remains a tremendous challenge for have been used in numerous physical A variety of UQ algorithms address many problems today. Many problems phenomena to incorporate random limitations of existing methodologies: the in geoscience and environmental effects arising from uncertainties in curse of dimensionalitgy, discontinous engineering are described by the system. In order to properly apply response surfaces, expensive function computationally expensive models. these equations in physical models, evaluations, etc. It is important to Multiple types of uncertainty need it is imperative to understand the assess the impact of UQ on industrial to be incorporated, including data mathematical structure and properties applications in view of these issues error, model error, parameter error, of these stochastic models and to study and to identify further opportunities randomness in model input (static and how they can be used to quantify the and remaining bottlenecks. The dynamic). The invited session is being uncertainty in the physical systems. minisymposium will address these proposed to highlight recent advances This minisymposium is intended questions through a discussion of recent in this field.ncluding determination of to bring together both theoreticians innovations in UQ algorithms and spatial distribution of geologic materials and practitioners to address a range specific UQ engineering applications in a in the subsurafce, determination of of applications of SPDEs, including variety of fields. location of oil reservoirs or underground fluid dynamics, optics and statistical Organizer: James G. Glimm water based on exploratory drilling (few inference of SPDE. State University of New York, Stony Brook, spatial points, high accuracy), forecast Organizer: Xiaoying Han USA of contaminant transport. Auburn University, USA Organizer: Gianluca Iaccarino Organizer: Bani Mallick Organizer: Chia Ying Lee Stanford University, USA Texas A&M University, USA University of North Carolina, USA 9:30-9:55 Uncertainty Quantification 9:30-9:55 Bayesian Uncertainty 9:30-9:55 Perspectives on Quantifying for Turbulent Mixing and Turbulent Quantification for Flows in Highly Uncertain Mechanisms in Dynamical Combustion Heterogeneous Media Systems James G. Glimm, State University of New Yalchin Efendiev, Texas A&M University, Jinqiao Duan, University of California, Los York, Stony Brook, USA USA Angeles, USA 10:00-10:25 Criteria for Optimization 10:00-10:25 Uncertainty 10:00-10:25 Stochastic Integrable Under Uncertainty Quantification for Reactive Transport Dynamics of Optical Pulses Domenico Quagliarella, Centro Italiano of Contaminants Propagating through an Active Ricerche Aerospaziali, Italy; G. Petrone, Gowri Srinivasan, Los Alamos National Medium Università degli Studi di Napoli Federico Laboratory, USA Gregor Kovacic, Rensselaer Polytechnic II, Italy; Gianluca Iaccarino, Stanford 10:30-10:55 A Framework for Institute, USA; Ethan Atkins, Courant University, USA Experimental Design for Ill-posed Institute of Mathematical Sciences, New 10:30-10:55 Chemical Kinetic Inverse Problems York University, USA; Peter R. Kramer, Uncertainty Quantification for Luis Tenorio, Colorado School of Mines, Rensselaer Polytechnic Institute, USA; High-Fidelity Turbulent Combustion USA Ildar R. Gabitov, University of Arizona Simulations and Los Alamos National Laboratory, 11:00-11:25 Emulators in Large-scale Michael Mueller, Gianluca Iaccarino, and USA Spatial Inverse Problems Heinz Pitsch, Stanford University, USA Anirban Mondal, Quantum Reservoir 11:00-11:25 A Reduced Order Model Impact, USA continued on next page for a Nonlinear, Parameterized Heat Transfer Test Case Paul Constantine and Jeremy Templeton, Sandia National Laboratories, USA; Joe Ruthruff, Lawrence Livermore National Laboratory, USA 2012 SIAM Conference on Uncertainty Quantification 43

10:30-10:55 Reduced Models for Wednesday, April 4 Wednesday, April 4 Mode-locked Lasers with Noise Richard O. Moore, New Jersey Institute IP5 MT8 of Technology, USA; Daniel S. Cargill, New Jersey Institute of Technology, USA; Model Reduction for Emulation, Elicitation and Tobias Schaefer, City University of New Uncertainty Quantification Calibration - Part III of III York, Staten Island, USA of Large-scale Systems 2:00 PM - 4:00 PM 11:00-11:25 Analysis and Simulations of a Perturbed Stochastic Nonlinear 1:00 PM-1:45 PM For Part 2 see MT5 Schrödinger Equation for Pulse Room:State C/D Room: State C Propagation in Broadband Optical Chair: Omar Ghattas, University of Texas at This minitutorial concerns statistical Fiber Lines Austin, USA approaches to UQ based on Bayesian Avner Peleg, State University of New York, statistics and the use of emulators. It is Uncertainty quantification is becoming Buffalo, USA; Yeojin Chung, Southern organised as three 2-hour sessions. The Methodist University, USA recognized as an essential aspect of first begins with an overview of UQ development and use of numerical tasks (uncertainty propagation, sensi- simulation tools, yet it remains tivity analysis, calibration, validation) computationally intractable for large- Lunch Break and of how emulation (a non-intrusive scale complex systems characterized technique) tackles those tasks efficiently. 11:30 AM-1:00 PM by high-dimensional uncertainty It continues with an introduction to spaces. In such settings, it is essential Attendees on their own elicitation, a key component of input to generate surrogate models -- low- uncertainty quantification in practice. The dimensional, efficient models that retain second session presents the basic ideas predictive fidelity of high-resolution of emulation and illustrates its power for simulations. This talk will discuss uncertainty propagation, etc. The third formulations of projection-based model session is about calibration, including reduction approaches for applications the importance of model discrepancy and in uncertainty quantification. For history matching. systems governed by partial differential equations, we demonstrate the use Organizer: of reduced models for uncertainty Anthony O’Hagan, University of Shef- propagation, solution of statistical field, United Kingdom inverse problems, and optimization under uncertainty. Speakers: Karen E. Willcox Peter Challenor, National Oceanography Massachusetts Institute of Technology, USA Centre, Southampton, United Kingdom Anthony O’Hagan, University of Shef- field, United Kingdom Intermission Ian Vernon, University of Durham, United Kingdom 1:45 PM-2:00 PM 44 2012 SIAM Conference on Uncertainty Quantification

Wednesday, April 4 Wednesday, April 4 Wednesday, April 4 CP14 CP15 MS52 Propagation & Prediction Reliability & Rare Events Climate Uncertainty 2:00 PM-3:40 PM 2:00 PM-3:00 PM Quantification - Part II of IV Room:University A Room:University B 2:00 PM-4:00 PM Chair: Nathan L. Gibson, Oregon State Chair: Aparna V. Huzurbazar, Los Alamos Room:State D University, USA National Laboratory, USA For Part 1 see MS45 2:00-2:15 Hybrid Stochastic 2:00-2:15 Glimpses of Uq, Qmu, and For Part 3 see MS59 Collocation - Stochastic Perturbation Reliability Uncertainty quantification of climate Method for Linear Elastic Problems Aparna V. Huzurbazar and David Collins, predictions is challenging. Climate with Uncertain Material Parameters Los Alamos National Laboratory, USA models used for making predictions Boyan S. Lazarov, Technical University of 2:20-2:35 Bayesian Subset Simulation contain not only many aleatoric Denmark, Denmark; Mattias Schevenels, Konstantin M. Zuev, University of Southern sources of uncertainty, many of their K.U. Leuven, Belgium California, USA; James Beck, California epistemological aspects are not well 2:20-2:35 Stochastic Analysis of Institute of Technology, USA defined. How can we test model the Hydrologic Cascade Model, a 2:40-2:55 Rare Events Detection and responses to a forcing for which we Polynomial Chaos Approach Analysis of Equity and Commodity do not have observations? How do we Franz Konecny and Hans-Peter Nachtnebel, High-Frequency Data separate observations used to drive model University of Natural Resources and Dragos Bozdog, Ionut Florescu, Khaldoun Applied Life Sciences, Austria development from those used for model Khashanah, and Jim Wang, Stevens evaluation? Climate models simulate Institute of Technology, USA 2:40-2:55 Likelihood-Based non-linear processes that interact Observability Analysis and on many time and space scales, so Confidence Intervals for Model Predictions representing, sampling, and computing Clemens Kreutz, Andreas Raue, and Jens aleatoric uncertainties alone is a major Timmer, University of Freiburg, Germany challenge. We welcome contributions that address any challenges in climate 3:00-3:15 Toward Reduction of Uncertainty in Complex Multi-Reservoir uncertainty quantification. River Systems Organizer: Guang Lin Nathan L. Gibson, Arturo Leon, and Pacific Northwest National Laboratory, USA Christopher Gifford-Miears, Oregon State University, USA Organizer: Charles Jackson University of Texas at Austin, USA 3:20-3:35 A Comparison Of Uncertainty Quantification Methods Organizer: Donald D. Lucas Under Practical Industry Requirements Lawrence Livermore National Laboratory, Liping Wang, Gulshan Singh, and Arun USA Subramaniyan, GE Global Research, USA 2:00-2:25 Spatial ANOVA Modeling of High-resolution Regional Climate Model Outputs from NARCCAP Emily L. Kang, University of Cincinnati, USA; Noel Cressie, Ohio State University, USA 2:30-2:55 Quantifying Uncertainties in Hydrologic Parameters in the Community Land Model Ruby Leung, Zhangshuan Hou, Maoyi Huang, Yinghai Ke, and Guang Lin, Pacific Northwest National Laboratory, USA 3:00-3:25 Uncertainty Propagation in Land-Crop Models Xiaoyan Zeng, Mihai Anitescu, and Emil M. Constantinescu, Argonne National Laboratory, USA 3:30-3:55 Statistical Issues in Catchment Scale Hydrological Modeling Cari Kaufman, University of California, Berkeley, USA 2012 SIAM Conference on Uncertainty Quantification 45

Wednesday, April 4 3:00-3:25 Error Analysis of a Wednesday, April 4 Stochastic Collocation Method MS53 for Parabolic Partial Differential MS54 Equations with Random Input Data Recent Advances in Guannan Zhang and Max Gunzburger, Uncertainty Characterization Numerical SPDES - Florida State University, USA and Management in Models Part II of II 3:30-3:55 A Stochastic Collocation of Dynamical Systems - Method Based on Sparse Grid for Part I of IV 2:00 PM-4:00 PM Stokes-Darcy Model with Random Room:State A Hydraulic Conductivity 2:00 PM-4:00 PM Max Gunzburger, Florida State University, For Part 1 see MS46 Room:State B USA; Xiaoming He and Xuerong Wen, It is well understood that effective Missouri University of Science and For Part 2 see MS61 numerical methods for stochastic partial Technology, USA Uncertainty in models of complex differential equations (SPDES) are dynamical systems affect their use in essential for uncertainty quantification. prediction and control. Most current In the last decade much progress has methods for addressing uncertainty either been made in the construction numerical rely on a linear Gaussian assumption or algorithms to efficiently solve SPDES suffer from the “curse-of-dimensionality” with random coefficients and white and become increasingly infeasible for noise perturbations. However, high high-dimensional nonlinear systems. This dimensionality and low regularity necessitates novel approaches for model is still the bottleneck in solving real reduction/refinement, statistical analysis world applicable SPDES with efficient of model performance, uncertainty-based numerical methods. This mini- design, model-data fusion, and control of symposium is intended to address the systems in the presence of uncertainty. mathematical aspects of numerical The aim of this invited session is to bring approximations of SPDES, including together researchers working in this area error analysis and complexity analysis and present their recent results to the and development of new efficient SIAM community. numerical algorithms. Organizer: Abani K. Patra Organizer: Yanzhao Cao State University of New York, Buffalo, USA Auburn University, USA Organizer: Puneet Singla Organizer: Clayton G. Webster State University of New York, Buffalo, USA Oak Ridge National Laboratory, USA Organizer: Sonjoy Das 2:00-2:25 Basis and Measure State University of New York, Buffalo, USA Adaptation for Stochastic Galerkin 2:00-2:25 Uncertainty Analysis of Projections Dynamical Systems -- Application to Roger Ghanem and Bedřich Sousedík, Volcanic Ash Transport University of Southern California, USA; Abani K. Patra, Puneet Singla, Marcus Eric Phipps, Sandia National Laboratories, Bursik, E. Bruce Pitman, Matthew Jones USA and Tarunraj Singh, State University of New 2:30-2:55 Adaptive Sparse Grid York, Buffalo, USA Generalized Stochastic Collocation 2:30-2:55 Retrospective-Cost-Based Using Wavelets Model Refinement of Systems with Clayton G. Webster, Oak Ridge National Inaccessible Subsystems Laboratory, USA; Max Gunzburger and Dennis Bernstein, Anthony D’Amato, and John Burkardt, Florida State University, Asad Ali, University of Michigan, USA USA 3:00-3:25 Multiscale Methods for Flows in Heterogeneous Stochastic Porous continued in next column Media Yalchin Efendiev, Texas A&M University, USA 3:30-3:55 Feedback Particle Filter: A New Formulation for Nonlinear Filtering Based on Mean-field Games Tao Yang, Prashant G. Mehta, and Sean Meyn, University of Illinois at Urbana- Champaign, USA 46 2012 SIAM Conference on Uncertainty Quantification

Wednesday, April 4 Wednesday, April 4 Wednesday, April 4 MS55 MS56 MS57 Gradient-based Intrusive UQ in Engineering Uncertainty Quantification Uncertainty Quantification Applications - Part II of III for Ice Sheet Models 2:00 PM-4:00 PM 2:00 PM-4:00 PM 2:00 PM-4:00 PM Room:State E Room:State F Room:Congressional A Gradient-based uncertainty quantification For Part 1 see MS49 Understanding the dynamics of polar holds the promise of more accurate For Part 3 see MS63 ice sheets is critical for projections of assessment for lower computational Uncertainty quantification plays future sea level rise. Yet, there remain cost, due to the favorable computational a critical role in model validation large uncertainties in the inputs of properties of adjoint calculations. and system design, reducing risks models that describe present and future Nevertheless, obtaining gradient associated with computations in evolutions of ice sheets, ice shelves or information has its own theoretical, engineering practice. A variety of glaciers. These uncertainties can be due practical, and methodological UQ algorithms address limitations of to unknown model parameters, noise complexities. In this minisymposium existing methodologies: the curse of in the observations, uncertain initial we discuss theoretical and practical dimensionalitgy, discontinous response and boundary conditions, or uncertain issues in obtaining and using gradient surfaces, expensive function evaluations, geometry. This session is intended information in the context of uncertainty etc. It is important to assess the impact to present recent developments in quantification. Speakers in the workshop of UQ on industrial applications in view uncertainty quantification methods for will discuss methods to efficiently of these issues and to identify further forward propagation of uncertainty in ice compute sensitivity information for opportunities and remaining bottlenecks. sheet models, as well as for the solution select applications, uncertainty models The minisymposium will address these of inverse ice sheet problems. that are suitable for use with derivative questions through a discussion of recent innovations in UQ algorithms and Organizer: Noemi Petra information, and computational patterns University of Texas at Austin, USA that are enhanced by gradient information. specific UQ engineering applications in a variety of fields. Organizer: Omar Ghattas Organizer: Mihai Anitescu University of Texas at Austin, USA Argonne National Laboratory, USA Organizer: James G. Glimm State University of New York, Stony Brook, Organizer: Georg Stadler 2:00-2:25 Gradient-based Optimization USA University of Texas at Austin, USA for Mixed Epistemic and Aleatory 2:00-2:25 Quantification of the Uncertainty Organizer: Gianluca Iaccarino Brian Lockwood and Dimitri Mavriplis, Stanford University, USA Uncertainty in the Basal Sliding University of Wyoming, USA Coefficient in Ice Sheet Models 2:00-2:25 Uncertainty Quantification Noemi Petra, Hongyu Zhu, Georg Stadler, 2:30-2:55 Gradient-based Data with Incomplete Physical Models and Omar Ghattas, University of Texas at Assimilation in Atmospheric Gianluca Iaccarino, and Gary Tang, Austin, USA Applications Stanford University, USA Adrian Sandu, and Mihai Alexe, Virginia 2:30-2:55 Toward Estimation of Sub-ice 2:30-2:55 Numerical Methods for Shelf Melt Rates to Ocean Circulation Polytechnic Institute & State University, Polynomial Chaos in Uncertain Flow USA Under Pine Island Ice Shelf, West Problems Antarctica 3:00-3:25 Optimal Use of Gradient Mass Per Pettersson, Stanford University, Patrick Heimbach, Massachusetts Institute of Information in Uncertainty USA Technology, USA; Martin Losch, Alfred Quantification 3:00-3:25 A Semi-Intrusive Wegener Institute, Germany Mihai Anitescu, Argonne National Laboratory, Deterministic Approach to 3:00-3:25 Ice Bed Geometry: Estimates USA; Fred J. Hickernell and Yiou Li, Uncertainty Quantifications Illinois Institute of Technology, USA; Oleg of Known Unknowns Remi Abgrall, INRIA and University of Charles Jackson, Chad Greene, John Roderick, Argonne National Laboratory, Bordeaux, France; James G. Glimm, State Goff, Scott Kempf, and Duncan Young, USA University of New York, Stony Brook, University of Texas at Austin, USA; Evelyn 3:30-3:55 Sensitivity Analysis and Error USA Powell, Institute for Geophysics, USA; Estimation for Differential Algebraic 3:30-3:55 Evidence Based Don Blankenship, University of Texas at Equations in Nuclear Reactor Multiciplinary Robust Design Austin, USA Applications Massimilian Vasile, University of 3:30-3:55 Bayesian Calibration Hayes Stripling, Texas A&M University, Strathclyde, United Kingdom USA; Mihai Anitescu, Argonne National via Additive Regression Trees with Laboratory, USA; Marvin Adams, Texas Application to the Community Ice A&M University, USA Sheet Model Matthew Pratola, Stephen Price, and David Higdon, Los Alamos National Laboratory, USA 2012 SIAM Conference on Uncertainty Quantification 47

Wednesday, April 4 Wednesday, April 4 Wednesday, April 4 MS58 MT9 CP16 Model Reduction for Uncertainty Quantification: Modeling Structured Systems Nonlinear Dynamical Foundations and Capabilities 4:30 PM-5:10 PM Systems for Model-Based Simulations Room:University A 2:00 PM-4:00 PM - Part III of III Chair: Yan Sun, Utah State University, USA Room:Congressional B 4:30 PM - 6:30 PM 4:30-4:45 Delay in Neuronal Spiking Mikhail M. Shvartsman, University of St. Model reduction methods have been For Part 2 see MT6 Thomas, USA successfully applied to linear dynamical Room: State C systems to drastically reduce the cost The minitutorial will present the physical 4:50-5:05 A Gaussian Hierarchical of computing the system’s time-history motivation and mathematical foundations Model for Random Intervals Yan Sun, Utah State University, USA; Dan using a set of reduced coordinates. Such necessary for the formulation of well- Ralescu, University of Cincinnati, USA reduction enables (1) real-time analysis posed UQ problems in computational and control for large-scale systems and science and engineering. In particular, (2) parameter studies (e.g., uncertainty the minitutorial will cover 1) aspects of quantification, sensitivity analysis, and probabilistic modeling and analysis, 2) design optimization), where simulations polynomial chaos representations, 3) are run for many input-parameter values. stochastic processes and Karhunen-Loeve One challenge facing model reduction expansions, 4) forward UQ including methods is application to nonlinear sampling, sparse-grid, stochastic Galerkin dynamical systems, where complexity and collocation, 5) inverse problems in reduction requires more sophisticated UQ, 6) overview of software resources, 7) approaches. This minisymposium will summary of advanced topics. explore state-of-the-art methods for nonlinear model reduction and their application to problems in uncertainty Organizer: quantification. Roger Ghanem, University of Southern Organizer: Kevin T. Carlberg California, USA Stanford University, USA Organizer: Paul Constantine Speakers: Stanford University, USA Roger Ghanem, University of Southern 2:00-2:25 Linearized Reduced-order California, USA Models for Optimization and Data Assimilation in Subsurface Flow Bert Debusschere, Sandia National Jincong He and Lou J. Durlofsky, Stanford Laboratories, USA University, USA 2:30-2:55 Decreasing the Temporal Complexity in Nonlinear Model Reduction Kevin T. Carlberg, Stanford University, USA 3:00-3:25 Reduced Basis, the Discrete Interpolation Method and Fast Quadratures for Gravitational Waves Harbir Antil, University of Maryland, USA 3:30-3:55 Error Analysis for Nonlinear Model Reduction Using Discrete Empirical Interpolation in the Proper Orthogonal Decomposition Approach Saifon Chaturantabut, Virginia Polytechnic Institute & State University, USA; Danny C. Sorensen, Rice University, USA Coffee Break 4:00 PM-4:30 PM Room:Pre-Function Area 48 2012 SIAM Conference on Uncertainty Quantification

Wednesday, April 4 Wednesday, April 4 5:30-5:55 An Overview of Uncertainty Quantification in the Community Land MS51 MS59 Model Daniel Ricciuto and Dali Wang, Oak Ridge PDE Constrained Climate Uncertainty National Laboratory, USA; Cosmin Safta, Optimization with Uncertain Quantification - Part III of IV Khachik Sargsyan, and Habib N. Najm, Coefficients Sandia National Laboratories, USA; Peter 4:30 PM-6:30 PM Thornton, Oak Ridge National Laboratory, 4:30 PM-6:30 PM Room:State D USA Room:State E For Part 2 see MS52 6:00-6:25 Testbeds for Ocean Model The appropriate treatment of uncertainty For Part 4 see MS66 Calibration in optimization problems governed Uncertainty quantification of climate James Gattiker and Matthew Hecht, Los Alamos National Laboratory, USA by partial differential equations predictions is challenging. Climate (PDEs) with random coefficients models used for making predictions raises many modeling, analytical, and contain not only many aleatoric computational challenges. The talks sources of uncertainty, many of their in this minisymposium present recent epistemological aspects are not well advances in the computational modeling defined. How can we test model of risk in PDE constrained optimization, responses to a forcing for which we techniques to efficiently sample the do not have observations? How do random parameters in the context of we separate observations used to PDE constrained optimization, and drive model development from those optimization algorithms tailored to used for model evaluation? Climate stochastic PDE constrained optimization. models simulate non-linear processes The theoretic and algorithmic advances that interact on many time and space are illustrated using a variety of scales, so representing, sampling, applications from optimal control and and computing aleatoric uncertainties shape optimization. alone is a major challenge. We welcome contributions that address Organizer: Matthias any challenges in climate uncertainty Heinkenschloss quantification. Rice University, USA Organizer: Guang Lin 4:30-4:55 Uncertainty Quantification Pacific Northwest National Laboratory, USA using Nonparametric Estimation and Epi-Splines Organizer: Charles Jackson Johannes O. Royset, Naval Postgraduate University of Texas at Austin, USA School, USA Organizer: Donald D. Lucas 5:00-5:25 An Approach for the Lawrence Livermore National Laboratory, Adaptive Solution of Optimization USA Problems Governed by PDEs with 4:30-4:55 Uncertainty in Regional Uncertain Coefficients Climate Experiments Drew Kouri, Rice University, USA Stephan Sain, National Center for 5:30-5:55 Risk Neutrality and Risk Atmospheric Research, USA Aversion in Shape Optimization with 5:00-5:25 Efficient Surrogate Uncertain Loading Construction for High-Dimensional Ruediger Schultz, University of Duisburg- Climate Models Essen, Germany Cosmin Safta and Khachik Sargsyan, 6:00-6:25 Numerical Methods for Sandia National Laboratories, USA; Shape Optimization under Uncertainty Daniel Ricciuto, Oak Ridge National Claudia Schillings and Volker Schulz, Laboratory, USA; Robert D. Berry and University of Trier, Germany Bert J. Debusschere, Sandia National Laboratories, USA; Peter Thornton, Oak Ridge National Laboratory, USA; Habib N. Najm, Sandia National Laboratories, USA continued in next column 2012 SIAM Conference on Uncertainty Quantification 49

Wednesday, April 4 5:30-5:55 Calibration, Model Wednesday, April 4 discrepancy and Extrapolative MS60 Predictions MS61 Dave Higdon, Los Alamos National From Model Calibration Laboratory, USA Uncertainty Characterization and Validation to Reliable 6:00-6:25 “Experiment” and and Management in Models Extrapolations - Part I of III “Traveling” Models, Extrapolation of Dynamical Systems - Risk from Undetected Model Bias, Part II of IV 4:30 PM-6:30 PM and Data Conditioning for Systematic Room:State A Uncertainty in Experiment Conditions 4:30 PM-6:30 PM Vicente J. Romero, Sandia National For Part 2 see MS67 Room:State B Laboratories, USA Computational models serve the ultimate For Part 1 see MS54 purpose of predicting the behavior of For Part 3 see MS68 systems under scenarios of interest. Uncertainty in models of complex Due to various limitations, models dynamical systems affect their use in are usually calibrated and validated prediction and control. Most current with data collected in scenarios other methods for addressing uncertainty either than the scenarios of interest, and rely on a linear Gaussian assumption or model extrapolation is thus required. suffer from the “curse-of-dimensionality” What are the necessary conditions and become increasingly infeasible for to claim that a model has predictive high-dimensional nonlinear systems. This capability and on how to quantify its necessitates novel approaches for model credibility? There is no agreement reduction/refinement, statistical analysis in the scientific community today on of model performance, uncertainty-based what are the best validation practices. design, model-data fusion, and control of This mini-symposium targets scientists systems in the presence of uncertainty. that develop and use calibration, The aim of this invited session is to bring validation, and uncertainty quantification together researchers working in this area methodologies to build confidence in and present their recent results to the model predictions. SIAM community. Organizer: Gabriel A. Terejanu Organizer: Puneet Singla University of Texas at Austin, USA State University of New York, Buffalo, USA Organizer: Ernesto E. Prudencio Organizer: Abani K. Patra Institute for Computational Engineering and State University of New York, Buffalo, USA Sciences, USA Organizer: Sonjoy Das 4:30-4:55 Towards Finding the State University of New York, Buffalo, USA Necessary Conditions for Justifying Extrapolations 4:30-4:55 Conjugate Unscented Gabriel A. Terejanu, University of Texas Transformation -- “Optimal at Austin, USA; Ernesto E. Prudencio, Quadrature” Institute for Computational Engineering Nagavenkat Adurthi, Puneet Singla, and and Sciences, USA Tarunraj Singh, State University of New York, Buffalo, USA 5:00-5:25 Calibration, Validation and the Importance of Model 5:00-5:25 A New Approach to Uq Discrepancy Based on the Joint Excitation-Response Anthony O’Hagan, University of Sheffield, Pdf: Theory and Simulation United Kingdom; Jenny Brynjarsdottir, Heyrim Cho, Daniele Venturi, and George E. Statistical and Applied Mathematical Karniadakis, Brown University, USA Sciences Institute, USA 5:30-5:55 A Random Iterative Proper continued in next column Orthogonal Decomposition Approach with Application to the Filtering of Distributed Parameter Systems Suman Chakravorty, Texas A&M University, USA 6:00-6:25 Bayesian UQ on Infinite Dimensional Spaces with Incompletely Specified Priors Houman Owhadi, California Institute of Technology, USA 50 2012 SIAM Conference on Uncertainty Quantification

Wednesday, April 4 Wednesday, April 4 Wednesday, April 4 MS63 MS64 MS65 UQ in Engineering Uncertainty in Inverse Modeling Networks in Applications - Part III of III Problems Dynamic Systems 4:30 PM-6:00 PM 4:30 PM-6:30 PM 4:30 PM-6:30 PM Room:State F Room:Congressional A Room:Congressional B For Part 2 see MS56 The solution of inverse problems is Many physical systems rely on complex Uncertainty quantification plays a critical used in applications ranging from oil and intricate network structures for role in model validation and system and mineral exploration to medical their proper function. Understanding design, reducing risks associated with imaging and surgery planning. the interaction between the network computations in engineering practice. Typically, a solution is presented to the structure and the global properties of A variety of UQ algorithms address practitioner without any assessment of the system is a crucial yet often difficult limitations of existing methodologies: the the errors that may be involved with problem to solve as the network may curse of dimensionalitgy, discontinous it. In this minisymposium we discuss be hard to experimentally determine response surfaces, expensive function how to quantify, compute and display a and/or requires a large number of evaluations, etc. It is important to measure of uncertainty. variables to characterize. The talks in assess the impact of UQ on industrial Organizer: Eldad Haber this mini- symposium will discuss the applications in view of these issues University of British Columbia, Canada statistical features of networks from and to identify further opportunities various physical systems and their level and remaining bottlenecks. The Organizer: Lior Horesh Emory University, USA of importance in determining global minisymposium will address these responses of the full physical system. questions through a discussion of recent 4:30-4:55 Prior Modelling for Inverse Organizer: Katherine Newhall innovations in UQ algorithms and Problems Using Gaussian Markov Random Fields Rensselaer Polytechnic Institute, USA specific UQ engineering applications in a Johnathan M. Bardsley, University of variety of fields. 4:30-4:55 Size of Synchronous Firing Montana, USA Events in Model Neuron Systems Organizer: James G. Glimm 5:00-5:25 Challenges in Uncertainty Katherine Newhall, Rensselaer Polytechnic State University of New York, Stony Brook, Quantification for Dynamic History Institute, USA USA Matching 5:00-5:25 The Influence of Topology on Organizer: Gianluca Iaccarino Lior Horesh, Emory University, USA; Sound Propagation in Granular Force Stanford University, USA Andrew R. Conn, IBM T.J. Watson Networks Research Center, USA; Gijs van Essen 4:30-4:55 Case Studies in Uncertainty Danielle S. Bassett, University of California, and Eduardo Jimenez, Shell Innovation Quantification for Aerodynamic Santa Barbara, USA; Eli Owens and Karen Research & Development, USA; Sippe Problems in Turbomachinery Daniels, North Carolina State University, Douma, Shell, USA; Ulisses Mello, IBM Sriram Shankaran, General Electric, USA USA; Mason A. Porter, University of T.J. Watson Research Center, USA Oxford, United Kingdom 5:00-5:25 Quantification of Uncertainty 5:30-5:55 Title Not Available at Time in Wind Energy 5:30-5:55 Asymptotically Inspired of Publication Karthik Duraisamy, Stanford University, USA Moment-Closure Approximation for Luis Tenorio, Colorado School of Mines, Adaptive Networks 5:30-5:55 Uncertainty Quantification USA Maxim S. Shkarayev, Rensselaer Polytechnic for Rayleigh-Taylor Turbulent Mixing 6:00-6:25 Evaluation of Covariance Institute, USA; Leah Shaw, College of Tulin Kaman and James Glimm, State Matrices and their use in Uncertainty William & Mary, USA University of New York, Stony Brook, Quantification USA 6:00-6:25 Network Analysis of Eldad Haber, University of British Anisotropic Electrical Properties Columbia, Canada in Percolating Sheared Nanorod Dispersions Feng B. Shi, and Mark Forest, University of North Carolina, Chapel Hill, USA; Peter J. Mucha, University of North Carolina, USA; Simi Wang, University of North Carolina, Chapel Hill, USA; Xiaoyu Zheng, Kent State University, USA; Ruhai Zhou, Old Dominion University, USA 2012 SIAM Conference on Uncertainty Quantification 51

Thursday, April 5 Thursday, April 5 Thursday, April 5 MT10 CP17 A Tutorial on Uncertainty Theory & Foundations Registration Quantification and Data 9:30 AM-11:30 AM 7:45 AM-1:30 PM Analysis for Inverse Room:University A Room:Chancellor and Pre-Function Area Problems Chair: Rafi L. Muhanna, Georgia Institute of 9:30 AM - 12:30 PM Technology, USA Room: State C 9:30-9:45 Interval-Based Inverse Closing Remarks Problems with Uncertainties We will start with a brief overview Rafi L. Muhanna and Francesco Fedele, 8:10 AM-8:15 PM of ill-posed inverse problems and Georgia Institute of Technology, USA regularization that includes a quick Room:State C/D 9:50-10:05 Cramer-Rao Bound for review of the necessary results from Models of Fat-Water Separation Using functional analysis. We then focus Magnetic Resonance Imaging on uncertainty quantification for Angel R. Pineda and Emily Bice, California IP6 a particular class of regularization State University, Fullerton, USA procedures using frequentist and Statistical Approaches to 10:10-10:25 Automated Exact Bayesian frameworks. We describe Calculation of Test Statistics in Combining Models and basic methods to assess uncertainty in Hypothesis Testing Observations each of these frameworks. This will Lawrence Leemis and Vincent Yannello, 8:15 AM-9:00 AM include a review of the basic statistics College of William & Mary, USA and probability tools needed. We end 10:30-10:45 Probability Bounds for Room:State C/D with an introduction to exploratory data Nonlinear Finite Element Analysis Chair: Anthony O’Hagan, University of analysis methods that can be used for Rafi L. Muhanna, Georgia Institute of Sheffield, United Kingdom model validation. Technology, USA; Robert Mullen, Numerical models and observational Organizer and Speaker: University of South Carolina, USA data are critical in modern science Luis Tenorio, Colorado School of 10:50-11:05 A Complete Closed-Form Solution to Stochastic Linear Systems and engineering. Since both of these Mines, USA information sources involve uncertainty, with Fixed Coefficients the use of statistical, probabilistic Elmor L. Peterson, Systems Science Consulting, USA methods play a fundamental role. I discuss a general Bayesian framework 11:10-11:25 Evidence-Based Approach for combining uncertain information for the Probabilistic Assessment of and indicate how various approaches Unknown Foundations of Bridges Negin Yousefpour, Zenon Medina –Cetina, and (ensemble forecasting, UQ, etc.) fit Jean-Louis Briaud, Texas A&M University, in this framework. A paleoclimate USA analysis illustrates the use of simple physics and statistical modeling to produce inferences. A second example involves glacial dynamics and illustrates how updating models and data can lead to estimates of model error. A third example involves the extraction of information from multi- model ensembles in climate projection studies. Mark Berliner Ohio State University, USA

Coffee Break 9:00 AM-9:30 AM Room:Pre-Function Area 52 2012 SIAM Conference on Uncertainty Quantification

Thursday, April 5 Thursday, April 5 Thursday, April 5 CP18 MS66 MS67 Sensitivity & Stochastic Climate Uncertainty From Model Calibration Representations Quantification - Part IV of IV and Validation to Reliable 9:30 AM-10:50 AM 9:30 AM-11:30 AM Extrapolations - Part II of III Room:University B Room:State D 9:30 AM-11:30 AM Chair: Jemin George, U.S. Army Research For Part 3 see MS59 Room:State A Laboratory, USA Uncertainty quantification of climate For Part 1 see MS60 9:30-9:45 Analysis of Quasi-Monte predictions is challenging. Climate For Part 3 see MS75 Carlo FE Methods for Elliptic PDEs with models used for making predictions Computational models serve the ultimate Lognormal Random Coefficients contain not only many aleatoric purpose of predicting the behavior of Robert Scheichl, and Ivan G. Graham, sources of uncertainty, many of their systems under scenarios of interest. University of Bath, United Kingdom; epistemological aspects are not well Due to various limitations, models are Frances Y. Kuo and James Nichols, defined. How can we test model usually calibrated and validated with University of New South Wales, Australia; responses to a forcing for which we Christoph Schwab, ETH Zürich, data collected in scenarios other than Switzerland; Ian H. Sloan, University of do not have observations? How do we the scenarios of interest, and model New South Wales, Australia separate observations used to drive model extrapolation is thus required. What are development from those used for model the necessary conditions to claim that a 9:50-10:05 An Approach to Weak evaluation? Climate models simulate Solution Approximation of Stochastic model has predictive capability and on Differential Equations non-linear processes that interact how to quantify its credibility? There is Jemin George, U.S. Army Research on many time and space scales, so no agreement in the scientific community Laboratory, USA representing, sampling, and computing today on what are the best validation aleatoric uncertainties alone is a major 10:10-10:25 Frechet Sensitivity Analysis practices. This minisymposium targets for the Convection-Diffusion Equation challenge. We welcome contributions scientists that develop and use calibration, Vitor Leite Nunes, Virginia Polytechnic that address any challenges in climate validation, and uncertainty quantification Institute & State University, USA uncertainty quantification. methodologies to build confidence in 10:30-10:45 Asymptotic Normality and Organizer: Guang Lin model predictions. Efficiency for Sobol Index Estimator Pacific Northwest National Laboratory, USA Organizer: Gabriel A. Terejanu Alexandre Janon, Université Joseph Fourier Organizer: Charles Jackson University of Texas at Austin, USA and INRIA, France; Thierry Klein, University of Texas at Austin, USA Organizer: Ernesto E. Prudencio Universite de Toulouse, France; Agnes Institute for Computational Engineering and Lagnoux, CNRS, France; Maëlle Nodet, Organizer: Donald D. Lucas Université Joseph Fourier, France and Lawrence Livermore National Laboratory, Sciences, USA INRIA, France; Clémentine Prieur, USA 9:30-9:55 Model Selection and Université Joseph Fourier and INRIA, 9:30-9:55 Propagating Uncertainty Inference for a Nuclear Reactor France from General Circulation Models Application through Projected Local Impacts Laura Swiler, Sandia National Laboratories, Peter Guttorp, University of Washington, USA; Brian Williams and Rick Picard, Los USA Alamos National Laboratory, USA 10:00-10:25 Covariance 10:00-10:25 Validation Experience for Approximation for Large Multivariate Stochastic Models of Groundwater Spatial Datasets with An Application Flow and Radionuclide Transport at to Multiple Climate Models Underground Nuclear Test Sites and the Huiyan Sang, Texas A&M University, USA Shift Away from Quantitative Measures and Toward Iterative Improvement 10:30-10:55 Measures of Model Skill Jenny Chapman, Desert Research Institute, and Parametric Uncertainty Estimation USA; Ahmed Hassan, Cairo University, for Climate Model Development Egypt; Karl Pohlmann, Desert Research Gabriel Huerta, Indiana University, USA; Institute, USA Charles Jackson, University of Texas at Austin, USA continued on next page 11:00-11:25 Optimal Parameter Estimation in Community Atmosphere Models Guang Lin, Ben Yang, Yun Qian, and Ruby Leung, Pacific Northwest National Laboratory, USA 2012 SIAM Conference on Uncertainty Quantification 53

Thursday, April 5 Thursday, April 5 10:00-10:25 Uncertainty Quantification and Model Validation in Flight Control MS67 MS68 Applications Raktim Bhattacharya, Texas A&M University, From Model Calibration Uncertainty USA Characterization and and Validation to Reliable 10:30-10:55 Existence and Stability Extrapolations - Part II of III Management in Models of of Equilibria in Stochastic Galerkin Dynamical Systems - Part III Methods 9:30 AM-11:30 AM of IV Roland Pulch, University of Wuppertal, continued Germany 9:30 AM-11:30 AM 11:00-11:25 A Nonlinear Dimension Room:State B Reduction Technique for Random 10:30-10:55 Validation and Data Fields Based on Topology-Preserving For Part 2 see MS61 Assimilation of Shallow Water Models Transformations For Part 4 see MS76 Clint Dawson, Jennifer Proft, J. Casey Daniele Venturi, Brown University, USA; Uncertainty in models of complex Dietrich, Troy Butler, and Talea Mayo, Guang Lin, Pacific Northwest National University of Texas at Austin, USA; dynamical systems affect their use in Laboratory, USA; George E. Karniadakis, Joannes Westerink, University of Notre prediction and control. Most current Brown University, USA Dame, USA; Ibrahim Hoteit and M.U. methods for addressing uncertainty Altaf, King Abdullah University of Science either rely on a linear Gaussian & Technology (KAUST), Saudi Arabia assumption or suffer from the “curse- 11:00-11:25 Quantifying Long-Range of-dimensionality” and become Predictability and Model Error through increasingly infeasible for high- Data Clustering and Information dimensional nonlinear systems. This Theory necessitates novel approaches for model Dimitris Giannakis, New York University, reduction/refinement, statistical analysis USA of model performance, uncertainty- based design, model-data fusion, and control of systems in the presence of uncertainty. The aim of this invited session is to bring together researchers working in this area and present their recent results to the SIAM community. Organizer: Abani K. Patra State University of New York, Buffalo, USA Organizer: Puneet Singla State University of New York, Buffalo, USA Organizer: Sonjoy Das State University of New York, Buffalo, USA 9:30-9:55 New Positive-definite Random Matrix Ensembles for Stochastic Dynamical System with High Level of Heterogeneous Uncertainties Sonjoy Das, State University of New York, Buffalo, USA

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Thursday, April 5 11:00-11:25 Stochastic-Integral Thursday, April 5 Models for Propagation- MS69 of-Uncertainty Problems in MS70 Nondestructive Evaluation Recent Advances and Elias Sabbagh, Kim Murphy, and Harold Data Assimilation and Applications of Stochastic Sabbagh, Victor Technologies, USA; Inverse Problems - Part I of II John Aldrin, Computational Tools, USA; Partial Differential Equations Jeremy Knopp and Mark Blodgett, Air 9:30 AM-11:30 AM - Part II of III Force Research Laboratory, USA Room:State F 9:30 AM-12:00 PM 11:30-11:55 Unbiased Perturbations of For Part 2 see MS78 the Navier-Stokes Equation Room:Congressional B Data assimilation is the process of fusing Chia Ying Lee, University of North information from imperfect models, noisy For Part 1 see MS62 Carolina, USA; Boris Rozovsky, Brown measurements, and priors, to produce an For Part 3 see MS77 University, USA Stochastic partial differential equations optimal representation of the state of a have been used in numerous physical physical system. Inverse problems infer phenomena to incorporate random parameter values from measurements effects arising from uncertainties in of reality. This minisymposium focuses the system. In order to properly apply on important problems related to data these equations in physical models, assimilation and inverse problems, it is imperative to understand the including: new computational algorithms mathematical structure and properties for large scale systems, both variational of these stochastic models and to study and ensemble based; sensitivity analysis; how they can be used to quantify the adjoint model development; modeling uncertainty in the physical systems. of model errors; impact of observations; This minisymposium is intended to quantification of the posterior uncertainty. bring together both theoreticians and Organizer: Adrian Sandu practitioners to address a range of Virginia Polytechnic Institute & State applications of SPDEs, including fluid University, USA dynamics, optics and statistical inference Organizer: Dacian N. Daescu of SPDE. Portland State University, USA Organizer: Xiaoying Han Organizer: Humberto C. Godinez Auburn University, USA Los Alamos National Laboratory, USA Organizer: Chia Ying Lee Organizer: Ralph C. Smith University of North Carolina, USA North Carolina State University, USA 9:30-9:55 Asymptotic Behavior 9:30-9:55 The Estimation of Functional of Stochastic Lattice Differential Uncertainty using Polynomial Chaos Equations and Adjoint Equations Xiaoying Han, Auburn University, USA Michael Navon, Florida State University, USA 10:00-10:25 Generalized Malliavin 10:00-10:25 FATODE: A Library for Calculus and Spdes in Higher-Order Forward, Tangent Linear, and Adjoint Chaos Spaces ODE Integration Sergey Lototsky, University of Southern Hong Zhang, and Adrian Sandu, Virginia California, USA; Boris Rozovskii, Brown Polytechnic Institute & State University, University, USA; Dora Selesi, University USA of Novi Sad, Serbia 10:30-10:55 Model Covariance 10:30-10:55 New Results for the Sensitivity as a Guidance for Stochastic PDEs of Fluid Dynamics Localization in Data Assimilation Nathan Glatt-Holtz, Indiana University, USA Humberto C. Godinez, Los Alamos National Laboratory, USA; Dacian N. Daescu, Portland State University, USA continued in next column 11:00-11:25 Hybrid Methods for Data Assimilation Haiyan Cheng, Willamette University, USA; Adrian Sandu, Virginia Polytechnic Institute & State University, USA 2012 SIAM Conference on Uncertainty Quantification 55

Thursday, April 5 Thursday, April 5 11:00-11:25 An Investigation of the Pineapple Express Phenomenon via MS71 MS72 Bivariate Extreme Value Theory Grant Weller and Dan Cooley, Colorado State Ensembles of Random Integrating Simulation, University, USA; Stephan Sain, National Points for Uncertainty Emulation and Extreme Center for Atmospheric Research, USA Quantification Value Methods for Rare 9:30 AM-12:00 PM Events Room:Congressional A 9:30 AM-11:30 AM Lunch Break We introduce random point and mesh Room:State E 11:30 AM-1:00 PM algorithms, and how they are used Quantitative risk assessment usually Attendees on their own for fracture mechanics uncertainty involves estimating small probabilities of quantification. We also discuss how rare, high consequence events. Relative random point cloud techniques might uncertainty is high due to extremely be extended to generate experimental limited data. Computer simulations designs. Some physics simulations can provide additional information are inherently dependent on the mesh but realistic stochastic models require or point cloud. For example, in some massive run times to generate useful fracture simulations cracks can only information, so efficient methods are propagate along mesh edges. Further, required. In many applications, the level mesh variability models some of the of the extreme quantity is also important, natural material strength variability. so the distribution tail becomes In this sense, a mesh is a multi- important. Extensions/combinations of dimensional uncertain input parameter computer model emulation and extreme to the simulation. Simulations over an value techniques are required to deal ensemble of (random) meshes can help with stochastic outputs and quantify quantify the range of outcomes. uncertainty in the output distribution Organizer: Scott A. Mitchell tail. We’ll discuss recent theoretical Sandia National Laboratories, USA and computational developments, 9:30-9:55 Random Poisson-Disk open research questions, and example Samples and Meshes applications. Scott A. Mitchell and Mohamed S. Ebeida, Organizer: Marc C. Kennedy Sandia National Laboratories, USA The Food and Environment Research 10:00-10:25 Upscaling Micro-scale Agency, United Kingdom Material Variability Through the use of 9:30-9:55 Sensitivity Analysis and Random Voronoi Tessellations Estimation of Extreme Tail Behaviour Joseph Bishop, Sandia National in Two-dimensional Monte Carlo Laboratories, USA Simulation (2DMC) 10:30-10:55 Simplex Stochastic Marc C. Kennedy and Victoria Roelofs, The Collocation Approach Food and Environment Research Agency, Gianluca Iaccarino and Jeroen Witteveen, United Kingdom Stanford University, USA 10:00-10:25 Methods for Assessing 11:00-11:25 Discrete Models of Chances of Rare, High-Consequence Fracture and Mass Transport in Events in Groundwater Monitoring Cement-based Composites Dave Higdon, Elizabeth Keating, Zhenxue John Bolander, University of California, Dai, and James Gattiker, Los Alamos Davis, USA; Peter Grassl, University of National Laboratory, USA Glasgow, Scotland, UK 10:30-10:55 Quantile Emulation for 11:30-11:55 Maximal Poisson-disk Non-Gaussian Stochastic Models Sampling for UQ Purposes Remi Barillec, Alexis Boukouvalas, and Dan Mohamed S. Ebeida, Sandia National Cornford, University of Aston, United Laboratories, USA Kingdom

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Thursday, April 5 Thursday, April 5 Thursday, April 5 CP19 CP20 MS73 Modeling & Estimation Representing Uncertainty & Uncertainty Quantification 1:00 PM-2:20 PM Structure for Large Climate Models Room:University A 1:00 PM-2:20 PM 1:00 PM-3:00 PM Chair: Hadi Meidani, University of Southern Room:University B Room:State C California, USA Chair: Marylesa Howard, University of Climate science depends on large, 1:00-1:15 Maximum Entropy Montana, USA computationally intensive simulators. Construction for Data-Driven Analysis 1:00-1:15 Computational Methods These include coupled simulators of of Diffusion on Random Manifolds for Statistical Learning Using Support the atmosphere, the ocean, sea ice and Hadi Meidani and Roger Ghanem, University Vector Machine Classifiers increasingly, the terrestrial and oceanic of Southern California, USA Marylesa Howard, University of Montana, biosphere and land ice. Because of the 1:20-1:35 Multiple Signal Classification USA political importance of the projections in Covariance Space of EEG Data 1:20-1:35 A Comparison of from such simulators it is important that Deepashree Sengupta and Aurobinda Routray, Dimensionality Reduction Techniques we quantify the uncertainty in them. This Indian Institute of Technology Kharagpur, in Scientific Applications mini-symposium looks at how we can India Ya Ju Fan, and Chandrika Kamath, Lawrence use emulator based methods to look at Livermore National Laboratory, USA 1:40-1:55 Random Matrix Based these problems. The size of these models Approach for Adaptive Estimation of 1:40-1:55 Determining Critical pose particular challenges to the methods Covariance Matrix Parameters of Sine-Gordon and and these will be discussed along with Sonjoy Das, and Kumar Vishwajeet, State Nonlinear Schrödinger Equations sensitivity analysis and how we can University of New York, Buffalo, USA; with a Point-Like Potential Using Puneet Singla, State University of New Generalized Polynomial Chaos use data to constrain and calibrate the York, Buffalo, USA Methods simulators. 2:00-2:15 Dynamic Large Spatial Debananda Chakraborty and Jae-Hun Jung, Organizer: Peter Challenor Covariance Matrix Estimation in State University of New York, Buffalo, National Oceanography Centre, United Application to Semiparametric Model USA Kingdom Construction Via Variable Clustering: 2:00-2:15 A Hidden Deterministic 1:00-1:25 An Introduction to Emulators the Sce Approach Solution to the Quantum and Climate Models Song Song, University of Texas, Austin, USA Measurement Problem Peter Challenor, National Oceanography Pabitra Pal Choudhury, ISI Kolkata, India; Centre, United Kingdom Swapan Kumar Dutta, Retired 1:30-1:55 Uncertainty in Modeled Upper Ocean Heat Content Change using a Large Ensemble Robin Tokmakian, Naval Postgraduate School, USA 2:00-2:25 Calibration of Gravity Waves in WACCM Serge Guillas, University College London, United Kingdom; Hanli Liu, National Center for Atmospheric Research, USA 2:30-2:55 Emulating Time Series Output of Climate Models Danny Williamson, Durham University, United Kingdom 2012 SIAM Conference on Uncertainty Quantification 57

Thursday, April 5 Thursday, April 5 2:00-2:25 Validation of a Random Matrix Model for Mesoscale Elastic Description MS74 MS75 of Materials with Microstructures Arash Noshadravan and Roger Ghanem, Inference for Models Using From Model Calibration University of Southern California, USA; Set-valued Inverses and Validation to Reliable Johann Guilleminot, Université Paris-Est, France; Ikshwaku Atodaria and Pedro Peralta, 1:00 PM-3:00 PM Extrapolations - Part III of III Arizona State University, USA Room:State D 1:00 PM-3:00 PM 2:30-2:55 Bayesian Filtering in Large- This minisymposia will explore the Room:State A Scale Geophysical Systems and Uncertainty Quantification use of set-valued inverses of models For Part 2 see MS67 Ibrahim Hoteit, King Abdullah University of for inference. Topics will include Computational models serve the ultimate approximation of set-valued inverses, Science & Technology (KAUST), Saudi purpose of predicting the behavior of Arabia; Bruce Cornuelle and Aneesh computation of inverse measures in systems under scenarios of interest. Subramanian, University of California, San parameter spaces for models, relation Due to various limitations, models Diego, USA; Hajoon Song, University of to fiducial inference and Dempster are usually calibrated and validated California, Santa Cruz, USA; Xiaodong and Shafer calculus, convergence with data collected in scenarios other Luo, King Abdullah University of Science & and accuracy of computed inverse than the scenarios of interest, and Technology (KAUST), Saudi Arabia measures, inversion using multiple model extrapolation is thus required. observations, and intrusive and non- What are the necessary conditions intrusive computational methods. to claim that a model has predictive Organizer: Donald Estep capability and on how to quantify its Colorado State University, USA credibility? There is no agreement 1:00-1:25 A Computational in the scientific community today on Approach for Inverse Sensitivity what are the best validation practices. Problems using Set-valued Inverses This minisymposium targets scientists and Measure Theory that develop and use calibration, Donald Estep, Colorado State University, validation, and uncertainty quantification USA methodologies to build confidence in 1:30-1:55 A Non-intrusive Alternative model predictions. to a Computational Measure Organizer: Gabriel A. Terejanu Theoretic Inverse University of Texas at Austin, USA Troy Butler, University of Texas at Austin, USA Organizer: Ernesto E. Prudencio Institute for Computational Engineering and 2:00-2:25 Inverse Problem and Sciences, USA Fisher’s View of Statistical Inference Jan Hannig, University of North Carolina, 1:00-1:25 Variable Selection and USA Sensitivity Analysis via Dynamic Trees with an application to Computer 2:30-2:55 Inverse Function-based Code Performance Tuning Methodology for UQ Robert Gramacy, University of Chicago, Jessi Cisewski, University of North USA Carolina at Chapel Hill, USA 1:30-1:55 On Data Partitioning for Model Validation Rebecca Morrison, Corey Bryant, Gabriel A. Terejanu, Serge Prudhomme, and Kenji Miki, University of Texas at Austin, USA

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Thursday, April 5 Thursday, April 5 Thursday, April 5 MS76 MS77 MS78 Uncertainty Characterization Recent Advances and Data Assimilation and and Management in Models Applications of Stochastic Inverse Problems - of Dynamical Systems - Partial Differential Equations Part II of II Part IV of IV - Part III of III 1:00 PM-3:00 PM 1:00 PM-2:30 PM 1:00 PM-3:00 PM Room:State F Room:State B Room:Congressional B For Part 1 see MS70 For Part 3 see MS68 For Part 2 see MS69 Data assimilation is the process of fusing Uncertainty in models of complex Stochastic partial differential equations information from imperfect models, noisy dynamical systems affect their use in have been used in numerous physical measurements, and priors, to produce an prediction and control. Most current phenomena to incorporate random optimal representation of the state of a methods for addressing uncertainty effects arising from uncertainties in physical system. Inverse problems infer either rely on a linear Gaussian the system. In order to properly apply parameter values from measurements assumption or suffer from the “curse- these equations in physical models, of reality. This minisymposium focuses of-dimensionality” and become it is imperative to understand the on important problems related to data increasingly infeasible for high- mathematical structure and properties assimilation and inverse problems, dimensional nonlinear systems. This of these stochastic models and to study including: new computational algorithms necessitates novel approaches for model how they can be used to quantify the for large scale systems, both variational reduction/refinement, statistical analysis uncertainty in the physical systems. and ensemble based; sensitivity analysis; of model performance, uncertainty-based This minisymposium is intended to adjoint model development; modeling design, model-data fusion, and control of bring together both theoreticians and of model errors; impact of observations; systems in the presence of uncertainty. practitioners to address a range of quantification of the posterior uncertainty. The aim of this invited session is to applications of SPDEs, including fluid Organizer: Adrian Sandu bring together researchers working in dynamics, optics and statistical inference Virginia Polytechnic Institute & State this area and present their recent results of SPDE. University, USA to the SIAM community. Organizer: Xiaoying Han Organizer: Dacian N. Daescu Organizer: Puneet Singla Auburn University, USA Portland State University, USA State University of New York, Buffalo, USA Organizer: Chia Ying Lee Organizer: Humberto C. Godinez Organizer: Abani K. Patra University of North Carolina, USA Los Alamos National Laboratory, USA State University of New York, Buffalo, USA 1:00-1:25 Adaptive Construction of Organizer: Ralph C. Smith Organizer: Sonjoy Das Surrogates for Bayesian Inference North Carolina State University, USA State University of New York, Buffalo, USA Jinglai Li and Youssef M. Marzouk, 1:00-1:25 Error Covariance Sensitivity Massachusetts Institute of Technology, and Impact Estimation with Adjoint 1:00-1:25 Characterization of the USA Effect of Uncertainty in Terrain 4D-Var Representations for Modeling 1:30-1:55 Statistical Inference Dacian N. Daescu, Portland State University, Geophysical Mass Flows Problems for Nonlinear SPDEs USA Ramona Stefanescu, Abani K. Patra, and Igor Cialenco, Illinois Institute of 1:30-1:55 Uncertainty Quantification Marcus Bursik, State University of New Technology, USA and Data Assimilation Issues for York, Buffalo, USA 2:00-2:25 Filtering the Navier Stokes Macro-Fiber Composite Actuators 1:30-1:55 Toward Analysis of Equations Ralph C. Smith and Zhengzheng Hu, North Uncertainty in Chaotic Systems Kody Law, University of Massachusetts, Carolina State University, USA; Nathanial Eleanor Deram, Todd Oliver, and Robert D. Amherst, USA Burch, SAMSI, USA Moser, University of Texas at Austin, USA 2:30-2:55 Reimagining Diffusion Monte 2:00-2:25 Computing and Using 2:00-2:25 A Dynamically Weighted Carlo for Quantum Monte Carlo, Observation Impact in 4D-Var Data Particle Filter for Sea Surface Sequential Importance Sampling, Rare Assimilation Temperature Modeling Event Simulation and More Alexandru Cioaca, and Adrian Sandu, Virginia Faming Liang, Texas A&M University, Jonathan Weare, University of Chicago, Polytechnic Institute & State University, USA; Duchwan Ryu, Medical College of USA; Martin Hairer, University of USA Georgia, USA; Bani Mallick, Texas A&M Warwick, United Kingdom 2:30-2:55 Lagrangian Data Assimilation University, USA Christopher Jones, University of North Carolina at Chapel Hill and University of Warwick, United Kingdom 2012 SIAM Conference on Uncertainty Quantification 59

Thursday, April 5 Thursday, April 5 MS79 MS80 Modeling Consequences Reduced Order Modeling of Parameter Uncertainty for High Dimensional 1:00 PM-3:00 PM Nonlinear Models Room:Congressional A 1:00 PM-2:30 PM Uncertainty in model parameters Room:State E and simplification of complex The trade-off between accuracy models can be used advantageously and computational efficiency has to regularize ill-posed inverse always played an essential role in problems, and to analyze predictive real world engineering calculations. uncertainty. The speakers in this The complexity of the models often minisymposium will discuss increases at a higher rate than the approaches to model simplification increase in computer power which and the effects of simplification on renders their repeated execution for model predictions. In addition, they engineering purposes computationally will discuss efficient algorithms for inefficient or impractical. To combat the direct evaluation of uncertainty this challenge, scientists have propagation. The applications will invested into strategies to develop include electrochemical impedance computationally efficient models with spectroscopy, groundwater, and soil reduced complexity and acceptable moisture modeling. accuracy. This approach is referred to Organizer: Jodi Mead as ‘reduced order modeling’ (ROM) Boise State University, USA which represents the subject of this session. The focus will be on obtaining 1:00-1:25 Modeling Spatial Variability as Measurement solutions and completing uncertainty Uncertainty quantification efficiently. Jodi Mead, Boise State University, USA Organizer: Hany S. Abdel-Khalik 1:30-1:55 Analyzing Predictive North Carolina State University, USA Uncertainty using Paired Complex 1:00-1:25 Hybrid Reduced and Simple Models order Modeling for Uncertainty John Doherty, Flinders University and Management in Nuclear Modeling Watermark Numerical Computing, Hany S. Abdel-Khalik, North Carolina State Australia University, USA 2:00-2:25 Quantifying Simplification- 1:30-1:55 Intrusive Analysis for induced Error using Subspace Uncertainty Quantification of Techniques Simulation Models Jeremy White, U. S. Geological Survey, Oleg Roderick, Argonne National USA; Joseph Hughes, U.S. Geological Laboratory, USA Survey, USA 2:00-2:25 Sparse Interpolatory 2:30-2:55 Using Electrochemical Reduced-Order Models for Impedance Spectroscopy for Simulation of Light-Induced Studying Respiration of Anode Molecular Transformations Respiring Bacteria for Solid Oxide Carl T. Kelley and David Mokrauer, North Fuel Cells Carolina State University, USA Rosemary A. Renaut, Arizona State University, USA 60 2012 SIAM Conference on Uncertainty Quantification

UQ12 Abstracts

Abstracts are printed as submitted by the authors. UQ12 Abstracts 61

IP1 Duke University Sparse Tensor Algorithms in Uncertainty Quantifi- [email protected] cation We survey recent mathematical and computational re- IP4 sults on sparse tensor discretizations of Partial Differential Large Deviation Methods for Quantifying Uncer- Equations (PDEs) with random inputs. The sparse Ten- tainty sor discretizations allow, as a rule, to overcome the curse of dimensionality in approximating infinite dimensional prob- Large deviation methods have been particularly successful lems. Results and Methods surveyed include a) regularity in assessing small probabilities of rare events, which are and N-term gpc approximation results and algorithms for difficult to compute. They are also at the center of many elliptic and parabolic PDEs with random coefficients [joint importance sampling methods that aim to estimate prob- work with A. Cohen, R. DeVore and V.H.Hoang] and b) ex- abilities of rare events by Monte Carlo methods. Since istence and regularity results for solutions of classes of cer- probabilities of rare events are an important part of the tain hyperbolic PDEs from conservation and balance laws. emerging field of uncertainty quantification in complex sci- Multi-Level Monte-Carlo (MLMC) [joint with A. Barth] entific problems, the question arises as to how effective they and Multi-Level Quasi-Monte-Carlo (MLQMC) [joint with are. This is because the results of large deviation theory de- I. Graham, R. Scheichl, F.Y.Kuo and I.M. Sloan] methods pend sensitively on details of the probabilistic model used, can be viewed as particular classes of sparse tensor dis- and such details may not be available or may themselves cretizations. Numerical MLMC and MLQMC results for be subject to uncertainty. I will address these issues with elliptic PDEs with random coefficients and for nonlinear some examples using mean-field models and conservation systems of hyperbolic conservation laws are presented [joint laws and attempt to draw some broader conclusions. work with S. Mishra and J. Sukys (ETH)]. We compare the performance of these methods with that of adaptive gen- George C. Papanicolaou eralized polynomial chaos discretizations. Stanford University Department of Mathematics Christoph Schwab [email protected] ETH Zuerich SAM [email protected] IP5 Model Reduction for Uncertainty Quantification of Large-scale Systems IP2 Integrating Data from Multiple Simulation Models Uncertainty quantification is becoming recognized as an - Prediction and Tuning essential aspect of development and use of numerical sim- ulation tools, yet it remains computationally intractable Simulation of complex systems has become commonplace for large-scale complex systems characterized by high- in most areas of science. In some settings, several simula- dimensional uncertainty spaces. In such settings, it is es- tors are available to explore the system, each with varying sential to generate surrogate models – low-dimensional, levels of fidelity. In this talk, Bayesian methodology for in- efficient models that retain predictive fidelity of high- tegrating outputs from multi-fidelity computer models, and resolution simulations. This talk will discuss formulations field observations, to build a predictive model of a physical of projection-based model reduction approaches for appli- system is presented. The problem is complicated because cations in uncertainty quantification. For systems governed inputs to the computer models are not all the same and by partial differential equations, we demonstrate the use the simulators have inputs (tuning parameters) that must of reduced models for uncertainty propagation, solution of be estimated from data. The methodology is demonstrated statistical inverse problems, and optimization under uncer- on an application from the University of Michigans Center tainty. for Radiative Shock Hydrodynamics. Karen E. Willcox Derek Bingham Massachusetts Institute of Technology Dept. of Statistics and Actuarial Science [email protected] Simon Fraser University [email protected] IP6 Statistical Approaches to Combining Models and IP3 Observations Polynomial Chaos Approaches to Multiscale and Data Intensive Computations Numerical models and observational data are critical in modern science and engineering. Since both of these infor- Prediction of multiscale systems is increasingly being based mation sources involve uncertainty, the use of statistical, on complex physical models that depend on large uncertain probabilistic methods play a fundamental role. I discuss data sets. In this talk, we will outline recent developments a general Bayesian framework for combining uncertain in- in polynomial chaos (PC) methods for uncertainty quantifi- formation and indicate how various approaches (ensemble cation in such systems. Implementations will be illustrated forecasting, UQ, etc.) fit in this framework. A paleoclimate in light of applications to chemical kinetics, and geophysi- analysis illustrates the use of simple physics and statistical cal flows. Conclusions are in particular drawn concerning modeling to produce inferences. A second example involves the potential of parallel databases in providing a platform glacial dynamics and illustrates how updating models and for discovery, assessing prediction fidelity, and decision sup- data can lead to estimates of model error. A third exam- port. ple involves the extraction of information from multi-model ensembles in climate projection studies. Omar M. Knio Mark Berliner 62 UQ12 Abstracts

The Ohio State University validate the numerical simulations. [email protected] Patrick R. Noble, Tam Doung Texas A&M University CP1 [email protected], [email protected] Capturing Signatures of microcracks from macrolevel Responses Zenon Medina-Cetina Zachry Department of Civil Engineering The current work considers the problem of characterizing Texas A&M University microcracks that are typically at 10–100 µm level (depend- [email protected] ing on the material). These microcracks are invisible to naked eyes, and can cause catastrophic failure once they grow to a certain critical length. A stochastic upscaling CP1 scheme based on previous work by Das is extended in the Random Fields for Stochastic Mechanics of Mate- present work to include the effects of microcracks. The rials uncertainty (due to microstructural heterogeneities, and random size, orientation, and distribution of microcracks) An approach based on a Hill-Mandel condition allows de- is accounted for in the macroscopic (continuum) consti- termination of scaling laws and mesoscale random fields tutive elasticity matrices by modeling them as bounded with continuous realizations from the microstructural prop- positive-definite random matrices. Distinct difference in erties described by random fields with discontinuous real- probabilistic characteristics of macrolevel response vari- izations, typically given by image analyses of just about ables is observed depending on the presence or absence of any microstructure. We discuss one- and two-point statis- microcracks. This finding opens up a new way of captur- tics of such fields, the (an)isotropy of realizations ver- ing signatures of microcracks from macrolevel experimental sus (an)isotropy of correlation functions, as well as their response measurements. unavoidable scale-dependence, non-uniqueness, and corre- spondence with specific variational principles of solid me- Sonjoy Das, Sonjoy Das, Sourish Chakravarty chanics. University at Buffalo sonjoy@buffalo.edu, sonjoy@buffalo.edu, Martin Ostoja-Starzewski sc267@buffalo.edu Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign [email protected] CP1 Identification of Uncertain Time-Dependent Mate- Luis Costa rial Behavior with Artificial Neural Networks Institute for Multiscale Reactive Modeling US Army ARL-ARDEC Reliability assessment of structures requires knowledge of [email protected] the structural behavior. In case of new materials, tests are required to investigate structural behavior. Obtained mea- surements are usually limited and imprecise, which leads Emilio Porcu to difficulties in selecting or developing material models Institute for Mathematical Stochastics (stress-strain-time dependencies) and determine their pa- Georg-August-Universitaet, Goettingen, Germany rameters. In this work, we will present an alternative ap- [email protected] proach that is based on artificial neural networks. Recur- rent neural networks are used to construct relationships CP1 between material-loads, and material-responses under un- certainty. Uncertainty Quantification in Image Processing Steffen Freitag, Rafi L. Muhanna Based on the polynomial chaos and stochastic finite ele- Georgia Institute of Technology ments we construct stochastic extensions of image process- steff[email protected], ing operators like Perona-Malik smoothing and Mumford- rafi[email protected] Shah resp. Ambrosio-Tortorelli segmentation and of the level set method. The stochastic extensions allow propa- gating information about the image noise from the acquisi- CP1 tion step to the result, thus equipping the image processing Uncertainty Quantification of Discrete Element results with reliability estimates. This modeling is impor- Micro-Parameters Conditioned on Sample Prepa- tant in medical applications where treatment decisions are ration of Homogeneous Particle Materials based on quantitative information extracted from the im- ages. This lecture analyzes the effect of varying micro- parameters of a Discrete Element Model (DEM) developed Torben P¨atz to analyze the effect of homogeneous particle materials. Jacobs University Bremen and Fraunhofer MEVIS An experimental database is populated using steel spheres [email protected] of constant diameter to build cylindrical specimens under controlled experimental conditions. Specimens vary from Michael Kirby the loosest to the densest conditions. A 3D-DEM model is University of Utah built to reproduce the same experimental sample prepara- School of Computing tion conditions, which is used to explore all varying micro- [email protected] parameters combinations that lead to the reference exper- imental samples. X-Ray Computer Tomography is used to Tobias Preusser Fraunhofer MEVIS, Bremen UQ12 Abstracts 63 [email protected] Netherlands [email protected]

CP1 Hester Bijl Statistics of Mesoscale Conductivities and Resis- Faculty Aerospace Engineering tivities in Polycrystalline Graphite Delft University of Technology, NL [email protected] We consider mesoscale heat conduction in random poly- crystalline graphite under uniform essential (Dirichlet) and uniform natural (Neumann) boundary conditions. Using CP2 numerical experiments, we obtain rigorous bounds on all Quantitative Model Validation Techniques: New the six independent components of the mesoscale con- Insights ductivity (and resistivity) tensor and thereby the three invariants. The bounds on conductivity obtained using This research develops new insights into quantitative model theproposedapproacharethetightestwhencomparedto validation techniques. Traditional Bayesian hypothesis the Voigt, Reuss, upper and the lower Hashin-Shtrikman testing is extended based on interval hypotheses on distri- bounds and incorporate the effects of scaling unlike the bution parameters and equality hypotheses on probability other bounds. The scale-dependent probability densities distributions. Two types of validation experiments (well of the invariants of the mesoscale conductivities (resistivi- characterized and partially characterized) are considered. ties) are also determined. It is shown that under some specific conditions, the Bayes factor metric in Bayesian equality hypothesis testing and Shivakumar I. Ranganathan the reliability-based metric can both be mathematically re- Department of Mechanical Engineering lated to the p-value metric in classical hypothesis testing. American University of Sharjah [email protected] You Ling Department of Civil and Environmental Engineering Martin Ostoja-Starzewski Vanderbilt University Department of Mechanical Science and Engineering [email protected] University of Illinois at Urbana-Champaign [email protected] Sankaran Mahadevan Vanderbilt University [email protected] CP2 Model Discrepancy and Uncertainty Quantification CP2 When quantifying uncertainty in computer models it is im- Dynamic Model Validation of a 160 Mw Steam Tur- portant to account for all sources of uncertainty. One im- bine Lp Last Stage (L-0) Blade portant source of uncertainty is model discrepancy; the difference between reality and the computer model output. Laboratory vibration testing of turbine blades has always However, the challenge with incorporating model discrep- provided a major contribution to the understanding, de- ancy in a statistical analysis of computer models is the tection and the possibility to predict the probable failures confounding with calibration parameters. In this talk we encountered under real operation conditions. The impor- explore, through examples, ways to include model discrep- tance of testing for large steam turbines, with long slen- ancy in a Bayesian setting. der blades with increased risk of fatal vibrations, is higher due to cost and safety. In this regard, the main focus of Jenny Brynjarsdottir this work is to identify the Siemens Co. benchmark blade Statistical and Applied Mathematical Sciences Institute modal model based on experimental test data, using SDOF [email protected] and MDOF methods. The accuracy of the Circle and line fit methods were compared with a state-space subspace Anthony O’Hagan method called N4SID. Furthermore, in order to validate Univ. Sheffield, UK the smaller size model with capability to capture main fea- a.ohagan@sheffield.ac.uk tures of the full model, SVD-based model approximation methods are used to achieve a minimal state space repre- sentation of the original model. Finally the accuracy and CP2 efficiency of a Hankel-norm based reduction and a balanced Model Inadequacy Quantification for Simulations truncation method are compared and the results are pre- of Structures Using Bayesian Inference sented. We quantify the level of model inadequacy (aka model Sadegh Rahrovani structure uncertainty) in simulations of the eigenfrequen- Chalmers University of Technology cies of a simple metal structure. Starting with a statisti- [email protected] cal model of the system, including parametric uncertainty, discretization error, as well as a generic representation of Thomas Abrahamsson model inadequacy, we calibrate against an extensive exper- Professor imental data-set, which includes attempts to identify and [email protected] estimate sources of measurement noise and bias. A reliable estimate of model inadequacy for this simple situation is obtained. Sadegh Sarvi Senior Engineer Richard Dwight [email protected] Delft University of Technology 64 UQ12 Abstracts

CP2 Universite’ de Liege Quantifying Uncertainty and Accounting Model [email protected] Discrepancy in Slider Air Bearing Simulations for Calibration and Prediction Roger Ghanem University of Southern California Coupled multiphysics simulation of a slider air-bearing is Aerospace and Mechanical Engineering and Civil routinely performed during a hard disk design process to Engineering achieve various critical performance requirements. Charac- [email protected] terizing uncertainty through these simulations is critical to predict variation in outputs of interest and to drive sigma Eric Phipps reduction of main contributing inputs. A non-intrusive Sandia National Laboratories sparse stochastic collocation scheme is used to propagate Optimization and Uncertainty Quantification Department uncertainty here and its efficiency compared to the Latin [email protected] hyper-cube Monte Carlo sampling approach. Experimen- tal results are used to update unknown functions in the model inputs using a Bayesian formulation and Markov John Red-Horse Chain Monte Carlo approach. In another specific appli- Validation and Uncertainty Quantification Processes cation, the discrepancy between the simulation and the Sandia National Laboratories experimental results is accounted for by augmenting the [email protected] model with discrepancy term and specifying a Gaussian Process model for the same. Two examples of applications CP3 in active fly height loss during environmental conditions and operational shock survival is presented here. Contour Estimation Via Two Fidelity Computer Simulators under Limited Resources Ajaykumar Rajasekharan, Paul J Sonda Mechanical Research & Development In this work, we study the contour estimation problem for Seagate Technology complex systems with two fidelity simulators. Using Gaus- [email protected], sian process for surrogate construction, the sequential pro- [email protected] cedure is designed to choose the best suited simulator and input location for each simulation trial so that the overall estimation of the desired contour can be as good as possible CP2 under limited resources. Finally, the methodology is illus- Integration of Verification, Validation, and Calibra- trated on a queueing system and its efficiency evaluated tion Activities for Overall Uncertainty Quantifica- via a simulation study. tion Ray-Bing Chen This talk presents a Bayesian methodology to integrate Department of Statistics information from verification, validation, and calibration National Cheng Kung University activities for overall prediction uncertainty quantification. [email protected] Multi-level systems are considered, with two types of infor- mation flow - (1) lower-level output becomes higher-level Ying-Chao Hung input, and (2) parameters calibrated with lower-complexity Department of Statistics models and experiments are applied to full system simula- National Chengchi University tion. The various sources of uncertainty, multiple levels [email protected] of models and experiments are connected through a Bayes network, to quantify the uncertainty in system-level pre- Weichung Wang diction. National Taiwan University Department of Mathematics Shankar Sankararaman, Sankaran Mahadevan [email protected] Vanderbilt University [email protected], Sung-Wei Yen [email protected] Department of Mathematics National Taiwan University CP3 [email protected] Dimension Reduction and Measure Transformation in Stochastic Multiphysics Modeling CP3 We present a computational framework based on stochas- An Uncertainty Quantification Approach to Assess tic expansion methods for the efficient propagation of un- Geometry-Optimization Research Spaces through certainties through multiphysics models. The framework Karhunen-Lo`eve Expansion leverages an adaptation of the Karhunen-Loeve decom- UQ is exploited to assess geometry-optimization research position to extract a low-dimensional representation of spaces and support the design of the optimization task. information passed from component to component in a A set of prescribed geometries defines the research space stochastic coupled model. After a measure transforma- through morphing. Karhunen-Lo`eve Expansion gives the tion, the reduced-dimensional interface thus created en- total geometric variance and the geometric variability of ables a more efficient solution in a reduced-dimensional each principal direction. This is used to compare different space. We demonstrate the proposed approach on an il- spaces and reduce their dimension and the computational lustration problem from nuclear engineering. costs. Finally, UQ methods identify the statistical proper- Maarten Arnst ties of the relevant objectives. Hydrodynamic application UQ12 Abstracts 65 in ship design is presented. differential equation for certain heat transfer problems. We use a polynomial chaos formulation that is super intrusive – Matteo Diez we use the structure of the equations to derive exact closed CNR-INSEAN, The Italian Ship Model Basin form expressions for the mean and standard deviation of [email protected] a random field (verified via Monte Carlo simulation). We harness the problem specific stochastic dependence struc- Daniele Peri ture in a way that could be useful in a variety of other INSEAN - The Italian Ship Model Basin applications with a similar mathematical structure. [email protected] Andrew Barnes Frederick Stern General Electric IIHR-Hydroscience and Engineering, The University of Global Research Center Iowa [email protected] [email protected] Jose Cordova Emilio Campana General Electric Global Research Center INSEAN The Italian Ship Model Basin [email protected] [email protected] CP4 CP3 A Library for Large Scale Parallel Modeling and Improvement in Multifidelity Modeling Using Simulation of Spatial Random Fields Gaussian Processes Spatial random fields (RFs) model heterogeneous fields in Using different types of fidelity measurements can result in computational simulations, including material properties, a large improvement of predictions by surrogate modeling boundary/initial conditions, and geometric properties. We in terms of computing time and precision. O’Hagan pro- present a parallel API/library for modeling spatial RFs posed an autoregressive Gaussian process to model the re- using either Karhunen-Loeve (KL) or Polynomial Chaos lationship between high and low accurate responses. How- (PC) expansions. In addition to generating KL/PC real- ever, we show that in practice the linearity is not always izations, the library includes a preprocessor to solve KL observed. Therefore in the present work the estimation of eigenproblems and a posteriori error estimators for the re- the relationship between the cheap and expensive responses sulting approximate solutions. Finally we describe several by using smoothing splines is studied. applications, including structural mechanics and flow in porous media. Celine Helbert Laboratoire Jean Kuntzmann Brian Carnes University of Grenoble Sandia National Laboratories [email protected] [email protected]

Federico Zertuche John Red-Horse University of Grenoble Validation and Uncertainty Quantification Processes FRANCE Sandia National Laboratories [email protected] [email protected]

CP3 CP4 A Multiscale Framework for Bayesian Inference in Efficient Evaluation of Integral Quantities in Rdo Elliptic Problems by Sequential Quadrature Formulas. Motivated by applications in hydrology, we present a mul- Accuracy of the computation of the integral quantities in- tiscale framework for efficient sampling of Bayesian posteri- volved in RDO represents a key element for the success of ors. The method is broadly applicable, but we concentrate the optimization. If numerical quadrature is adopted, a on length scales and a conditional independence structure convergence study of a benchmark UQ may be not suffi- defined by the multiscale finite element method. The prob- cient, due to the changing characteristics of the objective lem has two key components: construction of a coarse-scale function thru the optimization process. To preserve ac- prior, and an iterative method for conditioning fine-scale curacy, different sequential quadrature formulas are here realizations on coarse-scale constraints. Theoretical justi- applied to a practical application for ship design, compar- fication and numerical examples show that the framework ing their efficiency and the associated numerical effort. can strongly decouple scales and lead to more efficient in- Daniele Peri ference. INSEAN - The Italian Ship Model Basin Matthew Parno,YoussefM.Marzouk [email protected] Massachusetts Institute of Technology [email protected], [email protected] Matteo Diez CNR-INSEAN, The Italian Ship Model Basin [email protected] CP4 Super Intrusive Polynomial Chaos for An Elliptic Pde for Heat Transfer CP4 Application of a Novel Adaptive Finite Difference We study uncertainty quantification via an elliptic partial Solution of The Fokker-Planck Equation for Uncer- 66 UQ12 Abstracts tainty Quantification CP5 Constrained Gaussian Process Modeling An accurate and computationally efficient intrusive ap- proach for UQ is introduced. It utilizes the diffusionless In this paper, we introduce a new framework for incorpo- Fokker-Planck equation for the time evolution of the PDF. rating constraints in Gaussian process modeling, includ- This equation is solved numerically using a TVD finite dif- ing bound, monotony and convexity constraints. This new ference scheme and a novel method for obtaining the grid methodology mainly relies on conditional expectations of distribution. The results for some time-dependent prob- the truncated multinormal distribution. We propose sev- lems will be compared with exact solutions or other com- eral approximations based on correlation-free assumptions, putational UQ methodologies to demonstrate the method’s numerical integration tools and sampling techniques. From ability to accurately and efficiently obtain statistical quan- a practical point of view, we illustrate how accuracy of tities of interest. Gaussian process predictions can be enhanced with such constraint knowledge. Mani Razi, Peter Attar School of Aerospace and Mechanical Engineering Sebastien Da Veiga University of Oklahoma IFP Energies nouvelles [email protected], [email protected] [email protected]

Prakash Vedula Amandine Marrel University of Oklahoma CEA [email protected] [email protected]

CP4 CP5 Adjoint Error Estimation for Stochastic Colloca- A Learning Method for the Approximation of Dis- tion Methods continuous Functions in High Dimensions We use stochastic collocation on sparse grids for solving Tractable uncertainty quantification in high dimensions re- partial differential equations with random parameters. Our quires approximating computationally intensive functions aim is to combine the method with an adjoint approach in with fast and accurate surrogates. Functions exhibiting order to estimate and control the error of some stochastic discontinuities or sharp variations with respect to their quantity, such as the mean or variance of a solution func- inputs cause significant difficulty for traditional approxi- tional. Therefore, our major goal is to provide appropriate mation methods. We have developed an unstructured and error estimates that require less computational effort then sampling-based method to address such problems. First we the collocation procedure itself. locate discontinuities via a kernel SVM classifier and un- certainty sampling. Then we map each resulting smooth Bettina Schieche region to a regular domain on which to build sparse poly- Graduate School of Computational Engineering, TU nomial approximations utilizing existing theory. Darmstadt Department of Mathematics, TU Darmstadt Alex A. Gorodetsky [email protected] Massachussets Institute of Technology [email protected] Jens Lang Department of Mathematics Youssef M. Marzouk Technische Universit˚at Darmstadt Massachusetts Institute of Technology [email protected] [email protected]

CP4 CP5 Robust Approximation of Stochastic Discontinu- Improvement of the Accuracy of the Prediction ities Variance Using Bayesian Kriging. Application to Three Industrial Case Studies. The robust approximation of discontinuities in stochastic problems is important, since they can lead to high sensitiv- Kriging is often used in computer experiments, in par- ities and oscillatory interpolations. To that end, we intro- ticular because it quantifies the variance of prediction duce finite volume robustness concepts from computational which plays a major role in many applications (Efficient fluid dynamics into uncertainty quantification. The ap- Global Optimization, Uncertainty Quantification, Sensi- plication of these new uncertainty propagation algorithms tivity Analysis,...). In this talk we present three indus- to engineering problems shows that they require a mini- trial case studies from different application fields (reser- mal number of samples to resolve discontinuities, for ex- voir engineering, nuclear security, optics) where we show ample, in transonic airfoil flow simulations with uncertain how bayesian kriging provides an accurate variance of pre- free stream conditions. diction especially when prior information is available, for example when derived from less accurate but faster simu- Jeroen Witteveen lations. Stanford University Center for Turbulence Research Celine Helbert [email protected] Laboratoire Jean Kuntzmann University of Grenoble Gianluca Iaccarino [email protected] Stanford University [email protected] UQ12 Abstracts 67

CP5 els and Application to Robust Design Reduced Basis Surrogate Models and Sensitivity Analysis One of the major difficulties concerning uncertainty prop- agation techniques is to identify and quantify the sources Computation of Sobol indices requires a large number of of uncertainty. Predictive uncertainty of models has been runs of the considered model. These runs often take too defined as the main source of uncertainty in aircraft pre- much time, and one has to approximate the model by a sur- liminary design. Moreover, its quantification is made more rogate model which is faster to run. We present a reduced complex by model interdependencies. The aim of this basis method, a way to build efficient surrogate models, study is to propose a way to quantify model predictive un- coming with a rigorous error bound certifying the model certainty and propagate it through an overall design pro- approximation, which can be used to provide an error es- cess to figure out the robustness of its result. timation on the estimated Sobol indices. Jessie Birman Alexandre Janon, Maelle Nodet, Cl´ementine Prieur Airbus Operation S.A.S. LJK / Universit´e Joseph Fourier Grenoble (France) [email protected] INRIA Rhˆone Alpes, France [email protected], [email protected], clemen- [email protected] CP6 Path Variability Due To Sensor Geometry

CP5 The concept of Path Variability Due To Sensor Geometry Shape Invariant Model Approach to Functional (PVDSG) is fundamental to geomatic engineering. The Outputs Modelling PVDSG is a measure of the variability “built into’ a statis- tic based on the distances from a target to the elements of To tackle the problem of uncertainty propagation in dy- a sensor array, due to the particular geometry of that array, namic simulators such as multiphase flow transport we pro- as the target traverses a given path. This paper documents pose a response surface method based on Gaussian Process. PVDSG measures as functions of the covariance matrix of To reduce the dimension a shape invariant model approach the proportional target/sensor separations. is proposed. Multiple runs from the experimental design are modelled by a parametrical transformation applied to Timothy Hall a template curve. The response surface model is then ap- PQI Consulting plied to the reduced set of transformation parameters from [email protected] which the functional output is reconstructed. Ekaterina Sergienko CP6 University of Toulouse and IFP Energies Nouvelles Risk-Averse Control of Linear Stochastic Sys- [email protected] tems with Low Sensitivity: An Output-Feedback Paradigm Fabrice Gamboa The research investigation treats the problem of controlling Laboratory of Statistics and Probability stochastic linear systems with quadratic criteria, including University of Toulouse sensitivity variables is investigated, when noisy measure- [email protected] ments are available. It is proved that the low sensitivity control strategy with risk aversion can be realized by the Daniel Busby cascade of: i) the conditional-mean estimates of the cur- IFP Energies Nouvelles rent states using a Kalman filter and ii) optimally feedback, [email protected] which is comprised of a custom set of mathematical statis- tics associated with the finite-horizon quadratic random cost. In other words, the certainty equivalence principle CP5 still holds for this class of optimal statistical control prob- Svr Regression with Polynomial Kernel and Mono- lem. tonicity Constraints Khanh D. Pham Very often, regression models have to respect some ad- The Air Force Research Laboratory ditionnal constraints like monotonicity constraints. We Space Vehicles Directorate present here a new method based on Support Vector Re- [email protected] gression and Polynomial Kernel. As a major feature this method produces an equation valid in the whole domain of interest, which can be used without any additionnal work CP6 by engineers. Avoiding any discretization of the domain, An Information-Based Sampling Scheme with Ap- this method can be applied up to 10 regressions variables. plications to Reduced-Order Modeling This work presents a novel methodology to sample effec- Francois Wahl tively relevant points in the parameter space when de- IFPEN signing computer experiments, or collecting snapshots for [email protected] reduced-order models from an expensive to evaluate com- puter model. Principles from information geometry are employed, where the parameter space is interpreted as a CP6 Riemannian manifold equipped with a sensitivity related Quantification of Uncertainty of Low Fidelity Mod- metric. An adaptive Sequential Monte Carlo scheme en- ables an effective sampling of such points, while allowing a controlled computational cost related to the evaluations of 68 UQ12 Abstracts the computer model. Numerical examples, in the context els of reduced order modeling, are provided. Various fields of science/engineering have developed appli- Raphael Sternfels cation specific formulations of uncertainty quantification School of Civil & Environmental Eng, Cornell University with computational approaches. Such efforts in control [email protected] system analysis employ functional analysis and semidefi- nite programming, yielding tractable algorithms for quan- Christopher J. Earls tifying the effect of individual component uncertainty and Cornell University unknown external influences on behavior of large, hetero- [email protected] geneous interconnections of components. This talk will re- view the formalism, its use in practice, and explore the potential connections across other areas to better exploit CP7 each other’s successes. A Method for Solving Stochastic Equations by Re- duced Order Models Ufuk Topcu Caltech A method is developed for calculating statistics of the so- [email protected] lution U of a stochastic equation depending on an Rd- valued random variable Z. The method is based on two Peter Seiler recent developments. The first approximates the mapping U of Minnesota Z U(Z) by a finite family of hyperplanes tangent to [email protected] U(Z→) at points selected by geometrical considerations. The second represents Z by a simple random vector Z˜ delivered Michael Frenklach by an optimization algorithm minimizing the discrepancy University of California at Berkeley between properties of Z and Z˜. Themethodsusessamples [email protected] of Z˜ to construct approximate representations for U(Z), so that these representations account for the probability law Gary Balas of Z. U of Minnesota [email protected] Mircea Grigoriu School of Civil Engineering Andrew Packard Cornell University U of California at Berkeley [email protected] [email protected]

CP7 CP7 Effect of Limited Measurement Data on State and On-Line Parameter Estimation and Control of Sys- Parameters Estimation in Dynamic Systems tems with Uncertainties

This work characterizes the effect of data uncertainty on We present a method for parameter estimation and control estimates of state and parameters of dynamic systems. The of dynamical systems with uncertainties in real time. The sample moments of state and parameters of dynamic sys- method combines the polynomial chaos (PC) theory for tem based on limited available measurements are treated as uncertainty propagation and the Bayesian framework for random variates that characterize the effects of uncertainty parameter estimation in a novel way. The recursive nature due to limited measurement data. The Hankel matrices as- of the algorithm requires the estimation of the PC coeffi- sociated with each sample moment estimator (that arises cients of the parameters from their posterior distribution. in the context of corresponding Hamburger moment prob- We present methods for estimating these coefficients. The lem) and the covariance matrix (that characterizes statis- problem is motivated by a biological application. tical dependencies among the sample moment estimators), thus, turn out to be random positive-definite matrices. An Faidra Stavropoulou array of methodologies (Bayes’ theorem, random matrix Helmholtz Zentrum Muenchen theory, maximum entropy principle, and polynomial chaos [email protected] expansion) are employed to estimate the probability den- sity functions of these positive-definite random matrices. Johannes Mueller Efficient sampling schemes are also presented to sample TU Muenchen from these pdfs. [email protected] Sonjoy Das, Sonjoy Das, Reza Madankan University at Buffalo CP7 sonjoy@buffalo.edu, sonjoy@buffalo.edu, rm93@buffalo.edu Estimation and Verification of Curved Railway Track Geometry Using Monte Carlo Particle Fil- ters Puneet Singla Mechanical & Aerospace Engineering A railway track geometry differs from the pre-designed one. University at Buffalo It has track irregularities due to the frequent traffic of the [email protected] train. A railway track geometry of level and alignment is measured based on the principle of three-point chord measurement, called 10m chord versine. Reconstructing CP7 the true track geometry from the measured data is a kind of Managing Uncertainty in Complex Dynamic Mod- the inverse problem. In this study a method of estimating UQ12 Abstracts 69 and verifying the true track geometry in the curved section Ekaterina Sergienko from measured data using Monte Carlo particle filters is University of Toulouse and IFP Energies Nouvelles described. [email protected]

Akiyoshi Yoshimura Fabrice Gamboa Tokyo University of Technology Laboratory of Statistics and Probability Emeritus Professor University of Toulouse aki-yoshimura@kyi.biglobe.ne.jp [email protected]

CP8 Bertrand Iooss Investigations on Sensitivity Analysis of Complex EDF R&D Final Repository Models [email protected] The complex computation models for assessing the long- term safety of final repositories for radioactive waste typi- CP8 cally show a number of particularities that can cause prob- Fast and Rbd Revisited lems when a probabilistic sensitivity analysis is performed, such as skewed output distributions over many orders of This is a new introduction to the existing ANOVA-based magnitude, including the possibility of zero-output, or non- global sensitivity analysis methods: Fourier Amplitude continuous behavior. Several numerical experiments are Sensitivity Test (FAST) and Random Balance Design presented, demonstrating these problems and some ideas to (RBD). First this work consists in clarifying the under- deal with them. Different correlation-based and variance- lying mathematical theory, then in performing a rigorous based techniques of sensitivity analysis are applied and error analysis and last in suggesting some improvements compared. and generalizations of both these methods. Numerical ex- amples are also provided to illustrate this work. Dirk-Alexander Becker Gesellschaft fuer Anlagen- und Reaktorsicherheit (GRS) Jean-Yves Tissot mbH University of Grenoble - INRIA [email protected] [email protected]

Cl´ementine Prieur CP8 LJK / Universit´e Joseph Fourier Grenoble (France) Global Sensitivity Analysis for Disease and Popu- INRIA Rhˆone Alpes, France lation Models [email protected]

Variance based sensitivity measures are used to examine the structure of biological models. To limit expensive CP8 model evaluations we use a Gaussian process emulator to Locality Aware Uncertainty Quantification and estimate sensitivity indices. The use of a stochastic sur- Sensitivity Algorithms rogate model allows us to quantify the uncertainty due to lack of data in sensitivity estimates. Our methods are ap- A need exists for UQ and sensitivity analysis algorithms plied to an ODE based model for the spread of an epidemic that leverage information from one system realization to on a network and to an agent based model of disease in a another. Although the size of the computational models metropolitan region. used in many engineering and scientific simulations is ex- tremely large, i.e. millions of equations, the uncertainty Kyle S. Hickmann, James (Mac) Hyman, John E. present is oftentimes very localized to small regions of the Ortmann model. Here, recent efforts to develop computational meth- Tulane University ods that exploit this localization and the ensemble nature [email protected], [email protected], of the requisite iterative analyses will be discussed. [email protected] Steven F. Wojtkiewicz Department of Civil Engineering CP8 University of Minnesota A Global Sensitivity Analysis Method for Reliabil- [email protected] ity Based Upon Density Modification Erik A. Johnson For global sensitivity analysis of numerical models, vari- Astani Dept of Civil & Env Engrg ance decomposition is widely applied. However, when the University of Southern California quantity of interest is a failure probability this method [email protected] requires numerous function evaluations and does not al- ways provide relevant information . We propose a new importance sampling method based upon modification of CP9 the distribution of inputs controlled by Kullback-Leibler Emulating Dynamic Models - Numerical Challenge divergence. The function sample is evaluated only once, resulting in significant time saving. Dynamic models can be emulated by linearizing its equa- tions and compensating for the non-linearities with Gaus- Paul Lematre sian white noise. Coupling replica of the resulting lin- EDF R&D ear stochastic system according to the distance between INRIA Bordeaux their inputs and conditioning the coupled system on off- [email protected] line simulation outputs results in a mechanistic emulator. For piece-wise constant inputs, the covariance matrix of 70 UQ12 Abstracts the coupled system can be derived explicitly. Condition- CP9 ing of the emulator boils down to an (off-line) inversion of Uncertainty Quantification in the Ensemble this covariance matrix and the emulation to mere (on-line) Kalman Filter multiplications of matrices of the dimension of the state space. This approach is compared with Kalman filtering The Ensemble Kalman Filter (EnKF) is a data assimila- and smoothing. tion algorithm that over the last decade has been applied to numerous fields. However, it is well known that the Carlo Albert standard implementation of the EnKF will lead to an un- Eawag derrepresentation of the prediction uncertainty. In this talk [email protected] we will explain, using classical results from statistics, why the EnKF is not able to quantify the uncertainty correctly, and present statistical methods that can resolve this issue. CP9 Multi-Modal Oil Reservoir History Matching Using Jon Saetrom Clustered Ensemble Kalman Filter Statoil ASA [email protected] A multi-modal history-matching algorithm using Regular- ized Ensemble Kalman Filter was developed. The EnKF Henning Omre algorithm is augmented with k-means clustering algorithm Norwegian University of Science and Technology to form sub-ensembles that explore different parts of the [email protected] search space. Clusters are updated at regular intervals to merge clusters approaching the same local minima. The re- sulting mean of each sub-ensemble is used for robust pro- CP9 duction optimization. The proposed algorithm provides Collocation Inference for Nonlinear Stochastic Dy- an efficient method for parameter estimation, uncertainty namic Systems with Noisy Observations quantification and robust optimization of oil production. Collocation-based methods are proposed for estimating pa- Ahmed H. ElSheikh rameters and performing inference for nonlinear stochastic Department of Earth Science and Engineering continuous-time dynamic systems with noisy observations. Imperial College London, South Kensington Campus EM algorithm is applied to handle the systematic stochas- [email protected] tic input and the observational error simultaneously. The approaches use collocation method to avoid the computa- CP9 tional intensity. Two computation algorithms: Laplace ap- proximations and Monte Carlo integration are examined. A Spectral Approach to Linear Bayesian Updating The convergence rates are hp,whereh is the bandwidth The linear Bayesian methods of the family of low-rank of the approximation scheme for stochastic Ronge-Kutta Kalman filters have become popular for the solution of type penalty. inverse and data assimilation problems, with one exam- Yuefeng Wu ple being the ensemble Kalman filter. In this work we Department of Applied Mathematics and Statistics present a related approach which is based on well-known University of California Santa Cruz spectral expansions of the stochastic space, like the poly- [email protected] nomial chaos expansion. The connection of this ‘Bayes linear’ approach with the original Bayes formula is high- lighted, an it is demonstrated that spectral expansions can Giles Hooker be used directly in the update equation without any detour Biostatistics and Computational Biology Department to sampling. Numerical examples show the advantages and Cornell University challenges of this approach. Examples will be given involv- [email protected] ing the well-known Lorenz systems and the estimation of a diffusion coefficient. CP10 Oliver Pajonk Langevin Based Inversion of Pressure Transient Institute of Scientific Computing Testing Data Technische Universit¨at Braunschweig [email protected] In the oilfield, pressure transient testing is an ideal tool for determining average reservoir parameters, but this tech- nique does not fully quantify the uncertainty in the spa- Bojana V. Rosic tial distribution of these parameters. We wish to de- Institute of Scientific Computing termine plausible parameter distributions, consistent with TU Braunschweig both the pressure transient testing data and prior geolog- [email protected] ical knowledge. We used a Langevin-based MCMC tech- nique, adapted to the large number of parameters and data, Alexander Litvinenko to identify geological features and characterize the uncer- TU Braunschweig, Germany tainty. [email protected] Richard Booth,KirstyMorton Hermann G. Matthies Schlumberger Brazil Research and Geoengineering Center Institute of Scientific Computing [email protected], [email protected] Technische Universit¨at Braunschweig [email protected] Mustafa Onur Istanbul Technical University [email protected] UQ12 Abstracts 71

Fikri Kuchuk CP10 Schlumberger Riboud Product Center Inverse Problem: Information Extraction from [email protected] Electromagnetic Scattering Measurement The estimation of local radioelectric properties of materials CP10 from the global electromagnetic scattering measurement is Some Inverse Problems for Groundwater a challenging ill-posed inverse problem. It is intensively explored on High Performance Computing machines by a Perhaps the most appealing aspect of Bayesian inference Maxwell solver and statistically reduced to a simpler prob- in the context of groundwater engineering is that it makes abilistic metamodel. Considering the properties as a dy- proper use of data, and provides the engineer with a tool namic stochastic process, it is shown how advanced Markov that may be used to inform the judicious design of pump Chain Monte Carlo methods, called interacting Kalman fil- tests so that quantities of interest are determined within ters, can perform Bayesian inference to estimate the prop- acceptable bounds. Low dimensional inverse problems for erties and their associated uncertainties. groundwater may capture the essential physics and pro- vide guidance on what is important in the solution of their Pierre Minvielle-Larrousse, Marc Sancandi, FranC¸ois higher dimensional cousins; we present some recent work Giraud, Pierre Bonnemason on low and high dimensional inverse problems for ground- CEA, DAM, CESTA water. [email protected], [email protected], [email protected], [email protected] Nicholas Dudley Ward Otago Computational Modelling Group [email protected] CP10 Set-Based Parameter and State Estimation in Non- Tiangang Cui linear Differential Equations Using Sparse Discrete University of Auckland Measurements [email protected] Bounded experimental uncertainty and sparse measure- Jari P Kaipio ments limit our ability to generate estimates of compo- Department of Applied Physics, University of Eastern nent concentrations and kinetic parameters in biological Finland models because of algorithm instability and computational 2Department of Mathematics, University of Auckland intractability. We present a set-based approach for pro- [email protected] ducing estimates that address these issues. We use first- principles and a-priori knowledge to generate stabilizing bounds that maintain algorithm stability while removing CP10 spurious solutions that occur due to limited measurements. Bayesian Acoustic Wave-Field Inversion of a 1D This is implemented in a multithreaded architecture to ad- Heterogeneous Media dress computational limitations.

We discuss a Bayesian parameter estimation scheme to re- Cranos M. Williams, Skylar Marvel construct the distribution of the subsurface elastic char- North Carolina State University acteristics of a 1D heterogeneous earth model, given the [email protected], [email protected] probed medium’s response to interrogating acoustic waves measured at the surface. We consider a generic multilayer CP10 media where the number of layers along with their veloci- ties and thicknesses are treated as random variables, where Probabilistic Solution of Inverse Problems under the solution’s non-uniqueness is fully accounted for by the Varying Evidence Conditions posterior probability density of the unknowns. A synthetic Results of the impact of varying evidence conditions on study is provided to indicate the applicability of the tech- the probabilistic calibration of model parameters are pre- nique. sented. A synthetic case study is populated where data is Saba S. Esmailzadeh fully controlled, including the effect of location, number, Zachry Department of Civil Engineering, variance and correlation, when used to calibrate a simple Texas A&M University, College Station, TX, USA 77840 differential equation used to simulate diffusion problems. [email protected] Since the calibration follow a Bayesian approach, it is thus possible to describe the uncertainty changes on the model parameters as the evidence conditions vary, as this is re- Zenon Medina-Cetina flected on independent analyses of the posterior distribu- Zachry Department of Civil Engineering tion. Texas A&M University [email protected] Zenon Medina Cetina, Negin Yousefpour Texas A&M University Jun Won Kang [email protected], [email protected] Department of Civil Engineering New Mexico State University, NM 88003, USA. Hans Petter Langtangen, Are Magnus Bruaset, Stuart [email protected] Clark Simula Research Laboratory Loukas F. Kallivokas [email protected], [email protected], [email protected] The University of Texas at Austin [email protected] 72 UQ12 Abstracts

CP11 based physical model. Adaptive Markov chain Monte Carlo Adaptive Error Modelling in Mcmc Sampling for methods are used to efficiently explore a posterior that en- Large Scale Inverse Problems compasses models comprised of subsets of elementary reac- tions. In contrast to conventional techniques, our approach We present a new adaptive delayed-acceptance MCMC al- provides a statistically rigorous assessment of uncertainty gorithm (ADAMH) that adapts to the error of a reduced in reaction mechanism structure and in reaction rate pa- order model to enable efficient sampling from the posterior rameters. distribution arising in large scale inverse problems. This use of adaptivity differs from existing algorithms that tune Nikhil Galagali, Youssef M. Marzouk the proposals, though ADAMH also implements that. Con- Massachusetts Institute of Technology ditions given by Roberts and Rosenthal (2007) are used to [email protected], [email protected] give constructions that are provably convergent. We ap- plied ADAMH to several large scale groundwater studies. CP11 Tiangang Cui Inferring Bottom Bathymetry from Free-Surface University of Auckland Flow Features [email protected] We are solving an inverse problem of determining Nicholas Dudley Ward bathymetry of a channel from the mean flow features at Otago Computational Modelling Group the free surface. Our approach is optimization-based oper- [email protected] ating on a database of simulations with parameterized bed- forms. Sensitivity of the inversion process to noise (e.g., in- strument error, turbulence) is investigated. In the present Colin Fox framework, we rely on the time-averaged surface flow fea- University of Otago, New Zealand tures, although also consider a more complex problem of [email protected] using multiple free-surface snapshots of the unsteady flow. Mike O’Sullivan Sergey Koltakov, Gianluca Iaccarino The University of Auckland Stanford University [email protected] [email protected], [email protected]

Oliver Fringer CP11 Environmental Fluid Mechanics Laboratory Scalable Methods for Large-Scale Statistical In- Stanford University verse Problems, with Applications to Subsurface [email protected] Flow

We address the challenge of large-scale nonlinear statistical CP11 inverse problems by developing an adaptive Hessian-based Bayesian Updating of Uncertainty in the Descrip- non-stationary Gaussian process response surface method tion of Transport Processes in Heterogeneous Ma- to approximate the posterior pdf solution. We employ terials an adaptive sampling strategy for exploring the parame- ter space efficiently to find interpolation points and build a The prediction of thermo-mechanical behaviour of hetero- global analytical response surface far less expensive to eval- geneous materials such as heat and moisture transport is uate than the original. The accuracy and efficiency of the strongly influenced by the uncertainty in parameters. Such response surface is demonstrated with examples, including materials occur e.g. in historic buildings, and the durabil- a subsurface flow problem. ity assessment of these therefore needs a reliable and prob- abilistic simulation of transport processes, which is related H. Pearl Flath to the suitable identification of material parameters. In Institute for Computational Engineering and Sciences order to include expert knowledge as well as experimental The University of Texas at Austin results, we employ a Bayesian updating procedure. pfl[email protected] Jan Sykora Tan Bui-Thanh Faculty of Civil Engineering The University of Texas at Austin Czech Technical University in Prague [email protected] [email protected]

Omar Ghattas Anna Kucerova University of Texas at Austin Faculty of Civil Engineering, Prague, Czech TU [email protected] [email protected]

Bojana V. Rosic CP11 Institute of Scientific Computing Chemical Reaction Mechanism Generation Using TU Braunschweig Bayesian Variable Selection [email protected] The generation of detailed chemical reaction mechanisms, for applications ranging from electrochemistry to combus- Hermann G. Matthies tion, must often rely on noisy and indirect system-level Institute of Scientific Computing data. We present a novel approach to mechanism gen- Technische Universit¨at Braunschweig eration based on Bayesian variable selection and a PDE- [email protected] UQ12 Abstracts 73

CP12 and mode shape components. However, such an assump- Bayesian Models for the Quantification of Model tion is not expected to hold in case of mode shape compo- Errors in Pde-Based Systems nents identified from dense sensor networks. A correlated prediction error is therefore introduced and its effect on the Bayesian formulations offer a unified statistical treatment identification is investigated. for the solution of model-based inverse problems. Apart from the noise in the data, another source of uncertainty, Ellen Simoen which is largely unaccounted for, is model uncertainty.In K.U.Leuven general, there will be deviations between the physical real- [email protected] ity where measurements are made, and the idealized math- ematical/computational description (in our case a system Costas Papadimitriou of PDEs consisting of conservation laws and constitutive University of Thessaly equations). We propose an intrusive Bayesian strategy Dept. of Mechanical Engineering and efficient inference tools that are capable of quantifying [email protected] model errors in the governing equations. Guido De Roeck, Geert Lombaert Phaedon S. Koutsourelakis K.U.Leuven Heriot Watt University Dept. of Civil Engineering [email protected] [email protected], [email protected] CP12 Predictive Simulation for CO2 Sequestration in CP12 Saline Aquifers Investigating Uncertainty in Aerothermal Model One of the most difficult tasks in CO2 sequestration Predictions for Hypersonic Aircraft Structures projects is the reliable characterization of properties of the Validating compu- subsurface. A typical situation employs dynamic data in- tational models of fluid-thermal-structural interactions in tegration such as sparse CO2 measurement data in time hypersonic aircraft structures remains a challenge due to and sparse measurements of permeability and porosity in limited experimental data. This research investigates un- space to be matched with simulated responses associated certain model parameters and model errors in aerodynamic with a set of permeability and porosity fields. Among the pressure and heating predictions. The modeled conditions challenges found in practice are proper mathematical mod- correspond to aerothermal test data from hypersonic wind eling of the flow, persisting heterogeneity in porosity and tunnel experiments of a spherical dome protuberance on a permeability, and the uncertainties inherent in them. In flat plate. Bayesian calibration and sensitivity analysis are this talk, we propose a Bayesian framework Monte Carlo used with the test data to improve understanding of model Markov Chain simulation (MCMC) to sample a set of char- and experimental uncertainty. acteristics of the subsurface from the posterior distribution that are conditioned to the measured CO2 data. This pro- Benjamin P. Smarslok cess requires obtaining the simulated responses over many Air Force Research Laboratory iterations. We use the model proposed in Obi and Blunt [email protected] [Water Resources Research, 2006] to perform numerical simulations of the injection of CO2 in saline aquifers, and Sankaran Mahadevan illustrate the MCMC procedure and its use in predictive Vanderbilt University simulation for CO2 sequestration. [email protected] Victor E. Ginting, Marcos Mendes Department of Mathematics CP13 University of Wyoming [email protected], [email protected] Reservoir Uncertainty Quantification Using Clus- tering Methods

Felipe Pereira Quantifying uncertainty in reservoir predictions is impor- Center for Fundamentals of Subsurface Flow tant in the petroleum industry, since more accurate quan- University of Wyoming tification of the uncertainty contributes to prudent multi- [email protected] million dollar decision makings. Nowadays predictions are made from conditioned multi-model ensembles obtained in Arunasalam Rahunanthan history-matching using optimisation with evolutionary al- Center for Fundamentals of Subsurface Flow gorithms. These ensembles are usually multi-modal and University of Wyoming, Laramie, WY 82071 different models will result in different forecasts. We use [email protected] k-mean, probabilistic distance, and agglomerate clustering methods to locate and track multiple distinct optima rep- resenting uncertainties of the reservoir. CP12 The Effect of Prediction Error Correlation on Asaad Abdollahzadeh Bayesian Model Updating Heriot-Watt University [email protected] In this contribution, a Bayesian inference framework is adopted to quantify uncertainties due to measurement and Mike Christie modeling errors in vibration-based model updating. In Heriot-Watt University, UK most cases, independent normal distributions are assumed [email protected] for the observed prediction errors on natural frequencies 74 UQ12 Abstracts

David W. Corne Faculty of Civil Engineering Heriot-Watt University Czech Technical University in Prague [email protected] [email protected]

Bojana V. Rosic CP13 Institute of Scientific Computing Adaptive Smolyak Pseudospectral Expansions TU Braunschweig [email protected] Smolyak pseudospectral expansions provide an efficient and accurate approach for computing sparse polynomial chaos approximations of functions with weak coupling be- Hermann G. Matthies tween the input dimensions. We rigorously develop the Institute of Scientific Computing Smolyak algorithm and show that it is well behaved. Technische Universit¨at Braunschweig This behavior stands in contrast to the traditional sparse [email protected] quadrature approach for building polynomial expansions, which is either inaccurate or inefficient in almost all cases. CP13 Furthermore, we tailor the Smolyak algorithm to individ- ual functions at run-time through an adaptive strategy. Stochastic Anova-Galerkin Projection Schemes

Patrick R. Conrad We present numerical schemes based on ANOVA-Galerkin MIT projection for stochastic PDEs with large number of ran- [email protected] dom variables. The central idea is to represent the so- lution using a functional ANOVA decomposition supple- mented by appropriate orthogonality constraints so that Youssef M. Marzouk the weak form can be decoupled into a set of independent Massachusetts Institute of Technology low-dimensional subproblems. Numerical studies will be [email protected] presented for the steady-state and time-dependent stochas- tic diffusion equation with more than 500 variables. CP13 Prasanth B. Nair Uncertainty and Differences in Global Climate University of Southampton Models University of Southampton [email protected] Climate models have greatly aided investigation of global climate change. The uncertainty, similarities, and differ- ences between climate models can be examined using ex- Christophe Audouze ceedance regions. We propose methodology for drawing The laboratory of signals and systems (L2S) conclusions about entire exceedance regions with known University Paris-Sud Orsay - CNRS - Supelec confidence. The methodology uses kriging and conditional [email protected] simulation to create confidence regions having the neces- sary statistical properties. Discussion will include assess- CP13 ment of future climate change for several regions of North America and highlight differences between various climate Multilevel Monte Carlo for Uncertainty Quantifi- models. cation in Subsurface Flow

Joshua P. French Multilevel Monte Carlo is an efficient variance reduction University of Colorado Denver technique to quantify uncertainties in simulations of sub- [email protected] surface flows with highly varying, rough coefficients, e.g. in radwaste disposal. We study model elliptic problems of single phase flow in random media described by correlated Stephan Sain lognormal distributions, discretized in space via (standard Institute for Mathematics Applied to Geosciences and mixed) finite elements. We will demonstrate (theo- National Center for Atmospheric Research retically and numerically) significant gains with respect to [email protected] standard Monte Carlo, leading (in the best case) to an asymptotic cost that is proportional to solving one deter- CP13 ministic PDE. Comparison of Stochastic Methods for Bayesian Robert Scheichl Updating of Uncertainty in Parameters of Nonlin- Department of Mathematical Sciences ear Models University of Bath [email protected] An extensive development of efficient methods for stochas- tic modelling enabled uncertainty propagation through complex models. In this contribution, we present a review Andrew Cliffe and comparison of several approaches such as stochastic School of Mathematical Sciences Galerkin method or stochastic collocation method in con- University of Nottingham text of Bayesian uncertainty updating. andrew.cliff[email protected] Anna Kucerova Michael B. Giles Faculty of Civil Engineering, Prague, Czech TU Mathematical Institute [email protected] Oxford University [email protected] Jan Sykora UQ12 Abstracts 75

Minho Park Hans-Peter Nachtnebel University of Nottingham BOKU-University of Natural Resources and Life Sciences, [email protected] Vien hans [email protected] Aretha Teckentrup, Elisabeth Ullmann University of Bath [email protected], [email protected] CP14 Likelihood-Based Observability Analysis and Con- fidence Intervals for Model Predictions CP14 Toward Reduction of Uncertainty in Complex Nonlinear dynamic models of biochemical networks con- Multi-Reservoir River Systems tain a large number of parameters. This renders classi- cal approaches for the calculation of confidence regions for Uncertainties are inherent in the operation of any system, parameter estimates and model predictions hardly feasi- however assuming that they are all purely stochastic and ble. We present the so-called prediction profile likelihood independent, both spatially and temporally, may result in which is utilized to generate reliable confidence intervals for unnecessarily large uncertainties that may not be useful for model predictions and for a data-based observability anal- the operation of a system. In this paper we present a novel ysis. The presented approach constitutes a general concept framework for better modeling uncertainty in complex sys- and is therefore applicable for any kind of prediction model. tems and demonstrate the approach applied to regulated river systems. This framework aims to combine “purely stochastic processes’ (not well understood or unpredicted Clemens Kreutz at this stage) with the physical description of the system University of Freiburg (e.g., flow dynamics in the case of complex regulated river Institute of Physics systems) with the goal of better modeling uncertainties and [email protected] hence reduce the ranges of the confidence intervals. In this framework, only the stream inflows (external source) are Andreas Raue assumed to be purely stochastic. Other uncertain quanti- Physics Institute, University of Freiburg ties are correlated to the uncertainty of the stream inflows [email protected] using the dynamics of the river as the physical description of the system. In this framework the dynamics of the river Jens Timmer is simulated using the performance graphs approach. For University of Freiburg the quantification of uncertainty, rather than doing sam- Department of Physics pling of the input distributions, we explicitly model the [email protected] random space (via random variables and processes). We represent uncertainty in stream inflows via an error term modeled as a stochastic process. The resulting system is CP14 discretized (in random space) using stochastic collocation, Hybrid Stochastic Collocation - Stochastic Pertur- which is distinct from random sampling methods in that bation Method for Linear Elastic Problems with the Gaussian nodes are deterministic. By recycling exist- Uncertain Material Parameters ing deterministic codes, this non-intrusive approach is both more efficient than Monte-Carlo methods and as flexible in We propose a hybrid formulation combining the stochastic their application. collocation (SC) and stochastic perturbation (SP) methods to obtain the response of a linear elastic system with ma- Nathan L. Gibson terial uncertainties. The material properties are modelled Oregon State University as a memory-less transformation of a Gaussian field, which [email protected] discretized by a series expansion method. The response of the system is estimated using SC to account for the most Arturo Leon, Christopher Gifford-Miears important (lower) modes in the series expansion and SP School of Civil and Construction Engineering for the other (higher) modes. Oregon State University [email protected], giff[email protected] Boyan S. Lazarov Department of Mechanical Engineering Technical University of Denmark CP14 [email protected] Stochastic Analysis of the Hydrologic Cascade Model, a Polynomial Chaos Approach Mattias Schevenels Department of Civil Engineering, K.U.Leuven In this talk we analyse a Nash cascade of linear reservoirs Kasteelpark Arenberg 40, B-3001 Leuven, Belgium representing a watershed. It is specified by a system of cou- [email protected] pled linear differential equations with random coefficients. A stochastic spectral representation of these parameters is used, together with a polynomial chaos expansion. A CP14 system of differential equations is obtained which describe A Comparison Of Uncertainty Quantification the evolution of the mean and higher-order moments with Methods Under Practical Industry Requirements respect to time. The objective of this paper is to establish comprehensive Franz Konecny guidelines for engineers to effectively perform probabilis- BOKU-University of Natural Resources and Applied tic design studies through a systematically comparison of Life Sciences, Vienna uncertainty quantification or probabilistic methods. These [email protected] methods include 1) Simulation-based approaches such as 76 UQ12 Abstracts

Monte Carlo simulation, importance sampling and adap- CP15 tive sampling, 2) Local expansion-based methods such as Bayesian Subset Simulation Taylor series method or perturbation method, 3) First Or- der Second Moment (FOSM) based methods, 4) Stochas- One of the most important and computationally chal- tic expansion-based methods, such as Neumann expansion lenging problems in reliability engineering is to estimate and polynomial chaos expansion, 5) Numerical integration- the failure probability of a dynamic system. In cases based or moments-based methods, such as Point Estimate of practical interest, the failure probability is given by Method, Eigenvector Dimension Reduction, 6) Regression- an integral over a high-dimensional uncertain parameter or metamodel-based methods, 7) Bayesian methods, and space. Subset Simulation method, provides an efficient 8) Data classification methods. Both aleatory & epistemic algorithm for computing failure probabilities for general uncertainty will be addressed in the paper. A set of bench- high-dimensional reliability problems. In this work, a mark problems representing different levels of dimension- Bayesian counterpart of the original Subset Simulation ality, non-linearity and noise level will be used for the com- method is developed. parison. Konstantin M. Zuev Liping Wang, Gulshan Singh, Arun Subramaniyan Department of Mathematics GE Global Research University of Southern California [email protected], [email protected], [email protected] [email protected]

James Beck CP15 Division of Engineering and Applied Science Rare Events Detection and Analysis of Equity and California Institute of Technology Commodity High-Frequency Data [email protected] We present a methodology to detect unusual trading ac- tivity defined as high price movement with relatively little CP16 volume traded. The analysis is applied to high-frequency Delay in Neuronal Spiking transactions of thousands of equities and the probability of price recovery in the proximity of these rare events is We study how some delay mechanisms influence interac- calculated. Similar results are obtained when analyzing tion between a neuron and its network. Specifically, we commodities with different expiration dates. The propa- look at conduction delay, spike-timing dependent plastic- gation of rare events in the commodity structure and the ity, and time delay induced by the partial differential equa- liquidity problems are addressed. tion describing a particular neuron. We further compare the contribution of different delay mechanisms to numer- Dragos Bozdog, Ionut Florescu ical solutions of the governing cable equation. We study Stevens Institute of Technology two cases: the case of passive electrical activity and the Department of Mathematical Sciences case of propagating action potential. [email protected], ifl[email protected] Mikhail M. Shvartsman Khaldoun Khashanah, Jim Wang University of St. Thomas Stevens Institute of Technology [email protected] Financial Engineering Program [email protected], [email protected] CP16 A Gaussian Hierarchical Model for Random Inter- CP15 vals Glimpses of Uq, Qmu, and Reliability Many statistical data are imprecise due to factors such as We will provide an introduction to quantification of mar- measurement errors, computation errors, and lack of infor- gins and uncertainties (QMU) and reliability. QMU is a mation. In such cases, data are better represented by inter- summary number that is relatively easy to interpret for vals than single-valued numbers. To model both random- decision-making. Reliability is defined as the probability ness and imprecision, we propose a Gaussian hierarchical that a given item will perform its intended function for model for random intervals, and develop a minimum con- a given period of time under a given set of conditions. trast estimator that we show is both consistent and asymp- The underlying concepts in this definition are probability, totically normal. We extend this model to the time series intended function, time, and conditions. Reliability is a context and build an interval-valued GARCH model. quantity that can be very difficult to compute for complex systems, and viewed rigorously, is inherently a statistical Yan Sun distribution on the probability of success (or failure) of Department of Mathematics & Statistics a system. Both concepts are concerned with uncertainty Utah State University quantification. We will illustrate with examples from com- [email protected] plexsystemsfromourworkatLosALamosNationalLab- oratory. Dan Ralescu Department of Mathematical Sciences Aparna V. Huzurbazar, David Collins University of Cincinnati Los Alamos National Laboratory [email protected] [email protected], [email protected]

CP17 Interval-Based Inverse Problems with Uncertain- UQ12 Abstracts 77 ties and fat but most of the information is in the water signal. Different assumptions about the imaging conditions result Inverse problems in science and engineering aim at estimat- linear and non-linear models of the image generation. The ing model parameters of a physical system using observa- multiple parameters and non-linearity lead to a version of tions of the models response. However, response measure- the Cramer-Rao bound for a parameter if all other pa- ments are usually associated with uncertainties, and deter- rameters were known. We study how the choice in model ministic inverse algorithms hardly provide the associated affects the optimal data acquisition based on minimizing error estimates for the model parameters. In this work, we this Cramer-Rao bound. will present an interval-based iterative solution that pre- dicts such error exploiting an adjoint -based optimization Angel R. Pineda, Emily Bice and the containment-stopping criterion. California State University, Fullerton [email protected], [email protected] Rafi L. Muhanna, Francesco Fedele Georgia Institute of Technology rafi[email protected], [email protected] CP17 Automated Exact Calculation of Test Statistics in Hypothesis Testing CP17 Probability Bounds for Nonlinear Finite Element Many classical statistical tests rely on large-sample approx- Analysis imations for determining appropriate critical values. We use a computer algebra system to compute the exact dis- A set of possible cumulative probability distributions de- tribution of test statistics under the null hypothesis for the fined by its bounding functions is one way for representing Wilcoxon signed-rank test and the chi-square goodness of epistemic and aleatory uncertainty separately. Such sets fit test, which gives the exact critical value for small sample are known as a probability box (P-box). In this work we sizes. will present an interval Monte Carlo method for calculating the non-linear response of structures in terms of P-boxes Lawrence Leemis when system parameters and loading are described as P- College of William and Mary boxes. Results obtained show very tight enclosures even [email protected] for large uncertainties. Vincent Yannello Rafi L. Muhanna The College of William & Mary Georgia Institute of Technology [email protected] rafi[email protected]

Robert Mullen CP17 University of South Carolina Evidence-Based Approach for the Probabilistic As- [email protected] sessment of Unknown Foundations of Bridges As of 2005, there were approximately sixty thousand CP17 bridges throughout the US identified as having Unknown A Complete Closed-Form Solution to Stochastic Foundations. Missing substructure information has made Linear Systems with Fixed Coefficients safety monitoring of bridges very difficult for departments of transportation, especially for over-river bridges which Given a fixed but arbitrary coefficient matrix A and a are susceptible to scour. An evidence-based methodology meaningful input probability density d(b) that stochasti- is proposed in this paper to determine the unknown charac- cally describes the other input data b for the system Ax teristics of bridge foundations conditional on information = b, this paper: (1) derives explicit formulas for numeri- collected from existing bridges. The proposed approach cally computing the induced probability that this system combines the use of a Neural-Network model to compute has at least one solution x, (2) formulates and then de- the foundations bearing capacity, with a Bayesian formu- scribes the important properties of the optimization prob- lation that allows for defining probability distributions of lem whose solutions b* (if any) maximize d(b) over all the foundation type, size and embedment depth, as well as b for which Ax = b has at least one solution x, (3) for- of the soil properties supporting the foundation. mulates and then describes the important properties of a general optimization problem whose solutions x* (if any) Negin Yousefpour, Zenon Medina Cetina, Jean-Louis optimize a given function g(x) over all x for which Ax = Briaud b*. This methodology can numerically compete with both Texas A&M University the simulation approaches and the simplified deterministic [email protected], [email protected], approaches based on expected values and other moment [email protected] information. In modified form, it might also provide new approaches to systems Ax = b with ”fuzzy” data b. CP18 Elmor L. Peterson An Approach to Weak Solution Approximation of Systems Science Consulting Stochastic Differential Equations [email protected] This paper presents an approach to approximate the weak solution of nonlinear stochastic differential equations. Uti- CP17 lizing the results from the Radon-Nikodym theorem and Cramer-Rao Bound for Models of Fat-Water Sep- the Girsanov theorem, the proposed approach introduces aration Using Magnetic Resonance Imaging a measure transformation so that the Itˆo process under consideration becomes a Wiener process under the trans- Magnetic resonance images typically contain both water 78 UQ12 Abstracts formed measure. Here we propose the Euler-Maruyama to identify locations for new measurements or data sam- scheme to approximate the stochastic integral involved in ples. We also analyze an algorithm for approximating these calculating the Radon-Nikodym derivative associated with parametric variations. the measure transformation. A detailed analysis of the proposed approximation scheme reveals that the proposed Vitor Leite Nunes approach is exactly the same as calculating the weak so- Interdisciplinary Center for Applied Mathematics, lution using the traditional Euler-Maruyama scheme and Virginia Polytechnic Institute & State University thustheproposedapproachisweaklyconvergentwitha [email protected] convergence rate of γ = 1. A numerical example is pre- sented to validates the proposed approach and illustrate its capability. CP18 Analysis of Quasi-Monte Carlo FE Methods for El- Jemin George liptic PDEs with Lognormal Random Coefficients U.S. Army Research Laboratory [email protected] We devise, implement and analyse quasi-Monte Carlo methods for computing the expectations of (nonlinear) functionals of solutions of a class of elliptic partial differ- CP18 ential equations with lognormal random coefficients. Our Asymptotic Normality and Efficiency for Sobol In- motivation comes from fluid flow in random porous media, dex Estimator where a very large number of random variables is usually needed to give a realistic model of the coefficient field. By In this talk we will study the convergence and the efficiency using deterministically chosen sample points in an appro- of Sobol index estimators. More precisely, we will consider priate (usually high-dimensional) parameter space, quasi- the following model Monte Carlo methods can obtain substantially higher con- vergence rates than classical Monte Carlo. An analysis Y = f(X, Z) in appropriate function spaces confirms this also theoreti- cally. The analysis is particularly challenging since in the where X and Z are independent random vectors. The lognormal case the PDE is neither uniformly elliptic nor importance of each input variable can be measured by uniformly bounded and the parametrisation of the coeffi- Var(E(Y X)) Var(E(Y Z)) | | cient is nonlinear. S = Var(Y) , Var(Y) . We will construct an es- timator Sn of S and show that it is asymptotically normal Robert Scheichl and efficient. At the end of the talk, we will give similar Department of Mathematical Sciences results when f is replaced by some approximation f˜. University of Bath [email protected] Alexandre Janon LJK / Universit´e Joseph Fourier Grenoble (France) Ivan G. Graham INRIA Rhˆone Alpes, France University of Bath [email protected] [email protected]

Thierry Klein Frances Y. Kuo Institut de Math´ematiques de Toulouse School of Mathematics and Statistics UMR CNRS 5219 Universit´edeToulouse University of New South Wales [email protected] [email protected]

Agnes Lagnoux James Nichols Institut de Math´ematiques de Toulouse UMR CNRS 5219 University of New South Wales, Sydney Universi [email protected] [email protected] Christoph Schwab Ma¨elle Nodet ETH Zuerich Universit´e Joseph Fourier and INRIA, France SAM [email protected] [email protected]

Cl´ementine Prieur Ian H. Sloan LJK / Universit´e Joseph Fourier Grenoble (France) University of New South Wales INRIA Rhˆone Alpes, France School of Mathematics [email protected] [email protected]

CP18 CP19 Frechet Sensitivity Analysis for the Convection- Maximum Entropy Construction for Data-Driven Diffusion Equation Analysis of Diffusion on Random Manifolds In this work, we consider Frchet derivatives of solutions A data-driven approach is developed for the diffusion on to the convection-diffusion equation with respect to dis- manifolds with unknown geometry. Given limited number tributed parameters and demonstrate their applicability of samples drawn from the manifold, our objective is to in parameter estimation. Under certain conditions, the characterize the geometry, while accounting for inevitable Frchet derivative operator is Hilbert-Schmidt and thus uncertainties due to measurement noise and scarcity of there are parametric variations that have more impact on samples. We will present a MaxEnt construction for un- the solution than others. These variations can be used UQ12 Abstracts 79 certainty representation of the graph Laplacian used to ap- is directly treated as a symmetric, positive-definite random proximate the Laplace-Beltrami operator. We also discuss matrix unlike other approaches where each element of Q the adaptation of this formulation for information diffusion is treated as random variable or Q is itself parameterized in social networks. by a set of scalar-valued random variables. The probabil- ity density function (pdf) of Q is estimated by employing Hadi Meidani maximum entropy principle. The theory of multiple model University of Southern California and Kalman Filter are then used to update this pdf over [email protected] time, resulting in a pdf with sharp peak around the true covariance matrix once sufficient number of measurements Roger Ghanem are made. University of Southern California Aerospace and Mechanical Engineering and Civil Sonjoy Das, Sonjoy Das, Kumar Vishwajeet Engineering University at Buffalo [email protected] sonjoy@buffalo.edu, sonjoy@buffalo.edu, kumarvis@buffalo.edu

CP19 Puneet Singla Multiple Signal Classification in Covariance Space Mechanical & Aerospace Engineering of EEG Data University at Buffalo [email protected] The objective is to find discriminative features in the EEG signals to mark various stages of drowsiness in vehicle op- erators. Existing methods are only able to distinguish be- CP20 tween extreme stages. In this research, we are trying to use Determining Critical Parameters of Sine-Gordon metrics on the covariance space of EEG data to identify and Nonlinear Schr¨odinger Equations with a the evolution of the state of fatigue from low to high. We Point-Like Potential Using Generalized Polynomial have conducted experiments to induce continuous fatigue Chaos Methods in human subjects while keeping them awake for about 36 hours. The EEG data has been recorded over 3-hours in- We consider the sine-Gordon and nonlinear Schr¨odinger terval. Eventually we intend to build a spatio-temporal equations with a point-like singular source term. The soli- model of evolution of fatigue in the covariance space of ton interaction with such a singular potential yields a crit- EEG data. ical solution behavior. That is, for the given value of the potential strength or the soliton amplitude, there exists a Deepashree Sengupta critical velocity of the initial soliton solution, around which Indian Institute of Technology, Kharagpur the solution is either trapped by or transmitted through [email protected] the potential. In this talk, we propose an efficient method for finding such a critical velocity by using the general- Aurobinda Routray ized polynomial chaos (gPC) method. For the proposed Professor, Department of Electrical Engineering method, we assume that the soliton velocity is a random Indian Institute of Technology, Kharagpur variable and expand the solution in the random space us- [email protected] ing the orthogonal polynomials. We consider the Legendre and Hermite chaos with both the Galerkin and colloca- tion formulations. The proposed method finds the critical CP19 velocity accurately with spectral convergence. Thus the Dynamic Large Spatial Covariance Matrix Estima- computational complexity is much reduced. The very core tion in Application to Semiparametric Model Con- of the proposed method lies in using the mean solution in- struction Via Variable Clustering: the Sce Ap- stead of reconstructing the solution. The mean solution proach converges exponentially while the gPC reconstruction may fail to converge to the right solution due to the Gibbs phe- We consider estimating a large spatial covariance matrix of nomenon in the random space. Numerical results confirm the high-dimensional time series by thresholding, quantify the accuracy and spectral convergence of the method. the interplay between the spatial estimators’ consistency and the temporal dependence level, and prove a CV result Debananda Chakraborty for threshold selection. Given a consistently estimated ma- Ph.D. student trix and its natural links with semiparametrics, we screen, dc58@buffalo.edu cluster the explanatory variables and construct the cor- responding semiparametric model to be further estimated Jae-Hun Jung with sign constraints. We call this the SCE approach. Department of Mathematics SUNY at Buffalo Song Song jaehun@buffalo.edu University of California, Berkeley [email protected] CP20 CP19 A Comparison of Dimensionality Reduction Tech- niques in Scientific Applications Random Matrix Based Approach for Adaptive Es- timation of Covariance Matrix High-dimensional data sets, where each data item is rep- resented by many attributes or features, are a challenge in The work considers the problem of estimating unknown co- data mining. Irrelevant attributes can reduce the accuracy variance matrix, Q, of process noise in linear dynamic sys- of classification algorithms, while distance-based cluster- tem based on corrupted state measurements data. Here, Q ing algorithms suffer from a loss of meaning of the term 80 UQ12 Abstracts

”nearest neighbors”. Using data sets from scientific appli- MS1 cations, we present a comparison of different dimensional- Effective and Efficient Handling of Ill-Conditioned ity reduction methods, including various feature selection Correlation Matrices in Kriging and Gradient techniques, as well as linear and non-linear feature trans- Enhanced Kriging Emulators through Pivoted form methods. Cholesky Factorization Ya Ju Fan, Chandrika Kamath Kriging or Gaussian Process emulators are popular be- Lawrence Livermore National Laboratory cause they interpolate build data if the correlation ma- [email protected], [email protected] trix is R.S.P.D. and produce a spatially varying error estimate. However, handling ill-conditioned correlation matrices can be challenging. The rows/columns of an CP20 ill-conditioned matrix substantially duplicate information. Computational Methods for Statistical Learning Pivoted Cholesky ranks points by their new information Using Support Vector Machine Classifiers content; then low information points are discarded. Since discarded points contain the least new information, they An augmented Lagrangian algorithm for solving equality best remediate ill-conditioning and are the easiest to pre- and bound constrained quadratic problems will be pre- dict. sented for use in support vector machine (SVM) classifi- cation. Examples will include images and a diabetes data Keith Dalbey set. The algorithm will be compared with existing opti- Sandia National Laboratories mization techniques and the SVM method will be com- [email protected] pared with quadratic discriminant analysis, as well as a general linearized model for the diabetes data set. MS1 Marylesa Howard History Matching: An alternative to Calibration The University of Montana for a Galaxy Formation Simulation [email protected] In the context of computer models, calibration is a vital technique whereby an emulator is used to obtain a pos- CP20 terior distribution over the input space of the computer A Hidden Deterministic Solution to the Quantum simulator. However, this process can be extremely chal- Measurement Problem lenging. We discuss a powerful alternative known as his- tory matching that can either serve as a prelude to a full In this paper we present a nonconventional method of es- calibration to greatly improve efficiency, or that can in sev- tablishing a hidden but computationally realizable deter- eral cases replace calibration entirely. Work from Mitchell ministic solution to quantum measurement problems in the Prize winning paper. non-infinite, non-zero quantized energy limits. Our ap- proach is not in contradiction with Heisenberg’s Uncer- Ian Vernon tainty Principle, rather it determines energy (E) and mo- University of Durham, UK mentum (p) of a quantum particle as functions of uncer- [email protected] tainties,viz E = f(∆E)andp = f(∆p). Thus an observer gets E ±E and p ±p as the observed values of the energy and momentum of the said particle. MS1 Emulation of Count Data in Healthcare Models Pabitra Pal Choudhury Professor in Applied Statistics Unit, ISI Kolkata 700108 Natural History Models are simulators used in healthcare [email protected]; [email protected] applications to simulate patients’ outcomes from certain illnesses. Their output is typically count data and for rare Swapan Kumar Dutta illnesses zeros are common. The simulators rely on many Retired Scientist unknown parameters, but calibration using Monte Carlo [email protected] methods is impractical due to computational expense. In- stead we calibrate using an emulator as a surrogate for the simulator, showing how appropriate regions of parameter MS1 space are identified for the emulator to perform well. Super-parameterisation of Oceanic Deep Convec- tion using Emulators Ben Youngman University of Sheffield, UK Misrepresentation of sub-grid scale processes can increase b.youngman@sheffield.ac.uk the uncertainty in the results of large scale models. Despite the existence of detailed numerical models that resolve sub- grid scale processes, embedding these in a large scale model MS2 is often computationally prohibitive. A viable alternative Bayesian Inference with Optimal Maps is to encapsulate our knowledge about the sub-grid scale model in an emulator and use this as a surrogate. We ap- We present a new approach to Bayesian inference that en- ply this paradigm of ‘super-parameterisation’ to an oceanic tirely avoids Markov chain simulation, by constructing a deep convection problem. map that pushes forward the prior measure to the pos- terior measure. Existence and uniqueness of a suitable Yiannis Andrianakis measure-preserving map are established by formulating the National Oceanography Centre problem in the context of optimal transport theory. We University of Southampton, UK discuss various means of explicitly parameterizing the map [email protected] and computing it efficiently through solution of a stochas- tic optimization problem, exploiting gradient information UQ12 Abstracts 81 from the forward model. The resulting algorithm over- University of Texas at Austin comes many of the computational bottlenecks associated [email protected] with Markov chain Monte Carlo. Advantages of a map- based representation of the posterior include analytical ex- James R. Martin pressions for posterior moments and the ability to generate University of Texas at Austin arbitrary numbers of independent posterior samples with- Institute for Computational Engineering and Sciences out additional likelihood evaluations or forward solves. The [email protected] optimization approach also provides clear convergence cri- teria for posterior approximation and facilitates model se- Georg Stadler lection through automatic evaluation of the marginal like- University of Texas at Austin lihood. We demonstrate the accuracy and efficiency of the [email protected] approach on nonlinear inverse problems of varying dimen- sion, involving the inference of parameters appearing in ordinary and partial differential equations. Lucas Wilcox HyPerComp Tarek El Moselhy,YoussefM.Marzouk [email protected] Massachusetts Institute of Technology [email protected], [email protected] MS2 Nonparametric Bayesian Inference for Inverse MS2 Problems Sample-based UQ via Computational Linear Alge- bra (Not MCMC) I will consider the Bayesian approach to inverse prob- lems in the setting where Gaussian random field priors Sample-based inverse and predictive UQ has proven effec- are adopted. I will study random walk type Metropolis tive, though MCMC sampling is expensive. Several groups algorithms and demonstrate how small modifications in are now developing links between computational linear al- the standard algorithm can lead to an order of magnitude gebra and sampling algorithms with the aim of reducing speed up, in terms of the size of the discretization used. the cost of sampling. Currently these links are exact for Gaussian distributions, only, but do indicate how the more Andrew Stuart general case should look. Mathematics Institute, University of Warwick Colin Fox [email protected] University of Otago, New Zealand [email protected] MS3 Global Sensitivity Analysis with Correlated Inputs: MS2 Numerical Aspects in Distribution-Based Sensitiv- Toward Extreme-scale Stochastic Inversion ity Measures

We are interested in inferring earth models from global In this work, we address the sensitivity of model out- seismic wave propagation waveforms. This inverse prob- put utilizing density-based importance measures and a re- lem is most naturally cast as a large-scale statistical cently introduced sensitivity measures based on repeated inverse wave propagation problem in the framework of Kolmogorov-Smirnov Test. We offer a comparison of the Bayesian inference. The complicating factors are the high- two statistics which, as we are to see, are closely related. dimensional parameter spaces (due to discretization of We show that they hare closely related. We then show that infinite-dimensional parameter fields) and very expensive they can be estimated from given samples. We use this fact forward problems (in the form of 3D elastic-acoustic cou- to study their estimation in the presence of correlations. pled wave propagation PDEs). Here we present a so-called Numerical results for examples in which the analytical so- stochastic Newton method in which MCMC is accelerated lution is known are discussed. by constructing and sampling from a proposal density that builds a local Gaussian approximation based on local gradi- Emanuele Borgonovo ent and Hessian (of the log posterior) information. Hessian Bocconi University (Milan) manipulations (inverse, square root) are made tractable by ELEUSI Research Center a low rank approximation that exploits the compact nature [email protected] of the data misfit operator. This amounts to a reduced model of the parameter-to-observable map. We apply the method to 3D seismic inverse problems with several million MS3 parameters, illustrating the efficacy and scalability of the Sensitivity Indices Based on a Generalized Func- low rank approximation. tional ANOVA

Tan Bui Functional ANOVA allows defining variance based sensitiv- University of Texas at Austin ity indices of any order in the case of independent inputs. [email protected] Under a dependence-type condition on the joint inputs dis- tribution, we derive a generalization of Hoeffding decom- Carsten Burstedde position, from which we introduce sensitivity indices of any Institut fuer Numerische Simulation order even for correlated inputs. We also propose an algo- Universitaet Bonn rithm to compute these indices in the particular case where [email protected] inputs are correlated two by two. Cl´ementine Prieur Omar Ghattas LJK / Universit´e Joseph Fourier Grenoble (France) 82 UQ12 Abstracts

INRIA Rhˆone Alpes, France terest, and has recently inspired several strategies relying [email protected] on Kriging (e.g., Stepwise Uncertainty Reduction strate- gies). An even more challenging problem is to describe Gaelle Chastiang the set of all dangerous configurations, i.e. the set of in- Project-Team INRIA MOISE put parameters such the output of interest exceeds a given Grenoble threshold T. Mathematically, if f is the response, such set [email protected] of failure is denoted by G = x : f(x) T .EstimatingG in a severely limited budget of{ evaluations≥ } of f is a difficult Fabrice Gamboa problem, and a suitable use of Kriging may help solving it Laboratory of Statistics and Probability in practice. Starting from an initial set of evaluations of f University of Toulouse at an initial Design of Experiments, one can indeed calcu- [email protected] late coverage probabilities and/or simulate Gaussian Field realizations conditionally on the available information. We propose to use such notions to sum up the current knowl- MS3 edge on the excursion set, and also to define new SUR Global Sensitivity Analysis for Systems with Inde- strategies based on decreasing some measure of variabil- pendent and/or Correlated Inputs ity of the excursion set distribution. We recently revisited classical notions of random set theory to obtain candidate Structural and Correlative Sensitivity Analysis (SCSA) “expectations’ for random sets of excursion, as well as can- provides a new unified framework of global sensitivity anal- didate quantifications of uncertainty related to the inves- ysis for systems with independent and correlated variables tigated expectation notions. In this talk we focus on the based on a covariance decomposition of the output vari- so called Vorob’ev expectation (for which there is a can- ance. Three sensitivity indices were defined to give a full didate quantification of uncertainty naturally associated) description, respectively, of the total, structural and cor- and derive a new SUR sampling criterion associated to this relative contributions of the inputs upon the output. For uncertainty. Implementation issues are discussed and the independent inputs, these indices reduce to a single index criterion is illustrated on mono and multi-dimensional ex- consistent with the variance-based method as a special case amples. of the new treatment. Chevalier Cl´ement Herschel Rabitz IRSN and UNIBE Department of Chemistry [email protected] Princeton University [email protected] David Ginsbourger Department of Mathematics and Statistics, University of Genyuan Li Bern Princeton University [email protected] genyuan [email protected] Julien Bect SUPELEC, Gif-sur-Yvette, France MS3 [email protected] Variance-based Sensitivity Indices for Models with Correlated Inputs Using Polynomial Chaos Expan- Ilya Molchanov sions Department of Mathematics and Statistics University of Bern The variance decomposition techniques used for global sen- [email protected] sitivity analysis are well established as a means for quan- tifying the uncertainty of the output of a computer model that may be attributed to each input parameter. The clas- MS4 sical framework only holds for independent input parame- Sampling Strategy for Stochastic Simulators with ters. In this paper the covariance decomposition proposed Heterogeneous Noise by Rabitz is adapted to polynomial chaos expansions of the model response in order to estimate the structural and Kriging-based approximation is a useful tool to approxi- correlative importance of each input parameter. mate the output of a Monte-Carlo simulator. Such simula- tor has the particularity to have a known relation between Bruno Sudret its accuracy and its computational cost. Our objective is Universit´eParis-Est to find a sampling strategy optimizing the tradeoff between Laboratoire Navier the fidelity and the number of simulation given a limited [email protected] computational budget when the fidelity of the M-C simu- lator depends on the value of the input space parameter. Yann Caniou, Alexandre Micol The presented strategies are illustrated on an industrial Phimeca example of neutron transport code. [email protected], [email protected] Loic Le Gratiet CEA, DAM, DIF MS4 [email protected] Quantifying and Reducing Uncertainties on a Set of Failure Using Random Set Theory and Kriging Josselin Garnier Universite Paris 7 In computer-assisted robust design and safety studies, cal- [email protected] culating probability of failures based on approximation models of the objective function is a problem of growing in- UQ12 Abstracts 83

MS4 through an adaptive refinement algorithm where simple er- Optimization of Expensive Computer Experiments ror estimates are used to independently drive refinement of Using Partially Converged Simulations and Space- the stochastic basis at each point in the physical domain. time Gaussian Processes Results will be presented comparing the performance of this method with other embedded UQ techniques. To alleviate the cost of numerical experiments, it is some- times possible to stop at early stage the convergence of a Eric C. Cyr simulation and exploit the obtained response, the gain in Scalable Algorithms Department time being at the price of convergence error. We propose Sandia National Laboratotories to model such data using a GP model in the joint space of [email protected] design parameters and computational time, and perform optimization using an EGO-like strategy with the help of a new statistic: the Expected Quantile Improvement. MS5 Simultaneous Local and Dimension Adaptive Victor Picheny Sparse Grids for Uncertainty Quantification European Center for Research and Advanced Training in Scient Polynomial methods, such as Polynomial Chaos, are often [email protected] used to construct surrogates of expensive numerical mod- els. When the response surface is smooth these techniques accurately reproduce the model variance. However when MS4 discontinuities are present or local metrics, such as proba- Models with Complex Uncertain Inputs bility of failure, are of interest the utility of these methods decreases. Here we propose a greedy, locally and dimension We consider the problem of investigating the consequences adaptive sparse grid interpolation method which restricts of an event that releases contamination into the atmo- function evaluations to dimensions and regions of interest. sphere. Simulators for such events depend on atmospheric The adaptivity is guided by a weighted local interpolation and meteorological conditions over at least a six-hour time error estimate. The proposed method is highly efficient span. For example, wind strength and direction will be in- when only a sub-region of a high-dimensional input space fluential in assessing the severity of contamination across a is important. spatial window. The common strategy for simulating these conditions is to sample observed stretches of data. We con- John D. Jakeman sider how to generate an informative sample and how to Sandia National Labs carry out the subsequent analysis. [email protected]

David M. Steinberg Stephen G. Roberts Tel Aviv University Australian National University [email protected] [email protected]

MS5 MS5 Approximation and Error Estimation in High Di- A Posteriori Error Analysis and Adaptive Sampling mensional Stochastic Collocation Methods on Ar- for Probabilities using Surrogate Models bitrary Sparse Samples Surrogate methods have grown in popularity in recent years Stochastic collocation methods are an attractive choice to for stochastic differential equations due to their high-order characterize uncertainty because of their non-intrusive na- convergence rates for moments of the solution. Oftentimes, ture. High dimensional stochastic spaces can be approxi- however, the objective is to compute probabilities of cer- mated well for smooth functions with sparse grids. There tain events, which is performed by sampling the surrogate has been a focus in extending this approach to non-smooth model. Unfortunately, each of these samples contains dis- functions using adaptive sparse grids. This presentation cretization error which affects the reliability. We apply will present both adaptive approximation methods and er- adjoint techniques to quantify the accuracy of statistical ror estimation techniques for high dimension functions. quantities by estimating the error in each sample and seek to improve the surrogate model through drive adaptive re- Rick Archibald finement. Computational Mathematics Group Oak Ridge National Labratory Tim Wildey [email protected] Sandia National Laboratory [email protected] MS5 Troy Butler Spatially Varying Stochastic Expansions for Em- Institute for Computational Engineering and Sciences bedded Uncertainty Quantification University of Texas at Austin Existing discretizations for stochastic PDEs, based on a [email protected] tensor product between the deterministic basis and the stochastic basis, treat the required resolution of uncer- MS6 tainty as uniform across the physical domain. However, solutions to many PDEs of interest exhibit spatially local- Heat Kernel Smoothing on an Arbitrary Manifold ized features that may result in uncertainty being severely Using the Laplace-Beltrami Eigenfunctions over or under-resolved by existing discretizations. In this We present a novel kernel smoothing framework on curved talk, we explore the mechanics and accuracy of using a surfaces using the Laplace-Beltrami eigenfunctions. The spatially varying stochastic expansion. This is achieved 84 UQ12 Abstracts

Green’s function of an isotropic diffusion equation is ana- formation about the surface shape. lytically represented using the Laplace-Beltrami eigenfunc- tions. The Green’s function is then used in explicitly con- Laura M. Sangalli structing heat kernel smoothing as a series expansion. Our MOX Department of Mathematics analytic approach offers many advantages over previous fil- Politecnico Milano, Italy tering methods that directly solve diffusion equations using [email protected] FEM. The method is illustrated with various surfaces ob- tained from medical images. Laura Azzimonti MOX Department of Mathematics Moo Chung Politecnico di Milano, Italy Department of Biostatistics and Medical Informatics [email protected] University of Wisconsin-Madison [email protected] James O. Ramsay McGill University, Montreal, Canada MS6 [email protected] Sparse Grids for Regression Piercesare Secchi We consider the sparse grid combination technique for re- MOX - Department of Mathematics gression, which we regard as a problem of function re- Politecnico di Milano, ITALY construction in some given function space. We use a [email protected] regularised least squares approach, discretised by sparse grids and solved using the so-called combination technique, where a certain sequence of conventional grids is employed. MS7 The sparse grid solution is then obtained by the addition of Global Sensitivity and Reduction of Very High- these partial solutions with certain predefined combination Dimensional Models with Correlated Inputs coefficients. We show why the original combination tech- nique is not guaranteed to converge with higher discreti- Models originating from observed data or from computer sation levels in this setting, but that a so-called optimised code can be very high-dimensional. Total contribution combination technique can be used instead. from model input Xi to variance of model output Y is defined as VTi =Var(Y ) Var[E(Y X i)], where X i − | − − Jochen Garcke corresponds to all inputs except Xi. We develop an effi- University of Bonn cient algorithm to compute VTi for models with thousands [email protected] of possibly correlated inputs with arbitrary distributions. The number of required model samples is independent of the number of inputs. The resulting global sensitivities MS6 VTi /Var(Y ) can be used to create a reduced model for fast Second-Order Comparison of Random Functions output prediction and uncertainty quantification. The de- veloped algorithms are implemented in our software Go- Given two samples of random square-integrable functions, SUM (Global Optimizations, Sensitivity and Uncertainty we consider the problem of testing whether they share the in Models). same second-order structure. Our study is motivated by the problem of determining whether the mechanical prop- Vladimir Fonoberov erties of short DNA loops are significantly affected by their Chief Scientist base-pair sequence. The testing problem is seen to involve AIMdyn, Inc aspects of ill-posed inverse problems and a test based on a [email protected] Karhunen-Love approximation of the Hilbert-Schmidt dis- tance of the empirical covariance operators is proposed and Igor Mezic investigated. More generally, we develop the notion of a University of California, Santa Barbara dispersion operator and construct a family of tests. Our [email protected] procedures are applied to a sample of DNA minicircles ob- tained via the electron microscope. MS7 Victor M. Panaretos Uncertainty Quantification in Energy Efficient Section de Math´ematiques Building Retrofit Design EPFL victor.panaretos@epfl.ch One area of engineering where uncertainty quantification and mitigation is not only desired, but actually necessary is energy efficient building retrofit design. Buildings are MS6 complex systems with large number of parameters that are Spatial Spline Regression Models often not properly measured and recorded (e.g. equipment efficiencies) or that have inherently large uncertainties as- We deal with the problem of surface estimation over ir- sociated with them (e.g. occupancy patterns). In this talk regularly shaped domains, featuring complex boundaries, we discuss mathematical methods and technical challenges strong concavities and interior holes. Adopting an ap- involved with UQ for retrofit design. proach typical of Functional Data Analysis, we propose a Spatial Spline Regression model that efficiently handle Slaven Peles this problem; the model also accounts for covariate infor- United Technologies Research Center mation, can comply with general conditions at the domain [email protected] boundary and has the capacity to incorporate a priori in- UQ12 Abstracts 85

MS7 the sensitivity of global cloud condensation nuclei to 37 un- Iterative Methods for Propagating Uncertainty certain process parameters and emissions. We show global through Networks of Switching Dynamical Systems maps of the total uncertainty in several aerosol quantities as well as a breakdown of the main factors controlling the Networks of switching dynamical systems arise naturally in uncertainty. These results provide a very clear guide for a vast variety of applications. These systems can be chal- the reduction in model uncertainty through targeted model lenging for analysis due to non-smooth dynamics. Here, we development. develop methods to perform uncertainty quantification on switching systems using polynomial chaos based on wavelet Lindsay Lee, Kenneth Carslaw, Kirsty Pringle expansions. Since the number of equations required scales University of Leeds exponentially, we develop novel iterative methods to simu- [email protected], [email protected], late networks of switching dynamical systems. We demon- [email protected] strate these methods on a large network of switching oscil- lators. MS8 Tuhin Sahai Sensitivity Analysis for Complex Computer Models United Technologies [email protected] We discuss the problem of quantifying the importance of uncertain input parameters in a computer model; which input parameters should we learn about to best reduce MS7 output uncertainty? Two standard tools are reviewed: NIPC: A MATLAB GUI for Wider Usability of variance-based sensitivity analysis, and decision theoretic Nonintrusive Polynomial Chaos measures based on the value of information. For compu- tationally expensive models, computational methods are Polynomial Chaos theory is a sophisticated method for presented for calculating these measures using Gaussian- a fast stochastic analysis of dynamic systems with few process surrogate models. These tools will be applied in random parameters. Classically, all system laws are re- the remaining three talks. formulated into deterministic equations, but recently, a nonintrusive variation has been developed for application Jeremy Oakley with black boxes. After a brief introduction of this concept, University of Sheffield we would like to present a tool which makes the numerous j.oakley@sheffield.ac.uk adjustments and the understanding of the advanced math- ematical roots of Polynomial Chaos irrelevant for the user. MS8 Managing Model Uncertainty in Health Economic Kanali Togawa Decision Models E.ON Energy Research Center - RWTH Aachen University Health economic models predict the costs and health ef- [email protected] fects associated with competing decision options (e.g. rec- ommend drug X versus Y). Current practice is to quantify Antonello Monti input uncertainty, but to ignore uncertainty due to defi- E.ON Energy Research Center - RWTH Aachen ciencies in model structure. Given a relatively simple but University imperfect model, is there value in incorporating additional [email protected] complexity to better describe the decision problem? We derive the ‘expected value of model improvement’ via a de- cision theoretic sensitivity analysis of model discrepancy. MS8 Mark Strong, Jeremy Oakley Speeding up the Sensitivity Analysis of an Epi- University of Sheffield demiological Model m.strong@sheffield.ac.uk, j.oakley@sheffield.ac.uk This presentation describes a probabilistic sensitivity anal- ysis of an epidemiological simulator of rotavirus. We used MS9 both advanced input screening techniques and emulator- based methods to make the process more efficient and fo- Hybrid UQ Method for Multi-Species Reactive cussed on the relevant regions of the input space. The key Transport to successfully applying these methods was the quantifi- Uncertainty quantification (UQ) for multi-physics applica- cation of expert uncertainty about the input parameters. tions is challenging for both intrusive and non-intrusive The methods for expert elicitation will be described and methods. A question naturally arises: Can we take the their use in the sensitivity analysis will be illustrated. best of both worlds to introduce a ’hybrid’ UQ method- John Paul Gosling ology for multi-physics applications? This minisymposium University of Leeds brings together researchers who are exploring hybrid UQ [email protected] methods. In particular, we emphasize techniques that propagate global uncertainties yet allow individual physics components to use their local intrusive or non-intrusive MS8 UQ methods. Relevant issues for discussions are: hybrid Sensitivity Analysis of a Global Aerosol Model to uncertainty propagation algorithms, dimension reduction, Quantify the Effect of Uncertain Model Parameters Bayesian data fusion techniques, design of hybrid computa- tional framework, and scalable algorithms for hybrid UQ. We present a sensitivity analysis of a global aerosol model using Gaussian process emulation. We present results for Xiao Chen 86 UQ12 Abstracts

Lawrence Livermore National Laboratory Maarten Arnst Center for Applied Scientific Computing Universite’ de Liege [email protected] [email protected]

Brenda Ng, Yunwei Sun, Charles Tong Paul Constantine Lawrence Livermore National Laboratory Sandia National Labs [email protected], [email protected], [email protected] [email protected]

Roger Ghanem MS9 University of Southern California Preconditioners/Multigrid for Stochastic Polyno- Aerospace and Mechanical Engineering and Civil mial Chaos Formulations of the Diffusion Equation Engineering [email protected] This talk presents (parallel) preconditioners and multigrid solvers for solving linear systems of equations arising from stochastic polynomial chaos (PC) formulations of the dif- John Red-Horse fusion equation with random coefficients. These precondi- Validation and Uncertainty Quantification Processes tioners/solvers are an extension of the preconditioner de- Sandia National Laboratories veloped in [?] for strongly coupled systems of elliptic partial [email protected] equations that are norm equivalent to systems that can be factored into an algebraic coupling component and a diag- Tim Wildey onal differential component, as is the case for the systems Sandia National Laboratory produced by PC formulations of the diffusion equation. [email protected] Barry Lee Pacific Northwest National Laboratory MS10 [email protected] First Order k-th Moment Finite Element Analysis of Nonlinear Operator Equations with Stochastic Data MS9 A High Performance Hybrid pce Framework for We develop and analyze a class of efficient algorithms for High Dimensional UQ Problems uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretiza- In the domain of stochastic multi-physics problems, tradi- tions of tensorized linearizations at nominal parameters. tional non-intrusive and intrusive UQ methods are expen- Specifically, we analyze a class of abstract nonlinear, para- sive and preclude a much-needed modular plug and play metric operator equations solver infrastructure. We present a hybrid UQ method- ology to tackle these challenges. A conditional polyno- mial representation of the stochastic solution vector is used J(α, u)=0 to track local and global uncertainty propagation between modules. The frameworks parallel efficiency and spectral for random parameters α with realizations in a neighbor- accuracy is shown using a multi-species reaction-flow prob- hood of a nominal parameter α0. Under some structural lem modeled as a non-linear PDE system. assumptions on the parameter dependence, random param- eters α(ω)=α0 +r(ω) are shown to imply a unique random Akshay Mittal solution u(ω)=S(α(ω)). We derive an operator equation Department of Mathematics for the deterministic computation of k-th order statistical Stanford University moments of the solution fluctuations u(ω) S(α0), pro- [email protected] vided that statistical moments of the random− parameter perturbation r(ω) are known. This formulation is based MS9 on the linearization in a neighborhood of a nominal pa- rameter α0. We provide precise bounds for the lineariza- Stochastic Dimension Reduction Techniques for tion error by means of a Newton-Kantorovich-type theo- Uncertainty Quantification of Multiphysics Sys- rem. We present a sparse tensor Galerkin discretization for tems the tensorized first order perturbation equation and deduce Uncertainty quantification of multiphysics systems rep- that sparse tensor Galerkin discretizations of this equation resents numerous mathematical and computational chal- converge in accuracy vs. complexity which equals, up to lenges. Indeed, uncertainties that arise in each physics in logarithmic terms, that of the Galerkin discretization of a a fully coupled system must be captured throughout the single instance of the mean field problem. whole system, the so-called curse of dimensionality. We Alexey Chernov present techniques for mitigating the curse of dimensional- University of Bonn ity in network-coupled multiphysics systems by using the [email protected] structure of the network to transform uncertainty represen- tations as they pass between components. Examples from the simulation of nuclear power plants will be discussed. Christoph Schwab ETH Zuerich Eric Phipps SAM Sandia National Laboratories [email protected] Optimization and Uncertainty Quantification Department [email protected] MS10 An Adaptive Iterative Method for UQ12 Abstracts 87

High-dimensional Stochastic PDEs provided to demonstrate the flexibility of the methods.

A new approach for constructing low-rank solutions to Akil Narayan, Dongbin Xiu stochastic partial differential equations is presented. Our Purdue University algorithm exploits the notion that the stochastic solution [email protected], [email protected] and functionals thereof may live on low-dimensional man- ifolds, even in problems with high-dimensional stochastic inputs. We use residuals of the stochastic PDE to sequen- MS11 tially and adaptively build bases for both the random and A Dynamic Programming Approach to Sequential deterministic components of the solution. By tracking the and Nonlinear Bayesian Experimental Design norm of the residual, meaningful error measures are pro- vided to determine the quality of the solution. The ap- We present a framework for optimal sequential Bayesian proach is demonstrated on Maxwell’s equations with un- experimental design, using information theoretic objec- certain boundaries and on linear/nonlinear diffusion equa- tives. In particular, we adopt a “closed-loop” approach tions with log-normal coefficients, characterized by several that uses the results of intermediate experiments to guide hundred input dimensions. In these problems, we observe subsequent experiments in a finite horizon setting. Direct order-of-magnitude reductions in computational time and solution of the resulting dynamic programming problem is memory compared to many state-of-the-art intrusive and computationally impractical. Using polynomial chaos sur- non-intrusive methods. rogates, stochastic optimization methods, and value func- tion approximations, we develop numerical tools to identify Tarek El Moselhy,YoussefM.Marzouk sequences of experiments that are optimal for parameter Massachusetts Institute of Technology inference, in a computationally feasible manner. [email protected], [email protected] Xun Huan,YoussefM.Marzouk Massachusetts Institute of Technology MS10 [email protected], [email protected] Adjoint Enhancement Within Global Stochastic Methods MS11 This presentation will explore the use of local adjoint sen- Identification of Polynomial Chaos Representations sitivities within global stochastic approximation methods in High Dimension for the purposes of improving the scalability of uncer- tainty quantification methods with respect to random di- The usual identification methods of polynomial chaos ex- mension. Methodologies of interest include generalized pansions in high dimension are based on the use of a series polynomial chaos, based on regression over unstructured of truncations that induce numerical bias. We first quan- grids; stochastic collocation, based on gradient-enhanced tify the detrimental influence of this numerical bias, we interpolation polynomials on structured grids; and global then propose a new decomposition of the polynomial chaos reliability methods, using gradient-enhanced kriging on coefficients to allow performing relevant convergence anal- unstructured grids. Efficacy of these gradient-enhanced ysis and identification with respect to an arbitrary measure approaches will be assessed based on relative efficiency for the high dimension case. (speed-up with adjoint gradient inclusion) and numerical robustness (ill-conditioning of solution or basis generation). Guillaume Perrin Universit´eParis-Est Navier (UMR 8205 ENPC-IFSTTAR-CNRS) Michael S. Eldred [email protected] Sandia National Laboratories Optimization and Uncertainty Quantification Dept. Christian Soize [email protected] University of Paris-Est MSME UMR 8208 CNRS Eric Phipps [email protected] Sandia National Laboratories Optimization and Uncertainty Quantification Department Denis Duhamel [email protected] University of Paris-Est Navier (UMR 8205 ENPC-IFSTTAR-CNRS) Keith Dalbey [email protected] Sandia National Laboratories [email protected] Christine Funfschilling SNCF Innovation and Research Department MS10 [email protected] Stochastic Collocation Methods in Unstructured Grids MS11 We present a framework for stochastic collocation method Inverse Problems for Nonlinear Systems via on arbitrary grids. The method utilizes a newly devel- Bayesian Parameter Identification oped least orthogonal interpolation theory to construct high-order polynomial approximations of the stochastic so- Inverse problems are important in engineering science and lution, based on the collocation results of any type of grids appear very frequently such as for example in estimation in arbitrary dimensions. We present both the mathemat- of material porosity and properties describing irreversible ical theory and numerical implementation. Examples are behaviour, control of high-speed machining processes etc. At present, most of identification procedures have to cope 88 UQ12 Abstracts with ill-possedness as the problems are often considered in solution and derive optimality system. Computationally, a deterministic framework. However, if the parameters are we approximate the optimality system through the dis- modelled as random variables the process of obtaining more cretizations of the probability space and the spatial space information through experiments in a Bayesian setting be- by the finite element method; we also derive error estimates comes well-posed. In this manner the Bayesian information in terms of both types of discretizations. Some numerical update can be seen as a minimisation of variance. In this experiments are given. work we use the functional approximation of uncertainty and develop a purely deterministic procedure for the up- Hyung-Chun Lee dating process. This is then contrasted to a fully Bayesian Ajou University update based on Markov chain Monte Carlo sampling on Department of Mathematics a few numerical nonlinear examples. Examples are based [email protected] on plasticity and nonlinear diffusion models. Bojana V. Rosic MS12 Institute of Scientific Computing Generalized Methodology for Inverse Modeling TU Braunschweig Constrained by SPDEs [email protected] We formulate several stochastic inverse problems to esti- Oliver Pajonk mate statistical moments (mean value, variance, covari- Institute of Scientific Computing ance) or even the whole probability distribution of input Technische Universit¨at Braunschweig data, given the PDF of some response (quantities of phys- [email protected] ical interest) of a system of SPDEs. The identification ob- jectives minimize the expectation of a tracking cost func- tional or minimize the difference of desired statistical quan- Alexander Litvinenko tities in the appropriate norms. Numerical examples illus- TU Braunschweig, Germany trate the theoretical results and demonstrate the distinc- [email protected] tions between the various objectives. Hermann G. Matthies Catalin S. Trenchea Institute of Scientific Computing Department of Mathematics Technische Universit¨at Braunschweig University of Pittsburgh [email protected] [email protected]

Anna Kucerova Max Gunzburger Faculty of Civil Engineering, Prague, Czech TU Florida State University [email protected] School for Computational Sciences [email protected] Jan Sykora Faculty of Civil Engineering Clayton G. Webster Czech Technical University in Prague Oak Ridge National Laboratory [email protected] [email protected]

MS11 MS12 Data Analysis Methods for Inverse Problems Stochastic Inverse Problems via Probabilistic Graphical Model Techniques We present exploratory data analysis methods to assess inversion estimates using examples based on l2- and l1- We build a graphical model for learning the probabilistic regularization. These methods can be used to reveal the relationship between the input and output of a multiscale presence of systematic errors s and validate modeling as- problem (e.g. crystal plasticity based deformation). The sumptions. The methods include: confidence intervals and graphical model is first learned (parameters in potential bounds for the bias, resampling methods for model vali- functions) using a set of training data and suitable op- dation, and construction of training sets of functions with timization strategies (e.g. MLE, EM, etc.). After that, controlled local regularity. by applying belief propagation algorithm, we can solve the coarse to fine scale inverse problem (e.g. find the initial mi- Luis Tenorio crostructure given desired properties) or the forward prob- Colorado School of Mines lem (e.g. find the properties resulting from a given initial [email protected] microstructure).

Nicholas Zabaras,PengChen MS12 Cornell University Analysis and Finite Element Approximations of [email protected], [email protected] Optimal Control Problems for Stochastic PDEs In this talk, we consider mathematically and computation- MS12 ally optimal control problems for stochastic partial differ- Least-Squares Estimation of Distributed Random ential equations. The control objective is to minimize the Diffusion Coefficients expectation of a cost functional, and the control is of the deterministic distributed and/or boundary value type. The We formulate a stochastic inverse problem, estimating the main analytical tool is the Karhunen-Loeve (K-L) expan- random diffusion coefficient in an elliptic PDE, as a least sion. Mathematically, we prove the existence of an optimal squares problem in the space of functions with bounded UQ12 Abstracts 89 mixed derivatives. We prove existence and define the neces- MS13 sary optimality conditions using techniques from optimiza- A Randomized Iterative Proper Orthogonal De- tion theory. In addition, the regularization of the problem composition (RI-POD) Technique for Model Iden- connects the infinite dimensional problem with its finite tification noise discretization. Numerical results that validate our theory will be presented. In this talk, we shall present a data based technique for the identification of the eigenmodes of very high dimen- Hans-Werner van Wyk sional linear systems. Our technique is based on the snap- Virginia Tech shot proper orthogonal decomposition (POD) method. We [email protected] show that using the snapshot POD with randomized forc- ing or initial conditions, in an iterative fashion, we can Jeff Borggaard extract as many of the eigenmodes of the linear system as Virginia Tech required. The technique works for symmetric as well as Department of Mathematics non-symmetric systems. [email protected] Dan Yu Texas A&M University MS13 [email protected] Challenges on Incorporating Uncertainty in Com- putational Model Predictions Suman Chakravorty Texas A&M University Bayes’ theorem allows for the treatment of uncertainties College Station, TX in the whole model prediction process. It can be used [email protected] for model calibration (either batch or real-time), ranking of scientific hypotheses formulated as mathematical mod- els, ranking of data sets according to information content, MS13 and averaging of predictions made by competing models. Sparse Bayesian Techniques for Surrogate Creation We discuss the uncertainty quantification research we have and Uncertainty Quantification been pursuing in the context of realistic models, includ- ing sampling with MCMC algorithms and emulation with We develop a multi-output, Bayesian, generalized linear re- Gaussian processes. gression model with arbitrary basis functions. The model automatically excludes redundant basis functions while Ernesto E. Prudencio providing access to the full Bayesian predictive distribu- Institute for Computational Engineering and Sciences tion of the statistics. By employing a sequentially built [email protected] tree structure, we are able to demonstrate that it is ca- pable of identifying discontinuities in the response surface. Gabriel A. Terejanu We demonstrate our claims numerically using various ba- Institute for Computational Engineering and Sciences sis functions that vary from localized kernels to numerically University of Texas at Austin build Generalized Polynomial Chaos basis. [email protected] Nicholas Zabaras Cornell University MS13 [email protected] A Stochastic Collocation Approach to Constrained Optimization for Random Data Estimation Prob- Ilias Bilionis lems Center for Applied Mathematics Cornell University, Ithaca We present a scalable, parallel mechanism for identifica- [email protected] tion of statistical moments of input random data, given the probability distribution of some response of a system of stochastic partial differential equations. To character- MS14 ize data with moderately large amounts of uncertainty, we Application of Goal-Oriented Error Estimation introduce a stochastic parameter identification algorithm Methods to Statistical Quantities of Interest that integrates an adjoint-based deterministic algorithm with the sparse grid stochastic collocation FEM. Rigor- The objective here is to present an extension of goal- ously derived error estimates are used to compare the effi- oriented methods for a posteriori error estimation to the ciency of the method with other techniques. case of stochastic problems with random parameters. We shall consider the stochastic collocation method, for which Max Gunzburger estimates of statistical moments of the error in a quantity Florida State University of interest have been proposed in the past, but will focus School for Computational Sciences on estimating the error in these moments themselves and [email protected] on accurately representing the posterior distribution of the quantity of interest. Catalin S. Trenchea Department of Mathematics Corey Bryant University of Pittsburgh The University of Texas at Austin [email protected] Institute for Computational Engineering and Sciences [email protected] Clayton G. Webster Oak Ridge National Laboratory Serge Prudhomme [email protected] ICES 90 UQ12 Abstracts

The University of Texas at Austin by exploiting the fact that it is transported by the vector [email protected] field defining the ODE. As a consequence, one can design an iterative computation based on the transport of prob- ability. This transported probability is the solution of a MS14 PDE, which is solved by an Eulerian-Lagrangian scheme Estimating and Bounding Errors in Distributions with bi-orthogonal wavelets. Propagated via Surrogate Models Nicolas J-B Brunel, Vincent Torri We consider the problem of propagating distributions Universite d’Evry through quantities of interest to differential equations with [email protected], [email protected] parameters modeled as random processes. Polynomial chaos expansions approximate random processes, and the differential equations are solved numerically. We estimate MS15 discretization error, bound truncation error, and consider Large-scale Seismic Inversion: Elastic-acoustic the effect of finite sampling in the computed distribution Coupling, DG Discretization, and Uncertainty functions for both forward and inverse problems. The re- Quantification sults are computable error bounds for distribution func- tions that we demonstrate with numerical examples. We present our recent efforts on solving globally large- scale seismic inversion. We begin by a unified frame- Troy Butler, Clint Dawson work for elastic-acoustic coupling together with an hp- Institute for Computational Engineering and Sciences nonconforming discontinuous Galerkin (DG) spectral el- University of Texas at Austin ement method. Next, consistency, stability, and hp- [email protected], [email protected] convergence of the DG method as well as its scalability up to 224k cores are presented. Finally, a method for un- Tim Wildey certainty quantification based on the compactness of the Sandia National Laboratory data mistfit is presented, followed by a brief discussion on [email protected] a variance-driven adaptivity. Tan Bui MS14 University of Texas at Austin An Adjoint Error Estimation Technique Using Fi- [email protected] nite Volume Methods for Hyperbolic Equations Carsten Burstedde Many codes exist for hyperbolic equations that employ fi- Institut fuer Numerische Simulation nite volume methods, which are often nonlinear. A method Universitaet Bonn is presented for adjoint-based a posteriori error calculations [email protected] with finite volume methods. Conditions are derived under which the error in a quantity of interest may be recovered Omar Ghattas, Georg Stadler with guaranteed asymptotic accuracy, including for nonlin- University of Texas at Austin ear forward solvers and weak solutions. We demonstrate [email protected], [email protected] the flexibility in implementation of this post-processing technique and accuracy with smooth and discontinuous so- James R. Martin lutions. University of Texas at Austin Jeffrey M. Connors Institute for Computational Engineering and Sciences Lawrence Livermore National Laboratory [email protected] Center for Applied Scientific Computing [email protected] Lucas Wilcox University of Texas at Austin Jeffrey W. Banks [email protected] Lawrence Livermore National Laboratory [email protected] MS15 Nonparametric Estimation of Diffusions: A Differ- Jeffrey A. Hittinger ential Equations Approach Center for Applied Scientific Computing Lawrence Livermore National Laboratory We consider estimation of scalar functions that determine [email protected] the dynamics of diffusion processes. It has been recently shown that nonparametric maximum likelihood estimation Carol S. Woodward is ill-posed in this context. We adopt a probabilistic ap- Lawrence Livermore Nat’l Lab proach to regularize the problem by the adoption of a prior [email protected] distribution for the unknown functional. A Gaussian prior measure is chosen in the function space by specifying its precision operator as an appropriate differential operator. MS15 We establish that a Bayesian Gaussian conjugate analy- Computation of Posterior Distribution in Ordinary sis for the drift of one-dimensional non-linear diffusions is Differential Equations with Transport Partial Dif- feasible using high-frequency data, by expressing the log- ferential Equations likelihood as a quadratic function of the drift, with suffi- cient statistics given by the local time process and the end We consider the estimation of the initial conditions of an points of the observed path. Computationally efficient pos- Ordinary Differential Equation from a noisy trajectory in terior inference is carried out using a finite element method. a Bayesian setting. The posterior distribution is computed UQ12 Abstracts 91

We embed this technology in partially observed situations Sorin Mitran and adopt a data augmentation approach whereby we it- University of North Carolina Chapel Hill eratively generate missing data paths and draws from the [email protected] unknown functional. Our methodology is applied to esti- mate the drift of models used in molecular dynamics and Sunli Tang financial econometrics using high and low frequency obser- Rensselaer Polytechnic Institute vations. We discuss extensions to other partially observed Department of Mathematical Sciences schemes and connections to other types of nonparametric [email protected] inference. Omiros Papaspiliopoulos M.J. Bayarri Department of Economics University of Velacia Universitat Pompeu Fabra [email protected] [email protected] James Berger Yvo Pokern Duke University Department of Statistical Science, UCL [email protected] [email protected] Murali Haran Gareth O. Roberts Pennsylvania State University Warwick University Department of Statistics [email protected] [email protected]

Andrew M. Stuart Hans Rudolf Kuensch University of Warwick ETH Zurich [email protected] Department of Mathematics [email protected]

MS15 MS16 A Statistical Approach to Data Assimilation for Hemodynamics Improving Gaussian Stochastic Process Emulators

We discuss a Data Assimilation (DA) technique for hemo- Gaussian Stochastic Process (GASP) emulators are fast dynamics based on a Bayesian approach. DA is formulated surrogates to the output of computationally expensive sim- as a control problem minimizing a weighted misfit between ulators of complex physical processes used in many scien- data and velocity under the constraint of the Navier-Stokes tific applications. They have many advantages, but some equations. The control variable is the probability density improvements are still needed. The talk will present several function of the normal stress at the inflow; we derive sta- methods in a Bayesian context for improving the imple- tistical estimators (maximum a posteriori and maximum mentation of GASP emulators under computational con- likelihood) and confidence intervals for the velocity. We straints (including the use of large data sets) and obtaining compare statistical and deterministic estimators. statistical approximations to the computer model that are closer to the reality. Alessandro Veneziani MathCS, Emory University, Atlanta, GA Danilo Lopes [email protected] samsi [email protected] Marta D’Elia Department of Mathematics and Computer Science MS16 Emory University, Atlanta Emulating Dynamic Models: An Overview of Sug- [email protected] gested Approaches

Dynamic models are characterized by a large number of MS16 outputs in the time domain and by a strong dependence Toward Improving Statistical Components of of outputs conditional on recent past outputs. This makes Multi-scale Simulation Schemes it difficult to apply standard emulation techniques to such models. Several approaches have been suggested to over- I will describe an ongoing collaboration with Sorin Mi- come these problems. The talk will give an overview of tran and a group of statisticians to develop more so- these concepts, try to analyze which approach may be most phisticated approaches to handling some issues concern- promising under which circumstances, and identify needs ing representation of and communication between kinetic for further research. mesoscale PDFs and stochastically simulated microscale data in Mitran’s novel time-parallel Continuum-Kinetic- Peter Reichert Molecular (tpCKM) method. The mesoscale component eawag of this method can be viewed as an emulator for the mi- [email protected] croscale dynamics, and our research regards offline and on- line control of its quality. MS16 Peter R. Kramer Statistical Approximation of Computer Model Rensselaer Polytechnic Institute Department of Mathematical Sciences [email protected] 92 UQ12 Abstracts

Output aka Emulation of Simulation [email protected]

Computer model data can be used to construct a predictor Billaud Marie of the computer model output at untried inputs. Such con- GeM, LUNAM Universite, Ecole Centrale Nantes struction combined with assessment of prediction uncer- Universite de Nantes, CNRS tainty is an emulator or surrogate of the computer model. [email protected] A key strategy uses the Bayes paradigm to produce pre- dictors and quantify uncertainties. An overview of this strategy which uses gaussian stochastic processes as pri- Mathilde Chevreuil ors will include comments on connections with approaches GeM, L’UNAM Universite, Universite de Nantes such as polynomial chaos. Ecole Centrale Nantes, CNRS [email protected] Jerry Sacks National Institute of Statistical Sciences Rai Prashant, Zahm Olivier [email protected] GeM, L’UNAM Universite, Ecole Centrale Nantes [email protected] Universite de Nantes, CNRS [email protected], [email protected] MS17 Adaptive Sparse Grids for Stochastic Collocation MS17 on Hybrid Architectures PDE with Random Coefficient as a Problem in Infinite-dimensional Numerical Integration We discuss the algorithmic developments required to build a scalable adaptive sparse grid library tailored for emerg- This talk is concerned with the use of quasi-Monte Carlo ing architectures that will allow the solution of very large methods combined with finite-element methods to handle stochastic problems. We demonstrate the first results of an elliptic PDE with a random field as a coefficient. A adaptive sparse grids for hybrid systems and detail the al- number of groups have considered such problems (under gorithmic challenges that were overcome to get these tech- headings such as polynomial chaos, stochastic Galerkin and niques to work on these novel systems. stochastic collocation) by reformulating them as determin- istic problems in a high di- mensional parameter space, Rick Archibald where the dimensionality comes from the num- ber of ran- Computational Mathematics Group dom variables needed to characterise the random field. Oak Ridge National Labratory In recent joint work with Christoph Schwab (ETH) and [email protected] Frances Kuo (UNSW) we have treated a problem of this kind as one of infinite-dimensional integration - where in- tegration arises because a multi-variable expected value is MS17 a multidimensional integral - together with finite-element A Compressive Sampling Approach for the Solu- approximation in the physical space. We use recent devel- tion of High-dimensional Stochastic PDEs opments in the theory and practice of quasi-Monte Carlo integration rules in weighted Hilbert spaces, through which We discuss a non-intrusive sparse approximation approach rules with optimal properties can be constructed once the for uncertainty propagation in the presence of high- weights are known. The novel feature of this work is that dimensional random inputs. The idea is to exploit the spar- for the first time we are able to design weights for the sity of the quantities of interest with respect to a suitable weighted Hilbert space that achieve what is believed to be basis in order to estimate the dominant expansion coef- the best possible rate of convergence, under conditions on ficients using a number of random samples that is much the random field that are exactly the same as in a recent smaller than the cardinality of the basis. paper by Cohen, DeVore and Schwab on best N-term ap- Alireza Doostan proximation for the same problem. Department of Aerospace Engineering Sciences Ian H. Sloan University of Colorado, Boulder University of New South Wales [email protected] School of Mathematics [email protected] MS17 Tensor-based Methods for Uncertainty Propaga- MS18 tion: Alternative Definitions and Algorithms A Multiscale Domain Decomposition Method for Tensor approximation methods have recently received a the Solution of Stochastic Partial Differential Equa- growing attention in scientific computing for the solution tions with Localized Uncertainties of high-dimensional problems. These methods are of par- The presence of numerous localized sources of uncertain- ticular interest in the context of uncertainty quantification ties in physical models leads to high dimensional and com- with functional approaches, where they are used for the plex multiscale stochastic models. A numerical strategy is representation of multiparametric functionals. Here, we here proposed to propagate the uncertainties through such present different alternatives, based on projection or sta- models. It is based on a multiscale domain decomposition tistical methods, for the construction of tensor approxima- method that exploits the localized side of uncertainties. tions, in various tensor formats, of the solution of param- The separation of scales has the double benefit of improv- eterized stochastic models. ing the conditioning of the problem as well as the conver- Anthony Nouy gence of tensor based methods (namely Proper General- GeM, L’UNAM Universite, Ecole Centrale Nantes ized Decomposition methods) used within the strategy for University of Nantes, CNRS the separated representation of high dimensional stochastic UQ12 Abstracts 93 parametric solutions. Politecnico di Milano [email protected] Mathilde Chevreuil GeM, L’UNAM Universite, Universite de Nantes Raul F. Tempone Ecole Centrale Nantes, CNRS Mathematics, Computational Sciences & Engineering [email protected] King Abdullah University of Science and Technology [email protected] Anthony Nouy GeM, L’UNAM Universite, Ecole Centrale Nantes University of Nantes, CNRS MS18 [email protected] Solving Saddle Point Problems with Random Data

Safatly Elias Stochastic Galerkin and stochastic collocation methods LUNAM Universite, Ecole Centrale Nantes, GeM are becoming increasingly popular for solving (stochastic) [email protected] PDEs with random data (coefficients, sources, boundary conditions, domains). The former usually require the so- lution of a large, coupled linear system of equations while MS18 the latter require the solution of a large number of small Greedy Algorithms for Non Symmetric Linear systems which have the dimension of the corresponding Problems with Uncertainty deterministic problem. Although many studies on positive definite problems with random data can be found in the lit- Greedy algorithms, also called Progressive Generalized De- erature, there is less work on stochastic saddle point prob- composition algorithms, are known to give very satisfactory lems, both in terms of approximation theory, and solvers. results for the approximation of the solution of symmetric In this talk, we discuss some of the approximation theory uncertain problems with a large number of random param- and linear algebra issues involved in applying stochastic eters. Indeed, their formulation leads to discretized prob- Galerkin and collocation schemes to saddle point problems lems whose complexity evolves linearly with respect to the with random data. Model problems that will be used to il- number of parameters, while avoiding the curse of dimen- lustrate the main points, include: 1) a mixed formulation of sionality. However, naive adaptations of these methods a second-order elliptic problem (with random diffusion co- to non-symmetric problems may not converge towards the efficient), 2) the steady-state Navier-Stokes equations (with desired solution. In this talk, different versions of these al- random viscosity) and 3) a second-order elliptic PDE on a gorithms will be presented, along with convergence results. random domain, solved via the fictitious domain method. Virginie Ehrlacher Catherine Powell CERMICS - Ecole des Ponts Paristech / INRIA School of Mathematics [email protected] University of Manchester [email protected]

MS18 Optimized Polynomial Approximations of PDEs MS19 with Random Coefficients Optimization and Model Reduction for Parabolic PDEs with Uncertainties We consider the problem of numerically approximating sta- tistical moments of the solution of a partial differential Optimization of time-dependent PDEs with uncertain co- equation (PDE), whose input data (coefficients, forcing efficients is expensive, because the problem size depends terms, boundary conditions, geometry, etc.) are uncertain on the spatial and temporal discretization, and on sam- and described by a finite or countably infinite number of pling of the uncertainties. I analyze an approach based on random variables. This situation includes the case of in- stochastic collocation and model reduction, which are used finite dimensional random fields suitably expanded in e.g to decouple the subproblems and reduce their sizes. For a Karhunen-Lo`eve or Fourier expansions. We focus on poly- class of problems and methods, I prove an estimate for the nomial chaos approximations of the solution with respect to error between the full and the reduced order optimization the underlying random variables by either Galerkin projec- problem. Numerical illustrations are provided. tion; Collocation on sparse grids of Gauss points or discrete projection using random evaluations. We discuss in partic- Matthias Heinkenschloss ular the optimal choice of the polynomial space for linear Department of Computational and Applied Mathematics elliptic PDEs with random diffusion coefficient, based on Rice University a-priori estimates. Numerical results showing the effective- [email protected] ness and limitations of the approaches will be presented. Joakim Beck MS19 Applied Mathematics and Computational Science A Stochastic Galerkin Method for Stochastic Con- KAUST, Saudi Arabia trol Problems [email protected] We examine a physical problem, fluid flow in porous me- dia, which is represented by a stochastic PDE. We first give Fabio Nobile a priori error estimates for an optimization problem con- EPFL strained by the physical model. We then use the concept fabio.nobile@epfl.ch of Galerkin finite element methods to establish a numerical algorithm to give approximations for our stochastic prob- Lorenzo Tamellini lem. Finally, we develop original computer programs based MOX, Department of Mathematics on the algorithm and present several numerical examples 94 UQ12 Abstracts of various situations. with Intermittent Instabilities

Jangwoon Lee Methods based on truncated Polynomial Chaos Expansion University of Mary Washington (PCE) have been a popular tool for probabilistic uncer- [email protected] tainty quantification in complex nonlinear systems. We show rigorously that truncated PCE have fundamental lim- Hyung-Chun Lee itations for UQ in systems with intermittently positive Lya- Ajou University punov exponents, leading to non-realizability of probability Department of Mathematics densities and even a blow-up at short times of the second- [email protected] order statistics. Simple unambiguous examples are used to illustrate these limitations.

MS19 Michal Branicki Optimal New York University Control of Stochastic Flow Using Reduced-order [email protected] Modeling Andrew Majda We explore an stochastic optimal control problem for in- Courant Institute NYU compressible flow by using reduced-order modeling (ROM) [email protected] based on proper orthogonal decomposition (POD). The POD basis is constructed via a set of “snapshots’ obtained by sampling the solution of the Navier-Stokes system at MS20 several time instants and over several independent real- Physics-based Auto- and Cross-Covariance Models izations of the random data. Then, the stochastic ROM for Gaussian Process Regression is constructed via a Galerkin method with respect to the POD basis. Gaussian process analysis of systems with multiple out- puts is limited by the fact that far fewer good classes of Ju Ming covariance functions exist compared with the single-output Florida State University case. We propose analytical and numerical auto- and cross- [email protected] covariance models, which take a form consistent with phys- ical laws governing the underlying simulated process, and Max Gunzburger are suitable when performing uncertainty quantification Florida State University or inferences on multidimensional processes (co-kriging). School for Computational Sciences High-order closures are also derived for nonlinear depen- [email protected] dencies among the observables. Emil M. Constantinescu, Mihai Anitescu MS19 Argonne National Laboratory An Mathematics and Computer Science Division Efficient Sparse-Grid-Based Method for Bayesian [email protected], [email protected] Uncertainty Analysis We develop an efficient sparse-grid (SG) Bayesian approach MS20 for quantifying parametric and predictive uncertainty of Covariance Approximation Techniques in Bayesian physical systems constrained by stochastic PDEs. An ac- Non-stationary Gaussian Process Models curate surrogate posterior density is constructed as a func- tion of polynomials using SG interpolation and integration. Bayesian Gaussian processes have been widely used in It improves the simulation efficiency by accelerating the spatial statistics but face tremendous computational chal- evaluation of the posterior density without losing much ac- lenges for very large data sets. The full rank approximation curacy, and by determining an appropriate alternative den- is among the best approximation techniques used recently sity which is easily-sampled and captures the main features in statistics to deal with large spatial dataset. This tech- of the exact posterior density. nique is successfully applied in stationary spatial processes where the data are reasonably considered stationary but Guannan Zhang been tried with real non-stationary large spatial datasets. Florida State University The goal of this presentation is to generalize this method. [email protected] Bledar Konomi, Guang Lin Pacific Northwest National Laboratory Max Gunzburger [email protected], [email protected] Florida State University School for Computational Sciences [email protected] MS20 Inertial Manifold Dimensionality Finite-time In- Ming Ye stabilities in Fluid Flows Department of Scientific computing Florida State University We examine the geometry of the inertial manifold associ- [email protected] ated with fluid flows and relate its nonlinear dimensional- ity to energy exchanges among different dynamical compo- nents. Using dynamical orthogonality we perform efficient MS20 order-reduction and we prove and illustrate in 2D Navier- Fundamental Limitations of Polynomial Chaos Ex- Stokes that the underlying mechanism responsible for the pansions for Uncertainty Quantification in Systems finite dimensionality of the inertial manifold is, apart from UQ12 Abstracts 95 the viscous dissipation, the reverse flow of energy from Information Sciences Group large to small scales. We discuss implications on data as- Los Alamos National Laboratory similation schemes. [email protected]

Themistoklis Sapsis New York University MS21 [email protected] Sliced Cross-validation for Surrogate Models

Multi-fold cross-validation is widely used to assess the ac- MS21 curacy of a surrogate model. Despite its popularity, this A Matrix-Free Approach for Gaussian Process method is known to have high variability. We propose Maximum Likelihood Calculations a method, called sliced cross-validation, to mitigate this drawback. It uses sliced space-filling designs to construct In Gaussian processes analysis, the maximum likelihood structured cross-validation samples such that the data for approach for parameter estimation is limited by the use of each fold are space-filling. Numerical examples and the- the Cholesky factorization on the covariance matrix in com- oretical results will be given to illustrate the proposed puting the likelihood. In this work, we present a stochas- method. tic programming reformulation with convergence estimates for solving the maximum likelihood problem for large scale Peter Qian data. We demonstrate that the approach scales linearly University of Wisconsin - Madison with an increase in the data size on a desktop machine, [email protected] and show some preliminary results on supercomputers with parallel processing. Qiong Zhang Department of Statistics Jie Chen University of Wisconsin-Madison Argonne National Lab [email protected] [email protected]

MS22 MS21 Simulation Informatics Sequential Optimization of a Computer Model: Whats So Special about Gaussian Processes Any- Modern physical simulations produce large amounts of way? data. Proper uncertainty quantification on such data sets requires scalable, fault tolerant methods for feature extrac- In computer experiments, statistical models are commonly tion and machine learning. We frame the statistical ques- used as surrogates for slow-running codes. In this talk, the tions arising from uncertainty quantification as a machine usually ubiquitous Gaussian process models are nowhere learning problem, which leverages existing work in infor- to be seen, however. Instead, an adaptive nonparamet- matics. We focus particularly on scalable model reduction ric regression model (BART) is used to deal with nasty and surrogate modeling for parameterized simulations – a nonstationarities in the response surface. By providing common scenario in uncertainty quantification. both point estimates and uncertainty bounds for predic- tion, BART provdes a basis for sequential design criteria David F. Gleich to find optima with few function evaluations. Sandia National Labs [email protected] Hugh Chipman Acadia University, Canada [email protected] MS22 Scientific Data Mining Techniques for Extracting Pritam Ranjan Information from Simulations Acadia University [email protected] Techniques from scientific data mining have long been used for the analysis of data from various domains including astronomy, remote sensing, materials science, and simula- MS21 tions of turbulence in fluids and plasma. In this talk, I Extracting Key Features of Physical Systems for will present some of my work in classification of orbits in Emulation and Calibration Poincare plots in fusion simulations, analysis of coherent structures in Rayleigh-Taylor instability, and comparison Many physical models, such as material strength models, of experiments and simulations in Richtmyer-Meshkov in- rely on a large number of parameters describe the phys- stability. ical system over a large range of possible input settings. However, for particular model based prediction, the phys- Chandrika Kamath ical complexity of the system is much reduced, and as a Lawrence Livermore National Laboratory result, the effective physical model needed to make predic- [email protected] tions may be described by a few functions of the parameters (which we call feature).We present an example where physi- cal understanding and its implementation in the predictive MS22 computer code suggest a particular function of material Machine Learning to Recognize Phenomena in strength to focus on. This allows us to greatly reduce the Large Scale Simulations dimensionality and non-linearity of the problem, making emulation and calibration a much simpler task. Clustering, classification, and anomaly detection are among the most important problems in machine learning. Nicolas Hengartner The existing methods usually treat the individual data 96 UQ12 Abstracts points as the object of consideration. Here we consider that characterizes the uncertainty in predictive models by a different setting. We assume that each instance corre- relying on the dominant subspace occupied by a Quan- sponds to a group of data points. Our goal is to estimate tity of Interest. Orders of magnitude reduction in requi- the distances between these groups and use them to create site representation and associated computational costs are new clustering and classification algorithms, and recognize achieved in this manner. We demonstrate the methodology phenomena in large scale simulations. on an elliptic problem describing an elastically deforming body. Barnabas Poczos Carnegie Mellon University Roger Ghanem [email protected] University of Southern California Aerospace and Mechanical Engineering and Civil Engineering MS22 [email protected] Extracting Non-conventional Information in Simu- lation of Chaotic Dynamical Systems Ramakrishna Tippireddy University of Southern California Many state-of-the-art large scale simulations are chaotic. [email protected] Examples include turbulent fluid flows using techniques such as direct numerical simulation or large eddy simula- tion, protein folding using molecular dynamics, and nu- MS23 clear fusion engineering using plasma dynamics simula- Adaptive Basis Selection and Dimensionality Re- tion. Performing these simulations often produces very duction with Bayesian Compressive Sensing large amounts of data; however, to extract physical in- sight and understanding from the result of the simulation Bayesian inference is implemented to obtain a polynomial is nontrivial. This talk focuses on a method of extracting chaos expansion for the response of a complex model, given non-conventional information, such as robustness, sensitiv- a sparse set of training runs. For polynomial basis reduc- ity and quantified uncertainty, from the data produced by tion, Bayesian compressive sensing is employed to detect chaotic simulations. We will discuss methods for identify- basis terms with strong impact on model output via rele- ing the attractor of the chaotic simulation, and introduce vance vector machine. Furthermore, a recursive algorithm the attractor-Fokker-Planck equation that governs the er- is proposed to determine the optimal set of basis terms. godic density on the attractor. We then will introduce our The methodology is applied to global sensitivity studies of Monte Carlo solver for the adjoint of the Fokker-Planck the Community Land Model. equation, which can be used to compute the robustness and sensitivity of the chaotic simulation with respect to Khachik Sargsyan, Cosmin Safta, Robert D. Berry possible parameter changes. Finally, we will show how the Sandia National Laboratories resulting sensitivity can be used for uncertainty quantifi- [email protected], [email protected], cation. [email protected]

Qiqi Wang Bert J. Debusschere Massachusetts Institute of Technology Energy Transportation Center [email protected] Sandia National Laboratories, Livermore CA [email protected] MS23 Distinguishing and Integrating Aleatoric and Epis- Habib N. Najm temic Variation in UQ Sandia National Laboratories Livermore, CA, USA Much of UQ to date has focused on determining the effect [email protected] of variables modeled probabilistically, with known distri- butions. We develop methods to obtain information on a Daniel Ricciuto, Peter Thornton system when the distributions of some variables are known Oak Ridge National Laboratory exactly, while others are known only approximately. We [email protected], [email protected] use the duality between risk-sensitive integrals and rela- tive entropy to obtain bounds on performance measures over families of distributions. These bounds are computed MS23 using polynomial chaos techniques. Stochastic Collocation Methods for Stochastic Dif- ferential Equations Driven by White Noise Kenny Chowdhary Brown University We propose stochastic collocation methods for time- [email protected] dependent stochastic differential equations (SDEs) driven by white noise. To control the increasing dimensionality Jan S. Hesthaven in random space generated by the increments of Brownian Brown University motion, we approximate Brownian motion with its spectral Division of Applied Mathematic expansion. We also use sparse grid techniques to further [email protected] reduce the computational cost in random space. Numeri- cal examples shows the efficiency of the proposed methods. In particular, our proposed methods can run up to moder- MS23 ately large time with proper schemes in physical space and Stochastic Basis Reduction by QoI Adaptation time.

We describe a new stochastic model reduction approach Zhongqiang Zhang Brown University UQ12 Abstracts 97 zhongqiang [email protected] MS24 Computation of the Second Order Wave Equation George E. Karniadakis with Random Discontinuous Coefficients Brown University Division of Applied Mathematics In this talk we propose and analyze a stochastic collocation george [email protected] method for solving the second order wave equation with a random wave speed and subjected to deterministic bound- Boris Rozovsky ary and initial conditions. The speed is piecewise smooth Brown University in the physical space and depends on a finite number of ran- Boris [email protected] dom variables. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product MS24 orthogonal polynomials (Gauss points) in the probability Probabilistic UQ for PDEs with Random Data: A space. This approach leads to the solution of uncoupled Case Study deterministic problems as in the Monte Carlo method. We consider both full and sparse tensor product spaces of or- We present a case study for probabilistic uncertainty quan- thogonal polynomials. We provide a rigorous convergence tification (UQ) applied to groundwater flow in the context analysis and demonstrate different types of convergence of of site assessment for radioactive waste disposal based on the probability error with respect to the number of colloca- data from the Waste Isolation Pilot Plant (WIPP) in Carls- tion points for full and sparse tensor product spaces and un- bad, New Mexico. In this context, the primary quantity of der some regularity assumptions on the data. In particular, interest is the time it takes for a particle of radioactivity to we show that, unlike in elliptic and parabolic problems, the be transported with the groundwater from the repository solution to hyperbolic problems is not in general analytic to man’s environment. The mathematical model consists with respect to the random variables. Therefore, the rate of a stationary diffusion equation for the hydraulic head of convergence may only be algebraic. An exponential/fast in which the hydraulic conductivity coefficient is a random rate of convergence is still possible for some quantities of field. Once the (stochastic) hydraulic head is computed, interest and for the wave solution with particular types of contaminant transport can be modelled by particle trac- data. We present numerical examples, which confirm the ing in the associated velocity field. We compare two ap- analysis and show that the collocation method is a valid proaches: Gaussian process emulators and stochastic col- alternative to the more traditional Monte Carlo method for location combined with geostatistical techniques for deter- this class of problems. We also present extensions to the mining the parameters of the input random field’s prob- elastic wave equation. ability law. The second approach involves the numerical solution of the PDE with random data as a parametrized Mohammad Motamed deterministic system. The calculation of the statistics of KAUST the travel time from the solution of the stochastic model is [email protected] formulated for each of the methods being studied and the results compared. Fabio Nobile EPFL Oliver G. Ernst fabio.nobile@epfl.ch TU Bergakademie Freiberg Fakultaet Mathematik und Informatik Raul F. Tempone [email protected] Mathematics, Computational Sciences & Engineering King Abdullah University of Science and Technology [email protected] MS24 Proper Generalized Decomposition for Stochastic Navier-Stokes Equations MS24 A Predictor-corrector Method for Fluid Flow Ex- We propose an application of the Proper Generalized De- hibiting Uncertain Periodic Dynamics composition to the stochastic Navier-Stokes equations in the incompressible regime. The method aims at deter- Generalized Polynomial Chaos (gPC) is known to exhibit mining the dominant components of the stochastic flow by computational difficulties in context of dynamical systems means of suitable reduced bases approximations. The de- involving random coefficients. This can in particular be terministic reduced basis is here constructed using Arnoldi- attributed to the broadening of the solution spectrum as type iterations, which involve the resolution of a series of time evolves. In this work, an iterative numerical method deterministic problems whose structure is similar to the is developed to the computation of almost surely stable original deterministic Navier-Stokes equations such that limit cycles for the incompressible Navier-Stokes equations classical solvers can be re-used. The stochastic solution subject to random inflow boundary conditions. It relies on is then approximated in the reduced space of determin- the reformulation of the model equations in terms of an istic modes by means of a Galerkin projection, yielding uncertain period, which involves a rescaling of the physical a low dimensional set of coupled quadratic equations for time variable. Based on the scaled version, a predictor step the stochastic coefficients. The efficiency of the method estimates the period with respect to a deterministic refer- will be illustrated and its computational complexity will ence solution. Afterwards, a convex optimization problem be contrasted with the classical Galerkin Polynomial Chaos is solved to obtain a stochastic correction term to ensure a method. Computation of the reduced solution residual and minimal distance between an initial and terminal state of of the stochastic pressure field will also be discussed. the trajectory almost surely. An inexact Newton method provides a correction for the initial state such the distance Olivier LeMaitre can be decreased even further. The developed numerical LIMSI-CNRS method is applied to a benchmark problem given by a flow [email protected] 98 UQ12 Abstracts around a circular domain subject to uniformly distributed MS25 inflow boundary conditions. The numerical results demon- Toward Transparency and Refutability in Environ- strate the ability of capturing almost surely stable limit mental Modeling cycles with high accuracies, characterized by a vortex shed- ding scheme with an uncertain period. Environmental models would be made more effective by establishing a base set of model fit, sensitivity, and uncer- Michael Schick tainty measures. Reporting the results of this base set Karlsruhe Institute of Technology of methods consistently, along with any other methods [email protected] considered and as innovations in model analysis continue, would improve model transparency and refutability. This Vincent Heuveline work proposes two base set of methods: base set I for all Institute for Applied and Numerical Mathematics models; base set II for models with shorter execution times Karlsruhe Institute of Technology, Universit¨at Karlsruhe [email protected] Mary Hill USGS Olivier LeMaitre [email protected] LIMSI-CNRS [email protected] Dmitri Kavetski Faculty of Engineering and Built Environment The University of Newcastle Australia MS25 [email protected] Uncertainty Analysis in the Florida Public Hurri- cane Loss Model Martyn Clark National Center for Atmospheric Research The Florida Public Hurricane Loss Model was developed University of Colorado Boulder for the purpose of predicting annual insured hurricane loss [email protected] in the state of Florida. The model is an open public model comprised of atmospheric science, engineering, and actuar- Ming Ye ial science components and it serves as a benchmark against Department of Scientific computing existing proprietary commercial models. This talk will Florida State University present statistical techniques used to validate the model [email protected] with a focus on the uncertainty and sensitivity analysis for the loss costs. Mazdak Arabi Sneh Gulati Departmet of Civil and Environmental Engineering Department of Mathematics and Statistics Colorado State University Florida International University [email protected] gulati@fiu.edu Laura Foglia Shahid S. Hamid, Golam Kibria University of California Davis Florida International University [email protected] hamids@fiu.edu, golam.kibria@fiu.edu Steffen Mehl Steven Cocke Department of Civil Engineering Center for Ocean-Atmospheric Prediction Studies California State University Chico The Florida State University smehl @ csuchico.edu [email protected] MS25 Mark D. Powell Atlantic Oceanographic and Meteorological Laboratory Quantifying and Reducing Uncertainty through National Oceanic and Atmospheric Administration Sampling Design [email protected] Uncertainty reduction for geo-sphere based projects relies on data collection. A variety of performance measures and Jean-Paul Pinelli associated sample-designs have been proposed. These de- Civil Engineering Department signs are evaluated on a test problem with a focus on adap- Florida Institute of Technology tive sampling where information from previous samples is pinelli@fit.edu used to identify future sample locations. Example appli- cations of sampling design in from CO2 sequestration and Kurtis R. Gurley ground water contaminant detection are presented. Department of Civil and Coastal Engineering University of Florida Sean A McKenna [email protected]fl.edu Sandia National Laboratories [email protected] Shu-Ching Chen School of Computing and Information Sciences Jaideep Ray Florida International University Sandia National Laboratories, Livermore, CA chens@cs.fiu.edu [email protected]

Bart G. Van Bloemen Waanders UQ12 Abstracts 99

Sandia National Laboratories estimates). [email protected] Sankaran Mahadevan Vanderbilt University MS25 [email protected] Uncertainty Quantification of Shallow Groundwa- ter Impacts due to CO2 Sequestration You Ling Department of Civil and Environmental Engineering A suite of numerical tools including multi-phase and multi- Vanderbilt University component reactive transport modeling, uncertainty quan- [email protected] tification and risk assessment are used to develop risk pro- files for the National Risk Assessment Program for CO2 Se- Joshua Mullins, Shankar Sankararaman questration. Two quantities, pH and total dissolved solids, Vanderbilt University were chosen as proxies for assessing shallow groundwater [email protected], impacts due to CO2 and brine leakage in to the shallow [email protected] aquifer. A 3D flow and transport model of the Edwards aquiferisusedasasiteexample. MS26 Daniel M. Tartakovsky University of California, San Diego UQ in MD Simulations: Forward Propagation and [email protected] Parameter Inference This work focuses on quantifying uncertainty in molecular Hari Viswanathan dynamics (MD) simulations of TIP4P water accounting for Earth and Environmental Sciences Division intrinsic noise and parametric uncertainty. A functional Los Alamos National Laboratory relationship between selected macroscale observables and [email protected] uncertain atomistic model parameters is constructed via polynomial chaos expansions using a non-intrusive spectral Elizabeth Keating, Zhenxue Dai projection and a Bayesian inference approach. These PC Los Alamos National Laboratory representations are then exploited in an inverse problem [email protected], [email protected] involving the estimation of force-field parameters of the TIP4P model using bulk-phase properties of water. Rajesh Pawar Earth and Environmental Sciences Division Francesco Rizzi Los Alamos National Laboratory Department of Mechanical Engineering [email protected] Johns Hopkins University [email protected]

MS26 Omar M. Knio Random Fluctuations in Homogenization Theory; Duke University How Stochasticity Propagates Through Scales [email protected]

The influence of small scale fluctuations on the solutions of Habib N. Najm partial differential equations (PDE) is relatively well under- Sandia National Laboratories stood at the most macroscopic level, ie the homogenization Livermore, CA, USA level describing the ensemble average of the PDE solution. [email protected] Many uncertainty quantification contexts require that we understand, at least qualitatively, the random fluctuations Bert J. Debusschere of the PDE solution. Much less is known from the the- Energy Transportation Center oretical standpoint. This talk will review some existing Sandia National Laboratories, Livermore CA theories. [email protected] Guillaume Bal Columbia University Khachik Sargsyan Department of Applied Physics and Applied Mathematics Sandia National Laboratories [email protected] [email protected]

Maher Salloum MS26 Sandia National Laboratories Uncertainty Quantification in Multi-Scale, Multi- Scalable & Secure Systems Research Department Physics MEMS Performance Prediction [email protected]

This presentation describes a Bayes network approach to Helgi Adalsteinsson perform comprehensive uncertainty quantification in multi- Sandia National Laboratories, Livermore CA scale, multi-physics model prediction for a MEMS device. [email protected] The device performance is related to membrane deflection, affected by multiple physics: creep, damping, contact, and dielectric charging. The Bayes network is able to integrate MS26 epistemic and aleatory uncertainty information from multi- Quantifying Sampling Noise and Parametric Un- ple sources and activities (modeling, experiments, experts, certainty in Coupled Atomistic-Continuum Simu- calibration, verification, validation) and multiple formats (full distributions, sparse data, imprecise data, noise, error 100 UQ12 Abstracts lations a parellelized MCMC algorithm. Our approach handles datasets too massive to fit on any single data repository, We perform a coupled atomistic-to-continuum simulation and scales linearly in the number of processor cores. in a model operating under uncertainty. This latter has the form of parametric uncertainty and sampling noise in- Matthew Pratola trinsic in atomistic simulations. We present mathematical Los Alamos National Laboratory formulations that enable the propagation of uncertainty [email protected] between the discrete and continuum components and the solution of the exchanged variables in terms of polynomial chaos expansion. We consider a simple Couette flow model MS27 where the variable of interest is the wall velocity. Results High Performance Bayesian Assessment of Earth- show convergence of the exchanged variables at a reason- quake Source Models for Ground Motion Simula- able computational cost. tions Maher Salloum Reliable ground motion predictions, with quantified uncer- Sandia National Laboratories tainty, are very important for designing large civil struc- Scalable & Secure Systems Research Department tures. Using Bayesian analysis, we rank candidate kine- [email protected] matic earthquake model classes by comparing their com- puted quantities of interest (e.g. peak ground velocity, Khachik Sargsyan spectral acceleration) against reference attenuation rela- Sandia National Laboratories tions. The candidate model classes differ on hypotheses [email protected] about the physical parameters involved. We report results and give an overview of state of the art parallel statistical Reese Jones algorithms we have been researching. Co-author Ernesto E. Prudencio [email protected] Institute for Computational Engineering and Sciences [email protected] Bert J. Debusschere Energy Transportation Center Sandia National Laboratories, Livermore CA MS27 [email protected] Use of Gaussian Process Modeling to Improve the Perez Model in the Study of Surface Irradiance of Habib N. Najm Buildings Sandia National Laboratories Livermore, CA, USA In building energy simulations, a model due to Perez is [email protected] used to calculate the irradiance received by a tilted surface of a building based on the measurements of the irradiance Helgi Adalsteinsson on a horizontal surface. However, it is known that the pre- Sandia National Laboratories, Livermore CA diction from this model can have a substantial discrepancy [email protected] from the real measurement on a tilted surface. We treat this discrepancy as an integral of an unknown function over the space of the sky dome, and use Gaussian Process to MS27 model the integrated values in each small rectangular grid Evaluation of Mixed Continuous-Discrete Surro- of the sky dome. Nugget is used to stabilize the parameter gate Approaches estimation. Results from different scales of the grid are presented to illustrate this new approach. Evaluating the performance of surrogate modeling ap- proaches is essential for determining their viability in un- Heng Su certainty analysis. To this end, we evaluated categorical re- Georgia Tech gression, ACOSSO splines, Gaussian processes (GPs) with [email protected] specialized covariance models, and treed GPs on a set of test functions. We describe our evaluation principles and MS28 metrics, the characteristics of the test functions considered, and our software testbed. Additionally, we present our nu- Uncertainty Quantification of Building Energy merical results and discuss our observations regarding the Models merits of each approach. We discuss the NSF funded EFRI-SEED project for risk Patricia D. Hough conscious methods in the design and retrofit of buildings Sandia National Laboratories focusing on the quantification of parameter uncertainty in [email protected] building energy models, at different system scales and dif- ferent model fidelities. The UQ of the most sensitive pa- rameters is discussed and their influence on building per- MS27 formance predictions is demonstrated. A discussion of how Large-scale Surrogate Models the translation of uncertainties in risk measures will inform design and retrofit decisions concludes the presentation. The Bayesian Additive Regression Tree (BART) is a sta- tistical model that represents observed data as a sum of Godfried Augenbroe weak learners. Each tree represents a weak learner, and College of Architecture the overall model is a sum of such trees. In this work, we Georgia Institute of Technology extend the BART model to handle massive datasets using [email protected] UQ12 Abstracts 101

MS28 ciency applications. An Integrated Approach to Design and Operation of High Performance Buildings in the Presence of Charles Tong Uncertainty Lawrence Livermore National Laboratory [email protected] In this talk we introduce how to use uncertainty quantifi- cation to leverage the design and operation of high perfor- mance buildings. As buildings contain thousands of param- MS29 eters (from the way they are designed to the way they are Application of the Implicit Particle Filter to a occupied and operated), efficient parameter management Model of Nearshore Circulation and identification of critical parameters is the key. We dis- cuss uncertainty and sensitivity analysis in the context of Data assimilation is properly viewed as an exercise in con- ditional probabilities. Models of the ocean and atmosphere an integrated design process including model calibration, 5 7 optimization, and failure mode analysis. have typical state dimensions of O(10 10 ), so direct cal- culation of the relevant pdfs is not practical− and we must Bryan Eisenhower apply Monte-Carlo methods. We present results from an UCSB efficient Monte-Carlo method in which the conditional pdf [email protected] is sampled directly. We show applications of the method to high dimensional systems.

MS28 Robert Miller UQ for Better Commercial Buildings: From Design College of Oceanic and Atmospheric Sciences to Operation Oregon State University, Corvallis [email protected] Commercial buildings are expensive assets characterized by long lives and significant environmental and economic impact; demanding great care in both their design as well MS29 as ongoing operation. This talk discusses UQ for the ro- Implicit Particle Filtering for Geomagnetic Data bust design of high-performance buildings, their improved Assimilation operation using model based predictive control that relies on reduced order models and extracted near optimal rule A large amount of data of the earths magnetic field has sets in the face of uncertainty in human behavior, and fault recently become available due to satellite missions. This detection and diagnosis for existing buildings. data can be used to improve the predictions of geomagnetic models and the interest in data assimilation techniques has Gregor Henze thus grown in this field. Thus far, a 4D-Var approach and University of Colorado at Boulder a Kalman filter have been considered. Here, the implicit [email protected] particle filter is applied and its performance is compared to two competing Monte Carlo algorithms.

MS28 Matthias Morzfeld Sensitivity of Building Parameters with Building Department of Mathematic Type, Climate, and Efficiency Level Lawrence Berkeley National Laboratory [email protected] As one embarks on building an energy model of an exist- ing building there are parameters that are known, some- what unknown, and very unknown. Based on the type of MS29 building, the climate it is operating in, and its energy use A Tutorial on Implicit Particle Filtering for Data intensity, the uncertainty of the simulations energy results Assimilation based on the results sensitivity to the known and unknown parameters variations. Results will be presented of several I will give an introduction to implicit sampling, a new hundred thousand simulations showing these uncertainties methodology that finds high-probability samples of multi- and their corresponding parameter sensitivities. dimensional probability densities by solving equations with a random input. The implicit sampling strategy focuses John Kennedy attention on regions of high probability and, thus, is ap- Autodesk plicable even if the state dimension is large. I will present [email protected] details of implicit sampling in connection with data assim- ilation and will provide several examples to illustrate the efficiency and accuracy of the algorithm. MS28 Uncertainty Quantification Methods for Multi- Xuemin Tu physics Applications University of Kansas Lawrence, KS 66045-7594 Uncertainty quantification is increasingly recognized as a [email protected] key component in modeling and simulation-based science and engineering. There are, however, many UQ challenges for large-scale applications including expensive model eval- MS29 uation, large parameter space with complex correlations, An Application of Rare Event Tools to a Bimodal highly nonlinear models, diverse data sources for calibra- Ocean Current Model tion, model-form uncertainties, etc. This talk surveys current techniques for these challenges and also describes I will review some recent results on importance sampling a LLNL software package called PSUADE that captures methods for rare event simulation as well as discuss their many such techniques, may be applicable to energy effi- application to the filtering problem for a simple model of 102 UQ12 Abstracts the Kuroshio current. Assuming a setting in which both the case when the input data (coefficients, forcing terms, observation noise and stochastic forcing are present but boundary conditions, geometry, etc) are affected by large small, I will demonstrate numerically and theoretically that amounts of uncertainty. To approximate these higher di- sophisticated importance sampling techniques can achieve mensional problems we present an adaptive sparse grid very small statistical error. Standard filtering methods de- generalized stochastic collocation technique constructed teriorate in this small noise setting. from both global polynomial approximations and local mul- tiresolution decompositions. Rigorously derived error esti- Jonathan Weare mates, for the fully discrete problem, will be used to show University of Chicago the efficiency of the methods at predicting the behavior of Department of Mathematics both smooth and/or discontinuous solutions. [email protected] Clayton G. Webster Eric Vanden-Eijnden Oak Ridge National Laboratory Courant Institute [email protected] New York University [email protected] Max Gunzburger Florida State University School for Computational Sciences MS31 [email protected] Multiple Computer Experiments: Design and Modeling Fabio Nobile EPFL A growing trend in uncertainty quantification is to use mul- fabio.nobile@epfl.ch tiple computer experiments to study the same complex sys- tem. We construct a new type of design, called a sliced orthogonal array based Latin hypercube design, intended Raul F. Tempone for efficiently running such experiments. Such a design it- Mathematics, Computational Sciences & Engineering self achieves attractive uniformity and can be sliced into King Abdullah University of Science and Technology Latin hypercube designs. This sliced structure also leads [email protected] to a two-stage modeling strategy for integrating data from multiple computer experiments. MS31 Youngdeok Hwang,XuHe Uncertainty Quantification for Overcomplete Basis Department of Statistics Representation in Computer Experiments University of Wisconsin-Madison [email protected], [email protected] Overcomplete basis representation is a surrogate model formed by a linear combination of overcomplete basis func- tions. The method can be effectively used to mimic com- Peter Qian plicated and non-stationary response surfaces in computer University of Wisconsin - Madison experiments or numerical approximation. The coefficients [email protected] in the model are inferred via the matching pursuit tech- nique based on a sparse model assumption. Prediction is MS31 made based on the fitted model. Because it is a numeri- cal method without a stochastic structure, it cannot read- Efficient Analysis of High Dimensional Data in Ten- ily give an assessment of the prediction uncertainty. We sor Formats use a Bayesian approach to impose a multivariate normal In this article we introduce new methods for the analysis of prior on the collection of the coefficients in the overcom- high dimensional data in tensor formats, where the under- plete basis representation. Since this is a large dictionary, ling data come from the stochastic elliptic boundary value the prior is over a very large space. But the number of sig- problem. We approximate the high dimensional operator nificant coefficients in the representation is usually much via sums of elementary tensors. This tensors representation smaller (called effect sparsity in design of experiments). can be effectively used for computing different values of in- For a given data, we can thus collapse the large space to terest, such as maximum norm, level sets and cumulative a manageable size. This collapsing is achieved by using distribution function. As an intermediate step we describe a Bayesian variable selection technique called stochastic efficient iterative algorithms for computing the character- search variable selection. Once the Bayesian framework is istic and sign functions as well as pointwise inverse in the formulated, UQ can be readily implemented but the com- canonical tensor format. putational details need to be worked out. The proposed UQ approach can be used to simulate posterior samples for Alexander Litvinenko the predicted model, from which Bayesian credible inter- TU Braunschweig, Germany vals are constructed. Numerical study in two cases demon- [email protected] strates the success of the approach. (Based on joint work with R. B. Chen, W. C. Wang, and Rui Tuo.)

MS31 Jeff Wu An Adaptive Sparse Grid Generalized Stochastic Georgia Institute of Technology Collocation Method for High-dimensional Stochas- jeff[email protected] tic Simulations Our modern treatment of predicting the behavior of phys- MS32 ical and engineering problems relies on approximating so- Computational Nonlinear Stochastic Homogeniza- lutions in terms of high dimensional spaces, particularly in tion Using a Non-concurrent multiscale Approach UQ12 Abstracts 103 for Hyperelastic Heterogeneous Microstructures with only a few hundreds simulations and is suitable for Analysis practical complex system. Both mathematical analysis and numerical examples are provided. We present an analysis of the effects of stochastic dimension on a solver based on a tensorial product decomposition for Jing Li, Dongbin Xiu studying propagation of uncertainties in nonlinear bound- Purdue University ary value problems. An application to computational non- [email protected], [email protected] linear stochastic homogenization for hyperelastic heteroge- neous materials, where the geometry of the microstructure is random, is proposed. MS32 Hierarchical Multi-output Gaussian Process Re- Alexandre Cl´ement gression for Uncertainty Quantification with Arbi- Universit´e Paris-Est, Laboratoire Mod´elisation et trary Input Probability Distributions Simulation Multi Echelle, MSME UMR 8208 CNRS We develop an efficient, fully Bayesian, non-intrusive [email protected] framework for uncertainty quantification of computer codes. A hierarchical treed Gaussian process surrogate is Christian Soize built by adaptively decomposing the stochastic space in a University of Paris-Est sequential manner that calls upon Bayesian Experimental MSME UMR 8208 CNRS Design techniques for data gathering. The resulting surro- [email protected] gate provides point estimates as well as error-bars for the statistics of interest. We demonstrate numerically that the suggested framework can resolve local, non-isotropic fea- MS32 tures, e.g., discontinuities, slowly varying dimensions, etc. Pink and 1/f α Noise Inputs in Stochastic PDEs

We consider colored noise having a power spectrum that Ilias Bilionis decays as 1/f α,wheref denotes the frequency and α Center for Applied Mathematics (0, 2]. We study, in the context of both 1-D and 2-D differ-∈ Cornell University, Ithaca ential equations, methods for modeling random inputs as [email protected] 1/f α random fields. We show that the solutions to differen- tial equations exhibit a strong dependence on α, indicating Nicholas Zabaras that further examination of how randomness in differential Cornell University equation is modeled and simulated is warranted. [email protected] John Burkardt Department of Computational Science MS33 Florida State University Uncertainty in Geotechnical Engineering [email protected] The lecture will focus on the applications of probabilistic Max Gunzburger techniques to different problems in Geotechnical engineer- Florida State University ing. The theoretical background, including representation School for Computational Sciences of uncertainty on soil properties by means of random fields [email protected] will be briefly presented. A number of examples will illus- trate the important contribution of probabilistic techniques Miroslav Stoyanov to the assessment of geotechnical structures safety and reli- Florida State University ability and to decision taking in Geotechnical Engineering, Department of Scientific Computing including earth and rockfill dams, foundations, tunnels and [email protected] shafts. Gabriel Auvinet-Guichard MS32 Instituto de Ingenieria Universidad Nacional Autonoma de Mexico, UNAM Efficient Algorithm for Computing Rare Failure [email protected] Probability

Evaluation of failure probability is a fundamental task in MS33 many important applications such as aircraft design, risk management, etc. Mathematically it can be formulated Causality and Stochastic Processes with Varying easily as integrals. The difficulty lies in the fact that the Evidence Conditions integrals are usually of high dimensions and more impor- A methodology for introducing Causality and Stochastic tantly the geometry is irregular and known only through Processes into the probabilistic solution of inverse problems simulations of some complex systems under consideration. is presented. This is based on the representation on causal In practical applications when full-scale simulations are events by the use of Bayesian Networks when coupled time consuming, there exists no effective methods to accu- to different schemes of evidence availability. Particularly rately compute failure probability. The situation is more when evidence varies (data, model predictions and even severe when dealing with rare failure probability, i.e, fail- 5 expert’s beliefs) and this can be represented as stochastic ure probability less than 10− .Inthisworkwediscuss processes. Illustrative cases including Multi-Physics Ge- the strength and limitation of the existing popular meth- omechanics, Natural Hazards and Energy-Based Develop- ods. We further present an efficient algorithm to simulate ments are discussed. failure probability accurately at very low simulation cost. The algorithm is able to capture rare failure probability Zenon Medina-Cetina 104 UQ12 Abstracts

Zachry Department of Civil Engineering fication Needed to Support the Use of Computa- Texas A&M University tional Fluid Dynamics for Nuclear Reactor Design [email protected] and Safety Applications

Today, computational fluid dynamics (CFD) is being used MS33 extensively in support of nuclear reactor design and safety Modelling Uncertainty in Risk Assessment for Nat- analysis. Verification and Validation (VV) are the techni- ural Hazards cal tools (processes) by which CFD simulation credibility is quantified. In particular, code verification, solution veri- Optimal strategies for natural hazards risk mitigation, risk fication, and validation are coupled into an overall process analysis professionals must assess and quantify hazard, vul- for assessing the accuracy of the computed CFD solution. nerability and risk in the context of safety. These are sub- This presentation will discuss some of the specific require- ject to major uncertainties. Uncertainty in different steps ments, as well as challenges, for code verification needed to of the analysis is often categorized into alreatory (natu- support of the use of CFD for nuclear reactor design and ral variability) and epistemic (due to lack of knowledge). safety applications. Examples that illustrate how the uncertainty is modeled in quantitative risk analysis, and the shortcomings of the Hyung B. Lee existing methods, will be presented. Bettis Laboratory [email protected] Farrokh Nadim International Centre for Geohazards ICG Norwegian Geotechnical Institute NGI MS34 [email protected] Tools and Techniques for Code Verification using Manufactured Solutions MS33 Verifying computational science software using manufac- Estimation of Multiscale Fields Representing An- tured solutions requires the generation of the solutions with thropogenic CO2 Emissions from Sparse Observa- associated forcing terms and their reliable implementation tions in software. There are several issues that arise in generat- ing solutions, including ensuring that they are meaningful, We investigate spatial models of anthropogenic CO2 emis- and the algebraic complexity of the forcing terms. Ad- sions for use in inverse problems. Socioeconomic methods dressing these issues within the open source Manufactured of CO2 emissions estimation show that their spatial dis- Analytical Solution Abstraction (MASA) library, which is tribution is strongly multiscale. We investigate the use of designed to provide a reliable platform for verification with easily observed proxies e.g., images of nightlights and pop- manufactured solutions, will be discussed. ulation density for emission modeling. We consider bases drawn from them e.g. bivariate Gaussian kernels, or com- Nicholas Malaya, Roy Stogner, Robert D. Moser bine them to develop reduced wavelet representations. We University of Texas at Austin perform trade-offs between model complexity, reconstruc- [email protected], [email protected], tion accuracy and the uncertainty. [email protected]

Jaideep Ray Sandia National Laboratories, Livermore, CA MS34 [email protected] Code Verification: Practices and Perils

Bart G. Van Bloemen Waanders, Sean A McKenna As scientific codes become more complex through use of so- Sandia National Laboratories phisticated algorithms, parallelization procedures and lay- [email protected], [email protected] ers of interfaces, probability for implementation mistakes that affect the computed solution increases. In this envi- ronment, rigorous code verification through use of order- MS34 of-accuracy studies becomes essential to provide confidence Challenges in Devising Manufactured Solutions for that the intended code solves its governing equations cor- PDE Applications rectly. We will discuss a set of best practices for code ver- ification and some common issues that arise in their use. We describe some challenges we’ve encountered in devising manufactured solutions to specific PDE applications and Carol S. Woodward the ways in which the challenges were met. The applica- Lawrence Livermore Nat’l Lab tions are Darcy flow with discontinuous permeability co- [email protected] efficient, free surface flow with kinematic boundary condi- tion, the solute transport equations, and the drift-diffusion MS35 equations. The examples demonstrate the flexibility and wide applicability of manufactured solutions, along with Practical UQ for Engineering Applications with some limitations. DAKOTA

Patrick M. Knupp Through DAKOTA, we strive to deploy general-purpose Sandia National Laboratories UQ software to a broad range of engineering applica- [email protected] tions, supporting risk-informed design. Practical engineer- ing UQ methods must manage simulation cost, nonlin- earity, non-smoothness, and potentially large parameter MS34 spaces. Emerging reliability, stochastic expansion, and in- The Requirements and Challenges for Code Veri- terval estimation algorithms in DAKOTA address these challenges. These can be employed in mixed determinis- UQ12 Abstracts 105 tic/probabilistic analyses such as optimization under un- sists of a methodology and two breakthrough software suites certainty. This talk will highlight application and envi- for probabilistically tackling problems of any complexity in ronment complexities that can limit efficient uncertainty Design Engineering. Initially developed at Xerox Corpora- quantification. tion where variability of thousands of characteristics affect- ing system performance dominated product development Brian M. Adams efforts, the HPD software, in fact, liberates Applied Proba- Sandia National Laboratories bility and has exposed shortfalls of existing techniques! As Optimization/Uncertainty Quantification importantly, HPD revolutionizes Stochastic Analysis and [email protected] Optimization for manufacturing industries!

Laura Swiler Jean Parks,ChunLi Sandia National Laboratories Variability Associates Albuquerque, New Mexico 87185 [email protected], [email protected] [email protected] MS36 Michael S. Eldred Sandia National Laboratories Local-Low Dimensionality of Complex Atmo- Optimization and Uncertainty Quantification Dept. spheric Flows [email protected] We are investigating complex atmospheric flows in Owens Valley, California, using the Weather Research and Fore- MS35 casting (WRF) Model. Owens Valley is particularly in- teresting since it displays complex flows, including clear- Exact Calculations for Random Variables in Uncer- air turbulence and atmospheric rotors. We are explor- tainty Quantification Using a Computer Algebra ing whether a Local Ensemble Transform Kalman Filter System (LETKF) data assimilation scheme works well in such a The Maple-based APPL language performs exact proba- geographical setting. This work determines how small of bility calculations involving random variables. This talk an effective dimension the atmospheric dynamics reduce to introduces the langauge and presents several applications, over such a terrain. including bootstrapping, goodness-of-fit, reliability, prob- Thomas Bellsky ability distribution selection, stochastic activity networks, Michigan State University time series analysis, and transient queueing analysis. Department of Mathematics Lawrence Leemis [email protected] College of William and Mary [email protected] MS36 Assimilation of Thermodynamic Profiler Retrievals MS35 in the Boundary Layer: Comparison of Methods Open TURNS: Open source Treatment of Uncer- and Observational Error Specifications tainty, Risk ’N Statistics A 2009 National Research Council report recommended The needs to assess robust performances for complex sys- investing in a nationwide network of thermodynamic pro- tems have lead to the emergence of a new industrial sim- filing instruments for the atmospheric boundary layer to ulation challenge: to take into account uncertainties when better forecast mesoscale storm and rainfall events. In this dealing with complex numerical simulation frameworks. work, we complement the efforts of Otkin et al (2011) and Open TURNS is an Open Source software platform dedi- Hartung et al (2011) by considering variational and hy- cated to uncertainty propagation by probabilistic methods, brid data assimilation frameworks, and different approxi- jointly developed since 2005 by EDF RD, EADS Innova- mations of the retrieved observation error covariance ma- tion Works, and PhiMECA. This talk gives an overview of trices. the main features of the software from a user’s viewpoint. Sean Crowell Anne-Laure Popelin National Severe Storms Laboratory EDF R&D Norman, OK [email protected] [email protected]

Anne Dutfoy Dave Turner EDF, Clamart, France National Severe Storms Laboratory [email protected] NOAA [email protected] Paul Lematre EDF R&D MS36 INRIA Bordeaux Lagrangian Data Assimilation and Control: Hide [email protected] and Seek

Data Assimilation is the act of merging observed quan- MS35 tities of a physical system into a Mathematical model to HPD Liberates Applied Probability AND Enables provide an estimate of the state. The Lagrangian frame- Comprehensively Tackling Design Engineering work is utilised when the observations are of positions of underwater autonomous vehicles that move with the flow HPD, which stands for Holistic Probabilistic Design,con- 106 UQ12 Abstracts

field. In this talk I will incorporate the Data Assimilation to provide a quantitative measure of hazard at locations framework with techniques developed in control theory to downstream from the volcano. This approach draws on provide a novel approach in inferring on important struc- insight from the geo-science community, methods of high tures of the flow field. performance computing, and novel use of Bayesian statis- tics and mathematical modeling. Damon Mcdougall University of Warwick E. Bruce Pitman United Kingdom Dept. of Mathematics [email protected] Univ at Buffalo pitman@buffalo.edu

MS36 M.J. Bayarri Uncertainty Quantification and Data Assimilation University of Velacia in Multiscale Systems Using Stochastic Homoge- [email protected] nization

We study ensemble Kalman filtering on a low-dimensional James Berger multiscale system with fast and slow metastable regimes. Duke University We find that, surprisingly, a reduced forecast model with [email protected] stochastic parametrization of the fast dynamics can better capture transitions between slow metastable states than Eliza Calder when using the higher-dimensional, perfect deterministic University of Buffalo model. This is explained in terms of greater reliability ecalder@buffalo.edu of the ensemble or improved ensemble spread using the stochastic model. Implications for stochastic parametriza- Abani K. Patra tions in data assimilation are discussed. SUNY at Buffalo Dept of Mechanical Engineering Lewis Mitchell [email protected]ffalo.edu The University of Sydney [email protected] Elaine Spiller Marquette University Georg A. Gottwald [email protected] School of Mathematics and Statistics University of Sydney Robert Wolpert [email protected] Duke University [email protected] MS37 Overview of Volcanic Hazard Assessment MS37 Straight Monte-Carlo determination of the probability of Design and Use of Surrogates in Hazard Assess- rare catastrophic volcanic events is not possible. Our strat- ment egy uses a GaSP emulator to determine the region of the It is the rare, but large volume events that will cause some input space defining the catastrophic event. A suitable location of interest to be inundated by a volcanic flow. distribution on the inputs is then used to determine the Standard statistical sampling techniques would focus too probability of this region. Adequate handling of the many many samples (e.g. volcanic flow simulations) on small uncertainties present is possible by quantifying all uncer- volume events. Using a statistical emulator of flow sim- tainties in terms of probability distributions and combining ulations, we can focus attention on these infrequent but them in a Bayesian analysis. high-consequence events and construct a boundary in pa- M.J. Bayarri rameter space at the smallest volume events that would University of Velacia inundate a location of concern. [email protected] Elaine Spiller Marquette University MS37 [email protected] Modeling Large Scale Geophysical Flows: Physics and Uncertainty MS37 Mathematical simulations of volcanic mass flows supple- Combining Deterministic and Stochastic Models ment field deposit studies, providing data from which to For Hazard Assessment make predictions of volcanic hazards. Several parameters The deterministic flow model ”TITAN-2D” predicts course, and functions must be specified upon input, in order to depth, and velocity for pyroclastic flows following a dome start the simulation. These inputs include the total volume collapse events of specified volumes and initial directions, of the mass flow, the initial direction of the flow, friction for a region whose topography is available as digital ele- and dissipation factors, and the terrain over which the mass vation maps (DEMs). I describe how to combine evidence moves. These inputs are often poorly characterized, or are from TITAN-2D, a rapid stochastic emulator, and heavy- known to be inaccurate, and these inaccuracies affect the tailed stochastic models of flow volumes and directions, to simulation outputs. Here we study the interplay between quantify the hazard of a catastrophic inundation at speci- the physics of geophysical flows and the uncertain inputs, fied locations, reflecting uncertainty about the models and and examine the effect of uncertainty on outputs, in order UQ12 Abstracts 107 data. tion to Reliability Analysis

Robert Wolpert Among the most popular methods for computing failure Duke University probabilities is FORM. If the curvature of the failure func- [email protected] tion is large, FORM is known to become inaccurate. Un- der certain conditions the failure integral may be carried Elaine Spiller over to an expectation value. The computation of this inte- Marquette University grals leads to high dimensional integration over the random [email protected] space. Several sparse grid integration methods are consid- ered and compared on test examples from literature. The complete method is applied to the life cycle of a wheel set MS38 of a train. Numerical Strategies for Epistemic Uncertainty Analysis Utz Wever Siemens AG Most of the existing UQ analysis tools rely on the knowl- [email protected] edge of the probability distribution of the uncertain inputs, also known as aleatory uncertainty. In practice, more of- Albert B. Gilg ten one does not possess sufficient amount of knowledge Siemens AG to completely specify the distributions of the input un- Corporate Technology certainty — epistemic uncertainty. And most of the ex- [email protected] isting tools of UQ do not readily apply. In this talk we discuss some numerical strategies to efficiently quantify Meinhard Paffra the impacts of epistemic uncertainty. The methods are Siemens AG based on numerically creating accurate surrogate of the meinhard.paff[email protected] problem, without the need of input probability distribu- tions. And probabilistic analysis can then be conduct in a post-processing step, without incurring additional simu- MS38 lation effort. We present the numerical algorithms, their Uncertainty Quantification with High Dimensional, convergence analysis, and examples to demonstrate the ef- Experimentally Measured Inputs fectiveness of the strategies. In this work, we tackle in a holistic manner the prob- Xiaoxiao Chen lem of uncertainty quantification in the presence of high- Purdue University dimensional, experimentally measured inputs. Non-linear [email protected] model reduction techniques are used to reduce the dimen- sionality of the experimentally observed input and estimate Eun-Jae Park its probability density. A surrogate of the underlying sys- Dept of Computational Science and Engineering-WCU tem is created via interplay of High Dimensional Model Yonsei University Reduction (HDMR/ANOVA) and the treed Bayesian re- [email protected] gression frameworks developed recently by our group. Nu- merical emphasis is given in uncertainty quantification of Dongbin Xiu flow through porous media. Purdue University [email protected] Ilias Bilionis Center for Applied Mathematics Cornell University, Ithaca MS38 [email protected] A Localized Strategy for Generalized Polynomial Chaos Methods Nicholas Zabaras Cornell University We present a numerical strategy to treat stochastic differ- [email protected] ential equations in high dimensions. The approach utilizes a local generalized polynomial chaos (gPC) expansion to approximate the solution in ”elements”. And such a local MS39 expansion can be low dimensional. Then connecting con- Several Interesting Parabolic Test Problems ditions are imposed to enforce the solution to satisfy the desired mathematical properties of the original differential An important consideration for a posteriori error estima- equations. When properly implemented, the method can tion methods is their performance on nonlinear PDEs for reduce a high-dimensional SPDE in the global domain into problems that involve weak solution features or other de- a group of much lower dimensional SPDEs in elements. generacies. Typically, the errors in such regions are large, And the simulation speed-up could be highly significant. and nonlinear aspects of the error evolution cannot be We will discuss the technical details of the approach and neglected. To test error estimation techniques in this use examples to demonstrate its efficiency. regime, we have formulated several problems based on non- linear, parabolic PDEs. We will discuss these problems Yi Chen, Dongbin Xiu and demonstrate results from the nonlinear error transport Purdue University method. [email protected], [email protected] Jeffrey A. Hittinger Center for Applied Scientific Computing MS38 Lawrence Livermore National Laboratory Stochastic Integration Methods and their Applica- [email protected] 108 UQ12 Abstracts

Jeffrey W. Banks MS40 Lawrence Livermore National Laboratory Sampling and Inference for Large-scale Inverse [email protected] Problems Using an Optimization-based Approach

Jeffrey M. Connors In the Bayesian approach to inverse problems, a poste- Lawrence Livermore National Laboratory rior probability density function is written down that de- Center for Applied Scientific Computing pends upon the likelihood and prior probability density [email protected] functions. Estimators for unknown parameters can then be computed, and uncertainty quantification performed, Carol S. Woodward using output from an MCMC method which samples from Lawrence Livermore Nat’l Lab the posterior. In this talk, the focus is on efficient MCMC [email protected] sampling techniques for large-scale inverse problems that make using of optimization algorithms.

MS39 Johnathan M. Bardsley University of Montana Exact Error Behavior of Simple Numerical Prob- [email protected] lems

Although there is significant mathematical literature re- MS40 garding convergence analysis, actual testing of codes is done by numerical experiment. The gap between numeri- Approximate Marginalization of Uninteresting Dis- cal results and mathematical theory leaves many questions tributed Parameters in Inverse Problems unanswered. The most important being, how do we know In the Bayesian inversion framework, all unknowns are the observed convergence rate is the asymptotic one? In treated as random variables and all uncertainties can be this paper we outline a class of exact solutions for the mod- modeled systematically. Recently, the approximation er- ified equation that allow us to explore this and other ques- ror approach was proposed for handling model errors due tions in a more rigorous manner. to unknown nuisance parameters and model reduction. In Daniel Israel this approach, approximate marginalization of these errors Los Alamos National Laboratory is carried out before the estimation of the interesting vari- [email protected] ables. We discuss the adaptation of the approximation error approach for approximate marginalization of unin- teresting distributed parameters in inverse problems. MS39 Ville P. Kolehmainen Verification and Validation in Solid Mechanics Department of Applied Physics Verification and validation in solid mechanics lags behind University of Eastern Finland other disciplines, possibly because of the larger number of ville.kolehmainen@uef.fi variables involved. Verification in solid mechanics must extend from small deformations using simple constitutive Jari P Kaipio models to large deformations using complicated constitu- Department of Applied Physics, University of Eastern tive models. Innovative large-deformation manufactured Finland solutions, applicable to history-dependent materials, are 2Department of Mathematics, University of Auckland presented. Also, novel visualizations of stress states actu- [email protected] ally reached in applications are used to expose the need for experiments involving transient loading under massive Tanja Tarvainen deformations. Department of Applied Physics University of Eastern Finland Krishna Kamojjala, Rebecca Brannon tanja.tarvainen@uef.fi University of Utah [email protected], [email protected] Simon Arridge University College London [email protected] MS39 Cross-Application of Uncertainty Quantification MS40 and Code Verification Techniques Recovery from Modeling Errors in Non-stationary In most applications, sensitivity analysis (SA) and uncer- Inverse Problems: Application to Process Tomog- tainty quantification (UQ) ignore numerical error when ap- raphy plied to data from computer simulations, but in this work, In non-stationary inversion, time-varying targets are esti- numerical error is the focus. The differences in SA results mated based on measurements collected during the evo- for models with and without numerical error are examined, lutions of the targets. In the reconstructions, evolution with implications for SA and UQ consumers. Then, UQ models of the targets are utilized. The solutions of in- techniques are used to directly investigate the truncation verse problems are sensitive to errors in the models. We error of numerical methods. demonstrate that in some cases, however, it is possible to V. Gregory Weirs recover from modeling errors by statistical modeling of the Sandia National Laboratories error sources. As an example case, we consider imaging of [email protected] moving fluids in industrial process tomography. Aku Seppanen, Antti Lipponen UQ12 Abstracts 109

Department of Applied Physics MS41 University of Eastern Finland Uncertainty Quantification of Equation-of-state aku.seppanen@uef.fi, antti.lipponen@uef.fi Closures and Shock Hydrodynamics

Jari P. Kaipio We seek to propagate uncertainties in the experimental University of Eastern Finland, Finland and numerical atomistic data used to define multiphase University of Auckland, New Zealand equation-of-state (EOS) models to output quantities of in- [email protected] terest computed by the equations of shock hydrodynam- ics. A Bayesian inference approach for characterizing and representing the EOS parametric uncertainty and model MS40 discrepancy information is presented. Given the model un- Variational Approximations in certainty representation, we explicitly demonstrate a viable Large-scale Data Assimilation: Experiments with approach for tabular delivery of uncertain EOS information a Quasi-Geostrophic Model to the shock hydrodynamics modeling community. Sandia National Laboratories is a multi-program laboratory oper- The extended Kalman filter (EKF) is one of the most ated by Sandia Corporation, a wholly owned subsidiary of widely used data assimilation methods. However, EKF Lockheed Martin Corporation, for the U.S. Department of is computationally infeasible in large-scale problems, due Energy’s National Nuclear Security Administration under to the need to store full covariance matrices. Recently, contract DE-AC04-94AL85000. approximations to EKF have been proposed, where the covariance matrices are computed via Limited Memory Allen C. Robinson,RobertD.Berry,JohnH.Carpenter Broyden-Fletcher-Goldfarb-Shanno (LBFGS) and Conju- Sandia National Laboratories gate Gradient (CG) optimization methods. In this talk, [email protected], [email protected], we review the proposed methods and present data assimi- [email protected] lation results using a nonlinear Quasi-Geostrophic bench- mark model. Bert J. Debusschere Energy Transportation Center Antti Solonen Sandia National Laboratories, Livermore CA Lappeenranta University of Technology [email protected] Department of Mathematics and Physics [email protected] Richard R. Drake, Ann E. Mattsson Sandia National Laboratories MS41 [email protected], [email protected] A Spectral Uncertainty Quantification Approach in Ocean General Circulation Modeling William J. Rider Sandia National Laboratory We address the impact of uncertain model parameters on [email protected] simulations of the oceanic circulation. We focus on high- resolution simulations in Gulf of Mexico during the pas- sage of hurricane Ivan. Uncertainties in subgrid mixing MS41 and wind drag parametrizations for HYCOM are propa- Optimal Uncertainty Quantification and (Non- gated using Polynomial Chaos (PC) expansions. A non- )Propagation of Uncertainties Across Scales intrusive, sparse spectral projection is used to quantify the stochastic model response. A global sensitivity analysis is Posing UQ problems as optimization problems — over finally presented that reveals the dominant contributors to infinite-dimensional spaces of probability measures and re- prediction uncertainty. sponse functions — gives a method for obtaining sharp bounds on output uncertainties given generic information Alen Alexanderian, Justin Winokur, Ihab Sraj about input uncertainties. These problems can be solved Johns Hopkins University computationally and sometimes in closed form. Surpris- [email protected], [email protected], [email protected] ingly, our results show that input uncertainties may fail to propagate across scales if the probabilities and response Ashwanth Srinivasan functions are imperfectly known. University of Miami Tim Sullivan, Michael McKerns, Michael Ortiz [email protected] California Institute of Technology [email protected], [email protected], Mohamed Iskandarani [email protected] Rosenstiel School of Marine and Atmospheric Sciences University of Miami Houman Owhadi [email protected] Applied Mathematics Caltech WilliamCarlisle Thacker [email protected] National Oceanic and Atmospheric Administration [email protected] Clint Scovel Los Alamos National Laboratory Omar M. Knio [email protected] Duke University [email protected] Florian Theil University of Warwick Mathematics Institute 110 UQ12 Abstracts [email protected] MS42 Generalized Chapman-Kolmogorov Equation for Multiscale System Analysis MS41 Coarse Graining with Uncertainty: A Relative En- In multiscale system analysis, the effect of incertitude due tropy Framework to lack of knowledge may become significant such that it needs to be quantified separately from inherent random- In this work, we develop a generic framework for uncer- ness. A generalized Chapman-Kolmogorov equation based tainty propagation from an all-atom (AA) system to a on generalized interval probability is proposed to describe coarse-grained (CG) system. The AA system is assumed drift-diffusion and reaction processes under aleatory and to follow a probability law that depends on some uncertain epistemic uncertainties. Numerical algorithms are devel- parameters. The question we explore is how this uncer- oped to solve the generalized Fokker-Planck equation and tainty affects the induced probability law of the CG sys- interval master equation, where the respective evolutions tem. Our solution is posed as a stochastic optimization of the two uncertainty components are distinguished. problem in terms of relative entropies and an efficient so- lution scheme is developed. The efficacy of the framework Yan Wang is demonstrated numerically. Georgia Institute of Technology [email protected] Nicholas Zabaras Cornell University [email protected] MS43 Macroscopic Properties of Isotropic and Ilias Bilionis Anisotropic Fracture Networks from the Percola- Center for Applied Mathematics tion Threshold to Very Large Densities Cornell University, Ithaca [email protected] Some recent studies of fracture networks are summarized. They are made possible by a very versatile numerical tech- nique based on a three-dimensional discrete description of MS42 the fractures. Systematic calculations have been made up UQ Practices and Standards for Design and Man- to very large densities for isotropic, anisotropic networks ufacturing Process Engineering consisting of fractures distributed according to a power law. The percolation threshold and the macroscopic permeabil- Design and manufacturing process engineering have always ity are shown to be almost independent of the fracture necessitated some degree of uncertainty management. In- shape when displayed as functions of a dimensionless den- creasingly complicated systems, with greater performance sity calculated by means of the excluded volume. requirements/constraints, require corresponding advances in uncertainty quantification (UQ) practices. To make ef- Pierre Adler fective engineering decisions, these practices are typically Universit´e Pierre et Marie Curie implemented with software tools that must address mul- France tiple types of uncertainty across a spectrum of models, [email protected] measurements, and simulations. This talk discusses the present evolution of UQ practices and the potential for im- Jean Francois Thovert, Valeri Mourzenko provement through standards development. PPRIME PPRIME Mark Campanelli [email protected], [email protected] National Institute of Standards and Technology [email protected] MS43 Uncertainty Quantification Methods for Unsatu- MS42 rated Flow in Porous Media Systematic Integration of Multiple Uncertainty Sources in Design Process We present a stochastic collocation (SC) method to quan- tify epistemic uncertainty in predictions of unsaturated A design optimization methodology is presented that flow in porous media. SC provides a non-intrusive frame- systematically accounts for various sources of uncer- work for uncertainty propagation in models based on the tainty physical variability (aleatory uncertainty), data non-linear Richards’ equation with arbitrary constitutive uncertainty (epistemic) due to sparse or imprecise data, laws describing soil properties (relative conductivity and and model uncertainty (epistemic) due to modeling er- retention curve). To illustrate the approach, we use the rors/approximations. A Bayes network approach effec- Richards’ equation with the van Genutchen-Mualem model tively integrates both aleatory and epistemic uncertainties, for water retention and relative conductivity to describe in- and fuses multiple formats of information from models, ex- filtration into an initially dry soil whose uncertain param- periments, expert opinion, and model error estimates. The eters are treated as random fields. These parameters are methodology is illustrated using a three-dimensional wing represented using a truncated Karhunen-Lovve expansion; design problem involving coupled multi-disciplinary simu- Smolyak algorithm is used to construct a structured set of lation. collocation points from univariate Gauss quadrature rules. A resulting deterministic problem is solved for each collo- Sankaran Mahadevan cation point, and together with the collocation weights, the Vanderbilt University statistics of hydraulic head and infiltration rate are com- [email protected] puted. The results are in agreement with Monte Carlo sim- ulations. We demonstrate that highly heterogeneous soils (large variances of hydraulic parameters) require cubature UQ12 Abstracts 111 formulas of high degree of exactness, while their short cor- on series expansions in a variety of bases as well as using relation lengths increase the dimensionality of the problem. geostatistical libraries. The parameterizations employed Both effects increase the number of collocation points and allow integration of prior observations of the random sub- thus of deterministic problems to solve, affecting the overall strate. Pressures and fluxes are computed numerically and computational cost of uncertainty quantification. transport curves are compared under different stochastic regimes. David A. Barajas-Solano Dept. of Mechanical and Aerospace Engineering Mina E. Ossiander University of California, San Diego Math Dept [email protected] Oregon State University [email protected]

MS43 Malgorzata Peszynska, Veronika S. Vasylkivska A Comparative Study on Reservoir Characteriza- Department of Mathematics tion using Two Phase Flow Model Oregon State University [email protected], We consider the problem of characterization of porosity [email protected] and permeability of reservoir using a two phase flow model. We use a Bayesian MCMC framework to sample these pa- rameters conditioned to available dynamic measurement MS44 data. A prefetching procedure to parallelize the MCMC is Spatial Analysis of Energy Consumption by Non- studied and compared with the multistage MCMC. A set Domestic Buildings in Greater London numerical examples are presented to illustrate the compar- ison. This research investigates the influence of local tempera- tures, building shapes, and mix of buildings across districts Victor E. Ginting on heating energy consumed by non-domestic buildings in Department of Mathematics London. The goal is to reduce the uncertainty in energy University of Wyoming simulation model outputs of buildings by accounting for [email protected] spatial variations of energy consumption across the city. We explore (and compare) three statistical formulations to Felipe Pereira quantify the spatial autocorrelations: spatial autoregres- Center for Fundamentals of Subsurface Flow sive error model, Bayesian geographically weighted regres- University of Wyoming sion, and Bayesian CAR model. [email protected] Ruchi Choudhary Arunasalam Rahunanthan Department of Engineering Center for Fundamentals of Subsurface Flow University of Cambridge University of Wyoming, Laramie, WY 82071 [email protected] [email protected] Wei Tian university of cambridge MS43 [email protected] Adaptive AMG for Diffusion Equations with Stochastic Coefficients MS44 We are interested in solving a 2nd-order diffusion equation Spatial Statistical Calibration of a Turbulence where there is uncertainty in the conductivity field. Condi- Model tioning conductivity fields to dynamic data using Markov Chain Monte Carlo requires repeated solution of the for- The k-ε turbulence model is widely used in CFD model- ward problem for many thousands of realizations of the ing. However, it has problems predicting flow separation field. We present an adaptive algebraic multigrid method as well as unconfined and transient flows. We calibrate its which automatically adapts to the changing conductivity parameters against wind tunnel observations of turbulent field in an inexpensive manner. Numerical experiments are kinetic energy (TKE) distributed over a two-dimensional discussed for an interesting model problem. cross section of a street canyon. We use a sequential de- sign to pick optimal spatial locations. We then build an Christian Ketelsen emulator to quantify the uncertainty of the modeled TKEs. University of Colorado at Boulder [email protected] Nina Glover, Serge Guillas Panayot Vassilevski University College London Lawrence Livermore National Laboratory [email protected], [email protected] [email protected] Liora Malki-Epshtein UCL MS43 [email protected] Stochastic Models, Simulation and Analysis in Sub- surface Flow and Transport MS44 We discuss stochastic models for heterogeneous random Adding Spatial Dependence Constraints to a Geo- media in the context of numerically computing subsurface flow and transport of fluids. Simulated models are based 112 UQ12 Abstracts physical Inverse Problem with Intermittency

Given a geophysical model of seismic pressure wave at- Synergy between empirical information theory and tenuation, measurements of this attenuation at points in fluctuation-dissipation theorem provides a systematic space, and partial information on subsurface soil proper- framework for improving sensitivity and predictive skill for ties (model parameters), I am interested in estimating the imperfect models of complex natural systems. We utilize unknown soil properties. This inversion has been done via a suite of increasingly complex nonlinear models with in- a stochastic optimization routine because of the complex- termittent hidden instabilities and time-periodic features ity of the geophysical model. The goal here is to reduce to illustrate the advantages of such an approach, as well uncertainty in these estimates by incorporating spatial de- as the role of model errors due to coarse-graining, moment pendency constraints in the model inversion. closure approximations, and the memory of initial condi- tions in imperfect prediction. Eugene Morgan Department of Civil and Environmental Engineering Michal Branicki Duke University New York University [email protected] [email protected]

Andrew Majda MS44 Courant Institute NYU Asessing the Spatial Distribution of Fish Species [email protected] Using Bayesian Latent Gaussian Models

We describe the use of the integrated nested Laplace ap- MS45 proximation (INLA) approach to infer the spatial distri- Upper Ocean Singular Vectors of the North At- bution of fish species, taking into account the spatial au- lantic: Implications for Linear Predictability and tocorrelation, and quantifying the uncertainty. The type Observational Requirement of data available (and the methodology used to gather it) will determine the appropriate modelling scheme. In the Recent interest in decadal prediction in the Atlantic sec- first example, binary data has been collected that can be tor presumes that the ocean carries sufficient low-frequency regarded as randomly sampled. In the second example, we predictive skill. We explore the limits of predictability in analyze quantitative data with preferential sampling. sea surface temperature and meridional overturning cir- culation from singular vector calculations with combined Facundo Mu˜noz tangent linear and adjoint versions of an ocean general cir- University of Valencia culation model. [email protected] Patrick Heimbach Mar´ıa Pennino MIT Spanish Institute of Oceanography [email protected] [email protected] Laure Zanna David Conesa, Antonio L´opez-Qu´ılez Oxford University University of Valencia [email protected] [email protected], [email protected] Andrew M. Moore Univ. of California at Santa Cruz MS45 [email protected] Uncertainty Quantification for Large Multivariate Spatial Computer Model Output with Climate Ap- Eli Tziperman plications Harvard University Characterizing uncertainty in climate predictions and mod- [email protected] els is crucial for climate decision-making. One uncertainty source is due to inability to resolve complex physical pro- MS45 cesses, which is approximated using a parameterization. We characterize parameter uncertainty by calibrating the Quantifying Uncertainties in Fully Coupled Cli- model to physical observations. Both model output and mate Models observations are large multivariate space-time fields. We Fully coupled climate models are the most realistic tools use Bayesian methods to infer these parameters while in- used to simulate climate change. They incorporate corporating space-time dependence and other uncertainty highly detailed, interacting components for the atmo- sources using a Gaussian process emulator and dimension sphere, ocean, and sea ice. There is a dire need to quantify reduction. their uncertainties, but coupled climate models are com- K. Sham Bhat putationally very demanding and contain many sources of Los Alamos National Laboratory uncertainty. We describe efforts to quantify uncertainties [email protected] of the coupled climate system using perturbed-parameter ensembles of the Community Earth System Model.

MS45 Scott Brandon, Donald D. Lucas,CurtCovey,Davlid Domyancic, Gardar Johannesson, Stephen Klein, John Quantifying Uncertainty for Climate Change Pre- Tannahill, Yuying Zhang dictions with Model Errorin non-Gaussian Systems Lawrence Livermore National Laboratory [email protected], [email protected], [email protected], UQ12 Abstracts 113 [email protected], [email protected], Department of Mathematics [email protected], [email protected], [email protected] [email protected]

MS46 MS47 Efficient Spectral Garlerkin Method with Orthgo- Putting Computational Inference into an FPGA nal Polynomials for SPDES We are building a compiler to map large numerical com- In this talk we first develop a fast algorithm to evaluate putations into FPGAs (Field Programmable Gate Array). orthogonal polynomial expansions for d-variable functions Our target application is MCMC (Markov chain Monte in on sparse grids. Then we apply this fast algorithm to Carlo) based inference for ECT (Electrical Capacitance To- develop an efficient spectral method to approximate the so- mography). We aim to realize the good compute through- lutions of stochastic partial differential equations with ran- put of FPGAs, both in terms of performance-per-dollar and dom input data. Three aspects distinguishes work from the performance-per-Watt, to perform real-time UQ embedded existing ones: 1. Our algorithm is applicable L2 functions into industrial sensors. with arbitrary probability density weight; 2. The use of orthogonal polynomials results in matrix sparsity; 3. Ex- Colin Fox ponential rate of convergence of the numerical algorithm is University of Otago, New Zealand rigorously proved. [email protected]

Yanzhao Cao Department of Mathematics & Statistics MS47 Auburn University Model Reductions by MCMC [email protected] Identification of models is often complicated by the fact that the available experimental data from field measure- MS46 ments is noisy or incomplete. Moreover, models may be Adaptive Methods for Elliptic Partial Differential complex, and contain a large number of correlated param- Equations with Random Operators eters. As a result, the parameters are poorly identified by the data, and the reliability of the model predictions is Solutions of random elliptic boundary value problems ad- questionable. We consider a general scheme for reduction mit efficient approximations by polynomials on the param- and identification of dynamic models using two modern eter domain, but it is not clear a priori which polynomials approaches, Markov chain Monte Carlo sampling methods are most significant. I will present numerical methods that together with asymptotic model reduction techniques. The adaptively construct suitable spaces of polynomials. These ideas are illustrated with examples related to bio-medical methods are based on adaptive finite elements and adaptive applications and epidemiology. wavelet algorithms, with orthonormal polynomial systems in place of wavelet bases. They construct efficient sparse Heikki Haario representations of the approximate solution. Lappeenranta University of Technology Department of Mathematics and Physics Claude Gittelson heikki.haario@lut.fi Purdue University [email protected] MS47 Advanced Uncertainty Evaluation of Climate Mod- MS46 els by Monte Carlo Methods Efficient Nonlinear Filtering of a Singularly Per- turbed Stochastic Hybrid System Uncertainties in future climate projections are often evalu- ated based on the perceived spread of ensembles of multi- Astract not available at time of publication. model climate projections. Here we focus on the uncertain- ties related to a single climate model and its closure param- Boris Rozovski eters that are used in physical parameterization schemes Brown University and cover topics such as specification of the cost function boris [email protected] and parameter identification by Monte Carlo methods. Marko Laine MS46 Finnish Meteorological Institute Two Stochastic Modeling Strategies for Elliptic marko.laine@fmi.fi Problems In this talk, we compare two stochastic elliptic mod- MS47 els: (a(x, ω)  u(x, ω)) = f(x)and Covariance Estimation Using Chi-squared Tests  −∇ · ·∇ −∇ · 1 ( 1) a− − ∇u(x, ω) = f(x), where a(x, ω) is a log- Regularized solutions of ill-posed inverse problems can be normal random field, with respect to the two characteristic viewed as solutions of the original problem when the prob- parameters of the underlying Gaussian random field, i.e., lem is regularized by adding statistical information to it. the standard deviation and the correlation length. Some The discrepancy principle finds a regularization parameter related numerical issues and numerical results will be dis- by applying a chi-square test, and we extend and improve cussed. the approach to estimate a regularization matrix. This regularization matrix can be viewed as an estimate of an Xiaoliang Wan error covariance matrix. Results will be shown from an Louisiana State University 114 UQ12 Abstracts event reconstruction problem. MS49 A Reduced Order Model for a Nonlinear, Parame- Jodi Mead terized Heat Transfer Test Case Boise State University Department of Mathematics We present a reduced order model (ROM) for heat trans- [email protected] fer through a composite fiber with two material properties. The ROM is constructed by interpolating the components of a modal decomposition (SVD) of a sampling of high- MS48 fidelity models – each computed with different material Heterogeneous Deformation of Polycrystalline properties. We are able to scale the SVD using a novel Metals and Extreme Value Events implementation in MapReduce. We then use the ROM as a cheap surrogate to study the probability of failure of the Astract not available at time of publication. system. Curt Bronkhorst Paul Constantine, Jeremy Templeton Los Alamos National Lab Sandia Labs [email protected] [email protected], n/a

MS48 Joe Ruthruff Coupled Chemical Master Equation - Fokker Livermore Planck Solver for Stochastic Reaction Networks n/a Stochastic reaction networks are generally governed by the Chemical Master Equation (CME). While the CME, as MS49 a high-dimensional ODE system, is hard to solve in gen- Uncertainty Quantification for Turbulent Mixing eral, its continuum approximations, e.g. Focker-Planck and Turbulent Combustion equations (FPE), are reliable alternatives when the species count is large enough. We present a proof-of-concept Large eddy simulations of mixing and combustion with fi- methodology for a hybrid construction that effectively com- nite rate chemistry eliminate a major source of chemistry bines CME and FPE, employing a discrete scale CME so- model related (epistemic)uncertainty. The method is a no- lution in regions where the continuum FPE is inaccurate. tion of stochastic convergence, to generate space-time de- pendent PDFs (Young’s measures) out of a single simula- Khachik Sargsyan, Cosmin Safta tion via coarse graining with the multiple mesh values in a Sandia National Laboratories supercell to generate the PDF. Comparison to experimen- [email protected], [email protected] tal data related to a Scram jet is included. Comparison to RANS and other simulations allows model related error Bert J. Debusschere assessment and uncertainty quantification. Energy Transportation Center James G. Glimm Sandia National Laboratories, Livermore CA Stony Brook University [email protected] Brookhaven National Laboratory [email protected] or [email protected] Habib N. Najm Sandia National Laboratories Livermore, CA, USA MS49 [email protected] Chemical Kinetic Uncertainty Quantification for High-Fidelity Turbulent Combustion Simulations

MS48 Detailed chemical mechanisms consist of hundreds or thou- A New Approach for Solving Multiscale SPDEs us- sands of chemical reactions with an uncertain rate for each. ing Probabilistic Graphical Models Direct propagation of this very high-dimensional uncer- tainty through high-fidelity Large Eddy Simulation (LES) We propose a hierarchical representation of random fields of turbulent reacting flows is computationally intractable. by capturing the stochastic input at fine scale with locally Instead, a method is presented in which the pre-processing reduced models and combining them with graphical models portion of the turbulent combustion model is used to con- on the coarse scale. Regression models are constructed dition this very high-dimensional uncertainty, resulting in such that local features are taken as input and multiscale a lower-dimensional uncertainty space that is efficiently basis functions as output. In this way, we can make samples propagated through the LES. The approach is demon- of coarse scale properties from the graphical probabilistic strated with a laboratory-scale turbulent nonpremixed jet model, obtain multiscale basis functions with regression flame. models and solve SPDEs on the coarse scale. Michael Mueller Nicholas Zabaras Stanford Cornell University [email protected] [email protected] Gianluca Iaccarino Jiang Wan Stanford University Corness University [email protected] [email protected] Heinz Pitsch Stanford UQ12 Abstracts 115 na/ of Contaminants

The fate and transport of contaminants in the subsurface MS49 is strongly influenced by bio-geochemical reactions. Pre- Criteria for Optimization Under Uncertainty dictions are routinely compromised by both model (struc- tural) and parametric uncertainties. I will first present a In this work different criteria for robust optimization under set of computational tools for quantifying these two types uncertainty are compared. In particular, a framework pro- of uncertainties for multi-component nonlinear chemical re- posed by the authors and characterized by the use of all the actions. The second part of the talk will deal with the com- possible information in the probabilistic domain, namely bined effects of uncertainty in reactions and heterogeneity the Cumulative Distribution Function (CDF), is compared of the medium on the transport of reactive contaminants. to more classical approaches that rely on the usage of clas- sical statistical moments as deterministic attributes that Gowri Srinivasan define the objectives of the optimization process. Further- T-5, Theoretical Division, Los Alamos National more, the use of an area metric leads to a multi-objective Laboratory methodology which allows an a posteriori selection of the [email protected] candidate design based on risk/opportunity criteria defined by the designer. A comparison with another new technique based on Evidence Theory, proposed by different authors, MS50 is also introduced. A Framework for Experimental Design for Ill-posed Inverse Problems Domenico Quagliarella Centro Italiano Ricerche Aerospaziali A fremework for experimental design for ill-posed inverse [email protected] problems We consider the problem of experimental design for ill-posed inverse problems. The main difficulties we G. Petrone have to address are: the bias introduced by the regulariza- University Federico II of Naples tion of the inverse problem, and the parameter selection [email protected] required by the regularization. We propose a Bayesian approach based on a hierarchical sequence of prior mo- ment conditions. The methodology applies also to a non- Gianluca Iaccarino Bayesian mathod based on training models. We provide Stanford University generalization of the usual equivalence theorems and pro- [email protected] pose numerical methods to tackle large-scale problems.

Luis Tenorio MS50 Colorado School of Mines Bayesian Uncertainty Quantification for Flows in [email protected] Highly Heterogeneous Media

Abstract not available at time of publication. MS51 Yalchin Efendiev An Approach for the Adaptive Solution of Opti- Dept of Mathematics mization Problems Governed by PDEs with Un- Texas A&M University certain Coefficients [email protected] Using derivative based numerical optimization routines to solve optimization problems governed by partial differen- MS50 tial equations (PDE) with uncertain coefficients is com- putationally expensive due to the large number of PDE Emulators in Large-scale Spatial Inverse Problems solves required at each iteration. I propose a framework We consider a Bayesian approach to nonlinear inverse prob- for the adaptive solution of such optimization problems lems in which the unknown quantity (input) is a random based on the retrospective trust region algorithm. I prove field (spatial or temporal). The forward model is complex global convergence of the retrospective trust region algo- and non linear, therefore computationally expensive. We rithm under weak assumptions on gradient inexactness. If develop an emulator based approach where the Bayesian one can bound the error between actual and modeled gra- multivariate adaptive splines (BMARS) has been used to dients using reliable and efficient a posteriori error estima- model unknown functions of the model input. We consider tors, then the global convergence of the proposed algorithm discrete cosine transformation (DCT) for dimension reduc- follows. I present a stochastic collocation finite element tion of the input field. The estimation is carried out using method for the solution of the PDE constrained optimiza- trans dimensional Markov chain Monte Carlo. Numerical tion. In the stochastic collocation framework, the state and results are presented by analyzing simulated as well as real adjoint equations can be solved in parallel. Initial numer- data for reservoir characterization. ical results for the adaptive solution of these optimization problems are presented. Anirban Mondal Quantum Reservoir Impact Drew Kouri [email protected] Department of Computational and Applied Mathematics Rice University [email protected] MS50 Uncertainty Quantification for Reactive Transport MS51 Uncertainty Quantification using Nonparametric 116 UQ12 Abstracts

Estimation and Epi-Splines MS52 Spatial ANOVA Modeling of High-resolution Re- We address uncertainty quantification in complex systems gional Climate Model Outputs from NARCCAP by a flexible, nonparametric framework for estimation of density and performance functions. The framework sys- The differences between future (2041-2070) and current tematically incorporates hard information derived from (1971-2000) average seasonal temperature fields, from physics-based sensors, field test data, and computer sim- two regional climate models (RCMs) driven by the same ulations as well as soft information from human sources atmosphere-ocean general circulation model in the North and experiences. The framework is based on epi-splines American Regional Climate Change Assessment Program for consistent approximation of infinite-dimensional opti- (NARCCAP), are analyzed using a hierarchical two-way mization problems arising in the estimation process. Pre- ANOVA model with the factors of season, RCM, and their liminary numerical results indicate that the framework is interaction. The spatial variability across the domain is highly promising. modeled through the Spatial Random Effects (SRE) model, which allows for efficient computation. Johannes O. Royset Asst. Prof. Emily L. Kang Naval Postgraduate School Department of Mathematical Sciences [email protected] University of Cincinnati [email protected] Roger Wets University of California, Davis Noel Cressie [email protected] Ohio State University [email protected] MS51 Numerical Methods for Shape Optimization under MS52 Uncertainty Statistical Issues in Catchment Scale Hydrological Modeling The proper treatment of uncertainties in the context of aerodynamic shape optimization is a very important chal- Many uncertainty quantification methods currently in use lenge to ensure a robust performance of the optimized air- by the hydrological community make the mistake of im- foil under real life conditions. This talk will propose a gen- plicitly conflating the hydrological model with the true eral framework to identify, quantize and include stochastic physical system. Rather than using a framework with an distributed, aleatory uncertainties in the overall optimiza- additive discrepancy term, I will argue for making the hy- tion procedure. Appropriate robust formulations of the drological model itself stochastic, expressed using a system underlying deterministic problem and uncertainty quantifi- of stochastic differential equations. I will discuss Bayesian cation techniques in combination with adaptive discretiza- inference under this model, which falls under the difficult tion approaches are investigated in order to measure the category of dynamic models with non-time-varying param- effects of the uncertainties in the input data on quantities eters. of interest in the output. Finally, algorithmic approaches based on multiple-setpoint ideas in combination with one- Cari Kaufman shotmethodsaswellasnumericalresultsarepresented. University of California, Berkeley [email protected] Claudia Schillings University of Trier, Germany [email protected] MS52 Quantifying Uncertainties in Hydrologic Parame- Volker Schulz ters in the Community Land Model University of Trier Department of Mathematics Uncertainties in hydrologic parameters could have signifi- [email protected] cant impacts on the simulated water and energy fluxes and land surface state, which can affect carbon cycle and at- mospheric processes in coupled earth system simulations. MS51 In this study, we introduce an uncertainty quantification Risk Neutrality and Risk Aversion in Shape Opti- (UQ) framework for sensitivity analyses and uncertainty mization with Uncertain Loading quantification of selected parameters related to hydrologic processes in the Community Land Model. Ten flux tower Conceptually inspired by finite-dimensional stochastic pro- sites and over fifteen watersheds spanning a wide range of gramming with recourse we propose infinite-dimensional climate and site conditions were selected to perform sensi- two-stage stochastic models for shape optimization of elas- tivity analyses by perturbing the parameters identified. An tic bodies with linearized elasticity and stochastic load- Entropy-based approach was used to derive prior PDF for ing. Risk neutral and risk averse approaches, the latter each input parameter and the Quasi-Monte Carlo (QMC) involving suitable risk measures or dominance relations, approach was used to generate samples of parameters from will be discussed. Reporting illustrative computational ex- the prior PDFs. A simulation for each set of sampled pa- periments concludes the talk. rameters was performed to obtain response curves. Based on statistical tests, the parameters were ranked for their Ruediger Schultz significance depending on the simulated latent heat flux, University of Duisburg-Essen sensible heat flux, and total runoff. The study provides [email protected] the basis for parameter dimension reduction and guidance on parameter calibration framework design, under different UQ12 Abstracts 117 hydrologic and climatic regimes. MS53 A Stochastic Collocation Method Based on Sparse Ruby Leung Grid for Stokes-Darcy Model with Random Hy- Pacific Northwest National Laboratory draulic Conductivity [email protected] The Stokes-Darcy model has attracted significant attention Zhangshuan Hou, Maoyi Huang, Yinghai Ke since its higher fidelity than either Darcy or Stokes sys- Pacific Northwest National Lab tem is important for many applications, but uncertainties [email protected], [email protected], and coupling issues lead to a rather complex system. We [email protected] present a stochastic collocation method based on sparse grid for the Stokes-Darcy model with random hydraulic Guang Lin conductivity. This method is natural for parallel computa- Pacific Northwest National Laboratory tion and some numerical results are presented to illustrate [email protected] the features of this method. Max Gunzburger MS52 Florida State University Uncertainty Propagation in Land-Crop Models School for Computational Sciences [email protected] Crop models were recently included in the land model of the Community Earth System Model (CESM). Good es- Xiaoming He, Xuerong Wen timates of physiology parameters for crops are essential Department of Mathematics and Statistics to get accurate outputs, particularly carbon cycle ones. Missouri University of Science and Technology To that end, we investigate the potential of intrusive un- [email protected], [email protected] certainty quantity approaches when used in combination with maximum likelihood/ regression models for calibrat- ing the crop model parameters from Ameriflux data. Nu- MS53 merical tests for this approach using soybean data from the Adaptive Sparse Grid Generalized Stochastic Col- Bondville, IL site produced very promising initial results. location Using Wavelets Xiaoyan Zeng Accurate predictive simulations of complex real world ap- Argonne National Laboratory plications require numerical approximations to first, op- [email protected] pose the curse of dimensionality and second, converge quickly in the presence of steep gradients, sharp transitions, Mihai Anitescu, Emil M. Constantinescu bifurcations or finite discontinuities in high-dimensional Argonne National Laboratory parameter spaces. In this talk we present a novel multidi- Mathematics and Computer Science Division mensional multiresolution adaptive (MdMrA) sparse grid [email protected], [email protected] stochastic collocation method, that utilizes hierarchical multiscale piecewise Riesz basis functions constructed from interpolating wavelets. The basis for our non-intrusive MS53 method forms a stable multiscale splitting and thus, opti- Basis and Measure Adaptation for Stochastic mal adaptation is achieved. Error estimates and numerical Galerkin Projections examples will used to compare the efficiency of the method with several other techniques. Use of the stochastic Galerkin finite element methods leads to large systems of linear equations.These systems are typ- Clayton G. Webster ically solved iteratively.We propose a preconditioner which Oak Ridge National Laboratory takes advantage of the recursive hierarchy in the structure [email protected] of the global system matrices. Neither the global matrix, nor the preconditioner need to be formed explicitly.The Max Gunzburger ingredients include only the number of stiffness matrices Florida State University from the truncated Karhunen-Lo`eve expansion and a pre- School for Computational Sciences conditioner for the mean-value problem.The performance [email protected] is illustrated by numerical experiments. John Burkardt Roger Ghanem Department of Computational Science University of Southern California Florida State University Aerospace and Mechanical Engineering and Civil [email protected] Engineering [email protected] MS53 Bedˇrich Soused´ık Error Analysis of a Stochastic Collocation Method University of Southern California for Parabolic Partial Differential Equations with [email protected] Random Input Data

Eric Phipps A stochastic collocation method for solving linear parabolic Sandia National Laboratories PDEs with random input data is analyzed. The input data Optimization and Uncertainty Quantification Department are assumed to depend on a finite number of random vari- [email protected] ables. Unlike previous analysis, a wider range of situations is considered including input data that depend nonlinearly on the random variables and random variables that are 118 UQ12 Abstracts correlated or even unbounded. We demonstrate exponen- ing is presented, based on concepts from optimal control, tial convergence of the interpolation error for both a semi- and from mean-field game theory. The feedback particle discrete and a fully-discrete scheme. filter admits an innovations error-based feedback control structure: The control is chosen so that the posterior dis- Guannan Zhang tribution of any particle matches the posterior distribution Florida State University of the true state given the observations. The feedback par- [email protected] ticle filter is shown to have significant advantages over the conventional particle filter in the numerical examples con- Max Gunzburger sidered. Application to Bayesian inference in neural cir- Florida State University cuits is briefly discussed with the aid of coupled oscillator School for Computational Sciences models. [email protected] Tao Yang UIUC MS54 [email protected] Retrospective-Cost-Based Model Refinement of Systems with Inaccessible Subsystems Prashant G. Mehta Department of Mechanical and Industrial Engineering Spatially discretized models are typically constructed University of Illinois at Urbana Champaign based on physical laws and parameter estimates. These [email protected] models may be erroneous, however, due to unmodeled physics and numerical errors. These discrepancies become Sean Meyn apparent when model predictions disagree with measure- Department of Electrical and Computer Engineering ments. The goal of this research is to use data to im- University of Illinois at Urbana Champaign prove the fidelity of an initial model. The approach we [email protected] take is based on retrospective-cost-based optimization of subsystems that are inaccessible, that is, whose inputs and outputs are not measured. Applications to space weather MS54 modeling will be presented. Uncertainty Analysis of Dynamical Systems – Ap- Dennis Bernstein plication to Volcanic Ash Transport University of Michigan Uncertainty analysis of a number of societally important [email protected] physical systems may be posed in the dynamic systems framework. In this leadoff talk we will overview this Anthony D’Amato, Asad Ali minisymposium on this topic and frame issues using our Aerospace Engineering Department group’s work on transport of volcanic ash transport. Basic University of Michigan approaches and results of application of these methods to [email protected], asadali recent eruption events will be presented.

Abani K. Patra MS54 SUNY at Buffalo Multiscale Methods for Flows in Heterogeneous Dept of Mechanical Engineering Stochastic Porous Media [email protected]ffalo.edu

In this talk, I will discuss multiscale methods for stochas- Puneet Singla tic problems. The main idea of our approach is to con- Mechanical & Aerospace Engineering struct local basis functions that encode the local features University at Buffalo present in the coefficient to approximate the solution of [email protected] parameter-dependent flow equation. Constructing local basis functions involves (1) finding initial multiscale ba- sis functions and (2) constructing local spectral problems Marcus Bursik for complementing the initial coarse space. We use the Re- Dept. of Geology duced Basis (RB) approach to construct a reduced dimen- SUNY at Buffalo sional local approximation that allows quickly computing mib@buffalo.edu the local spectral problem. I will present the details of the algorithm, numerical results, and computational cost. Ap- E. Bruce Pitman plications to Bayesian Uncertainty Quantification will be Dept. of Mathematics discussed. This is a joint work with Juan Galvis (TAMU) Univ at Buffalo and Florian Thomines (ENPC). pitman@buffalo.edu

Yalchin Efendiev Matthew Jones Dept of Mathematics Center for Comp. Research, Texas A&M University Univ. at Buffalo, Buffalo, NY 14260 [email protected] jonesm@buffalo.edu

MS54 Tarunraj Singh Dept of Mechanical Engineering Feedback Particle Filter: A New Formulation for SUNY at Buffalo Nonlinear Filtering Based on Mean-field Games tsingh@buffalo.edu A new formulation of the particle filter for nonlinear filter- UQ12 Abstracts 119

MS55 Applications Optimal Use of Gradient Information in Uncer- tainty Quantification Adaptivity in space and time is ubiquitous in modern nu- merical simulations. To date, there is still a considerable We discuss methods that use derivative information for gap between the stateoftheart techniques used in direct probabilistic uncertainty propagation in models of com- (forward) simulations, and those employed in the solution plex system. We demonstrate that such methods needs of inverse problems, which have traditionally relied on fixed less sampling information compared to their derivative- meshes and time steps. This talk describes a framework for free version. Here we discuss the importance of several building a space-time consistent adjoint discretization for algorithmic choices, such as the choice of basis in regres- a general discrete forward problem, in the context of adap- sion with derivative information, the choice of error model tive mesh, adaptive time step models. by means of Gaussian processes, and the choice of sam- pling points based on optimal design considerations. We Adrian Sandu demonstrate in particular that standard choices originat- Virginia Polytechnic Institute and ing from derivative-free methods are not suitable in this State University circumstance, and we define criteria adapted to the use [email protected] of derivative information that result in novel designs and bases. We demonstrate our findings on models from nu- Mihai Alexe clear engineering. Virginia Tech Department of Computer Science Mihai Anitescu [email protected] Argonne National Laboratory Mathematics and Computer Science Division [email protected] MS55 Sensitivity Analysis and Error Estimation for Dif- Fred J. Hickernell ferential Algebraic Equations in Nuclear Reactor Illinois Institute of Technology Applications Department of Applied Mathematics [email protected] We develop a general framework for computing the adjoint variable to nuclear engineering problems governed by a set of differential-algebraic equations. We use an abstract vari- Yiou Li ational approach to develop the framework, which provides Illinois Institute of Technology flexibility in modification and expansion of the governing [email protected] equations. Using both a simplex example with known so- lution and a dynamic reactor model, we show both theo- Oleg Roderick retically and numerically that the framework can be used Argonne National Laboratory for both parametric uncertainty quantification and the es- [email protected] timation of global time discretization error. Hayes Stripling MS55 Texas A&M University Gradient-based Optimization for Mixed Epistemic Nuclear Engineering Department and Aleatory Uncertainty [email protected]

Within this talk, a novel sampling/optimization approach Mihai Anitescu to mixed aleatory/epistemic uncertainty quantification is Argonne National Laboratory presented for hypersonic computational fluid dynamic sim- Mathematics and Computer Science Division ulations. This approach uses optimization to propagate [email protected] epistemic uncertainty to simulation results while sampling of these optimization results is used to characterize the distribution due to aleatory variables. To reduce the re- Marvin Adams quired number of optimizations, a Kriging surrogate is em- Texas A&M University ployed. For this talk, this combined sampling/optimization [email protected] approach will be demonstrated for analytic functions and simulations drawn from hypersonic fluid flows. Addition- MS56 ally, the performance of a similar uncertain optimization approach is tested for this application. A Semi-Intrusive Deterministic Approach to Un- certainty Quantifications Brian Lockwood University of Wyoming This paper deals with the formulation of a semi-intrusive [email protected] (SI) method allowing the computation of statistics of lin- ear and non linear PDEs solutions. This method shows to be very efficient to deal with probability density function Dimitri Mavriplis of whatsoever form, long-term integration and discontinu- Department of Mechanical Engineering ities in stochastic space. The effectiveness of this method University of Wyoming is illustrated for a modified version of Kraichnan-Orszag [email protected] three-mode problem where a discontinous pdf is associated to the stochastic variable, and for a nozzle flow with shocks. MS55 The results have been analyzed in terms of accuracy and probability measure flexibility. Finally, the importance of Gradient-based Data Assimilation in Atmospheric the probabilistic reconstruction in the stochastic space is shownuponanexamplewheretheexactsolutioniscom- 120 UQ12 Abstracts putable, in the resolution of the viscous Burgers equations. MS57 We expect some more applications by the time of the con- Toward Estimation of Sub-ice Shelf Melt Rates ference. to Ocean Circulation Under Pine Island Ice Shelf, West Antarctica Remi Abgrall INRIA Bordeaux Sud-Ouest Increased melt rates under ice shelves around Antarctica Universite de Bordeaux have been suggested as a dominant cause for observed ac- [email protected] celeration of the ice sheet near its marine margin. The melt rates are difficult to observe directly. We present first steps James G. Glimm towards estimating the melt rates from accessible hydrog- Stony Brook University raphy and optimal control methods. We address to which Brookhaven National Laboratory extent hydrographic observations away from the ice-ocean [email protected] or [email protected] boundary can be used to constrain melt rates. We derive sensitivity patterns of melt rates to changes in ocean circu- lation underneath the Pine Island Ice-Shelf. The sensitivity MS56 patterns are computed with an adjoint model of an ocean Uncertainty Quantification with Incomplete Phys- general circulation model that resolves the sub-ice shelf cir- ical Models culation. Inverting for best-estimate melt rates presents a first step towards backward propagation of uncertainties. The emergence of uncertainty quantification (UQ) has been a critical development towards the goal of predic- Patrick Heimbach tive science. The many efficient, non-intrusive, intuitive MIT approaches of probabilistic uncertainty have accelerated [email protected] the widespread adoption of the methodology. The addi- tional uncertainty arising from incomplete physical models Martin Losch makes the analysis much less obvious. This work exam- Alfred Wegener Institute ines how optimization over a restricted class of functionals [email protected] can bound the analysis of the true model if it were avail- able. Furthermore, these bounds provide insight into the sensitivity of this knowledge-gap relative to the overall pre- MS57 diction. Ice Bed Geometry: Estimates of Known Unknowns Gianluca Iaccarino For ice sheets, kilometer scale features in bed geometry may Stanford University dominate scenarios of ice mass loss. We developed a radar [email protected] sensor model for Thwaites basin in West Antarctica and use conditional simulations of off-track features to char- Gary Tang acterize unknown knowns of its bed geometry. We shall Stanford discuss the observational, scientific, and statistical strate- [email protected] gies for quantifying effects of bed geometry uncertainties on estimates of sea level rise. MS56 Charles Jackson Numerical Methods for Polynomial Chaos in Un- UTIG certain Flow Problems University of Texas at Austin [email protected] The Euler equations subject to input uncertainty are inves- tigated via the stochastic Galerkin approach. We present a Chad Greene fully intrusive method based on a variable transformation Department of Geological Sciences of the continuous equations. Roe variables are employed The University of Texas at Austin to get quadratic dependence in the flux function. The Roe chad allen greene ¡[email protected]¿ formulation saves computational cost compared to the for- mulation based on expansion of conservative variables, and John Goff, Scott Kempf, Duncan Young can handle cases of supersonic flow, for which the conser- Institute for Geophysics vative variable formulation leads to instability. The University of Texas at Austin Mass Per Pettersson goff@ig.utexas.edu, [email protected], Stanford University [email protected] [email protected] Evelyn Powell Institute for Geophysics MS56 evelyn powell ¡[email protected]¿ Evidence Based Multiciplinary Robust Design Don Blankenship Abstract not available at time of publication. UTIG University of Texas at Austin Massimilian Vasile [email protected] University of Strathclyde [email protected] MS57 Quantification of the Uncertainty in the Basal Slid- UQ12 Abstracts 121 ing Coefficient in Ice Sheet Models Model Reduction

The estimation of uncertainty in the solution of ice sheet in- UQ for nonlinear dynamical systems presents a challenge: verse problems within the framework of Bayesian inference uncertainty-space sampling requires thousands of large- is considered. We exploit the fact that for Gaussian noise scale simulations. To mitigate this burden, researchers and prior probability densities and linearized parameter- have developed model-reduction techniques that decrease to-observable map the posterior density (i.e., the solution the model’s ‘spatial complexity’ by decreasing 1) the num- of the statistical inverse problem) is Gaussian and hence is ber of degrees of freedom and 2) the complexity of non- characterized by its mean and covariance. The method is linear functions evaluations. However, when an implict applied to quantify uncertainties in the inference of basal time integrator is used, the number of time steps remains boundary conditions for ice sheet models. very large. This talk presents a strategy for decreasing the model’s ‘temporal complexity’. Noemi Petra Institute for Computational Engineering and Sciences Kevin T. Carlberg University of Texas at Austin Stanford University [email protected] [email protected]

Hongyu Zhu Institute for Computational Engineering and Sciences MS58 The University of Texas at Austin Error Analysis for Nonlinear Model Reduction Us- [email protected] ing Discrete Empirical Interpolation in the Proper Orthogonal Decomposition Approach Georg Stadler, Omar Ghattas Discrete Empirical Interpolation Method (DEIM) is an University of Texas at Austin efficient technique for resolving the complexity issue of [email protected], [email protected] the standard projection-based model reduction methods, such as the popular Proper Orthogonal Decomposition MS57 (POD) approach, due to nonlinearities of dynamical sys- tems. Recently, the hybrid approach combining POD with Bayesian Calibration via Additive Regression Trees DEIM has been successfully used to obtain accurate low- with Application to the Community Ice Sheet complexity reduced systems in many applications. How- Model ever, error analysis for this approach has not been inves- Quantifying uncertainties in calibration experiments in- tigated yet. This work provides state space error bounds volving complex computer models with high dimensional for the solutions of reduced systems constructed from this input spaces and large outputs is often infeasible. We de- POD-DEIM approach. The analysis is particularly rele- velop a non-parametric Bayesian trees model that scales vant to ODE systems arising from spatial discretizations to challenging calibration problems. Here, each tree repre- of parabolic PDEs. The resulting error bounds reflect the sents a weak learner and the overall model is a sum-of-trees. POD approximation property through the decay of singu- The idea is to learn locally-adaptive bases while retaining lar values, as well as explain how the DEIM approximation efficient MCMC sampling of the posterior distribution. We error involving the nonlinear term comes into play. The demonstrate our method by calibrating the Community Ice conditions under which the stability of the original system Sheet Model. is preserved and the reduction error is uniformly bounded will be discussed. Matthew Pratola,StephenPrice,DavidHigdon Los Alamos National Laboratory Saifon Chaturantabut [email protected], [email protected], [email protected] Virginia Tech [email protected]

MS58 Danny C. Sorensen Reduced Basis, the Discrete Interpolation Method Rice University and Fast Quadratures for Gravitational Waves [email protected]

Finding gravitational waveforms (GWs) is potentially go- ing to open a new window to the universe. Einstein’s MS58 equations are nonlinear parameter dependent (mass, spin Linearized Reduced-order Models for Optimization etc.) PDEs that approximate the post-Newtonian equa- and Data Assimilation in Subsurface Flow tions (PN). PN without spin gives stationary phase ap- proximations (SPA) to waveforms. Using matched filter- Trajectory piecewise linearization (TPWL) is a reduced- ing techniques, a LIGO search to find GWs, requires about order modeling approach where new solutions for non- 10,000 SPA templates and several months on supercomput- linear problems are represented using linear expansions ers. Reduced basis and using DEIM points as quadrature around previously simulated (and saved) solutions. The nodes leads to significant savings. high-dimensional representation is projected into a low- dimensional subspace using proper orthogonal decompo- Harbir Antil sition, which results in very large runtime speedups. We The University of Maryland describe the application of TPWL for the optimization of [email protected] well settings in oil reservoir simulation and for inverse prob- lems involving the determination of geological parameters.

MS58 Jincong He Decreasing the Temporal Complexity in Nonlinear Stanford University [email protected] 122 UQ12 Abstracts

Lou J. Durlofsky continuities in the climate model observables. Stanford University Dept of Petroleum Engineering Cosmin Safta, Khachik Sargsyan [email protected] Sandia National Laboratories [email protected], [email protected]

MS59 Daniel Ricciuto Testbeds for Ocean Model Calibration Oak Ridge National Laboratory [email protected] Tuning and uncertainty quantification in ocean models is challenging particularly because of the lack of suitable ob- Robert D. Berry servation datasets, and the computational expense in run- Sandia National Laboratories ning full-Earth simulations. Ocean models can be run [email protected] in limited instances at an eddy-resolving resolution, so high-resolution runs can be a target response for lower- resolution parameterization. Testbed configurations are Bert J. Debusschere then sufficient to expose effects of concern. We show re- Energy Transportation Center sults from a channel model representative of the Antarctic Sandia National Laboratories, Livermore CA Circumpolar Current (ACC), emphasizing eddy heat trans- [email protected] port. Peter Thornton James Gattiker, Matthew Hecht Oak Ridge National Laboratory Los Alamos National Laboratory [email protected] [email protected], [email protected] Habib N. Najm Sandia National Laboratories MS59 Livermore, CA, USA An Overview of Uncertainty Quantification in the [email protected] Community Land Model

The Community Land Model (CLM) is the terrestrial com- MS59 ponent of the Community Earth System Model (CESM), Uncertainty in Regional Climate Experiments which is used extensively for projections of the future cli- mate system. CLM has over 100 uncertain parameters, climate models are subject to a number of different sources contains multiple nonlinear feedbacks, and is computation- of uncertainty. Regional climate modeling introduce addi- ally demanding, presenting a number of challenges for UQ tional uncertainties associated with the boundary condi- efforts. CLM modeling has benefitted from our initial UQ tions and resolution of the models. In this talk, based on efforts through a new ability to rank parameters by relative the ensemble being generated as part of the North Ameri- importance and to identify unrealistic parameter combina- can Regional Climate Assessment Program (NARCCAP), tions. we will present statistical methodology for the analysis of the spatial-temporal output in the ensemble and quantify- Daniel Ricciuto,DaliWang ing the uncertainties associated with the NARCCAP ex- Oak Ridge National Laboratory periment. [email protected], [email protected] Stephan Sain Cosmin Safta, Khachik Sargsyan Institute for Mathematics Applied to Geosciences Sandia National Laboratories National Center for Atmospheric Research [email protected], [email protected] [email protected]

Habib N. Najm Sandia National Laboratories MS60 Livermore, CA, USA Calibration, Model discrepancy and Extrapolative [email protected] Predictions In the presence of relevant physical observations, one can Peter Thornton usually calibrate a computer model, and even estimate sys- Oak Ridge National Laboratory tematic discrepancies of the model from reality. Estimating [email protected] and quantifying the uncertainty in this model discrepancy can lead to reliable predictions - so long as the prediction MS59 is ”similar” to the available physical observations. Exactly how to define ”similar” has proven difficult. Clearly it de- Efficient Surrogate Construction for pends on how well the computational model captures the High-Dimensional Climate Models relevant physics in the system, as well as how portable In this study we explore the use of non-intrusive meth- the model discrepancy is, going from the available physical ods to construct surrogate approximations for the Com- data to the prediction. This talk will discuss these con- munity Land Model (CLM). Relevant vector machine tech- cepts using computational models ranging from simple to niques are used to reduce the dimensionality of the input very complex. space. This approach is used in conjunction with adaptive Dave Higdon constrained sparse quadrature to construct the surrogate Los Alamos National Laboratory model coefficients. Domain clustering methodologies are Statistical Sciences also employed to properly model plateaus and sharp dis- UQ12 Abstracts 123 [email protected] Ernesto E. Prudencio Institute for Computational Engineering and Sciences [email protected] MS60 Calibration, Validation and the Importance of Model Discrepancy MS61 A Random Iterative Proper Orthogonal Decompo- Extrapolation is inevitably accompanied by substantial un- sition Approach with Application to the Filtering certainty. To manage and quantify that uncertainty, cali- of Distributed Parameter Systems bration and validation are important tasks. But a funda- mental feature underlying all these activities is model dis- We consider the problem of filtering systems governed by crepancy, which is the difference between reality and the partial differential equations. We propose a randomly per- simulator output with ”best” or ”true” input values. This turbed iterative version of the snapshot proper orthogonal talk will show, both conceptually and through examples, decomposition (POD) technique, termed RI-POD, to con- that unless model discrepancy is acknowledged and care- struct an ROM to capture the systems global behaviour. fully modeled calibration and extrapolations will be biased The technique is data based, and is applicable to forced as and over-confident. well as unforced systems. The ROM generated is used to construct reduced order Kalman filters to solve the filtering Anthony O’Hagan problem. Univ. Sheffield, UK a.ohagan@sheffield.ac.uk Suman Chakravorty Texas A&M University Jenny Brynjarsdottir College Station, TX Statistical and Applied Mathematical Sciences Institute [email protected] [email protected] MS61 MS60 A New Approach to Uq Based on the Joint ”Experiment” and ”Traveling” Models, Extrapola- Excitation-Response Pdf: Theory and Simulation tion Risk from Undetected Model Bias, and Data Conditioning for Systematic Uncertainty in Exper- We study the evolution equation of joint excitation- iment Conditions response PDF obtained by Hopf functional approach for various stochastic systems. Some issues arising in this for- This talk will discuss some fundamental concepts and is- mulation are examined including, multiple available equa- sues related to extrapolative prediction risk associated with tions, representation of correlated random process, and etc. model validation and conditioning. Topics will include: This approach is tested with Nonlinear Advection equa- ”traveling model” which travels to predictions beyond the tion, Tumor cell model, Duffing Oscillator, and Limit Cycle validation or conditioning setting as a subset of the larger Oscillator, and the results are compared. ”experiment model” of the experiments; handling uncer- tainties accordingly; consistent and non-consistent bias and Heyrim Cho uncertainty in extrapolation; Type X validation or condi- Brown University tioning error from neglected systematic experimental un- Providence, RI certainty; data conditioning to mitigate associated predic- heyrim [email protected] tion risk. Daniele Venturi Vicente J. Romero Brown University Validation and Uncertainty Quantification Department daniele [email protected] Sandia National Laboratories [email protected] George E. Karniadakis Brown University Division of Applied Mathematics MS60 george [email protected] Towards Finding the Necessary Conditions for Jus- tifying Extrapolations MS61 A comprehensive approach is proposed to justify extrap- Bayesian UQ on Infinite Dimensional Spaces with olative predictions for models with known sources of er- Incompletely Specified Priors ror. The connection between model calibration, validation and prediction is made through the introduction of alterna- The Bayesian framework is popular way of handling data tive uncertainty models used to model the localized errors. in UQ. This is done by defining priors on (possibly infinite In addition a validation metric is introduced to provide a dimensional) spaces of measures and functions and con- quantitative characterization of consistency of model pre- ditioning those priors after the observation of the sample dictions when compared with validation data. The talk will data. It has been known since the earlier work of Diaconis discuss the challenges in caring out the proposed method- and Freedman that, when the probability space allows for ology. an infinite number of outcomes, the Bayesian posteriors, in general, do not converge towards the “true distribution.’ In Gabriel A. Terejanu this work we compute optimal bounds on posteriors when Institute for Computational Engineering and Sciences priors in incompletely specified (through finite-dimensional University of Texas at Austin marginals for instance). These bounds show that: (1) pri- [email protected] ors sharing the same finite dimensional marginals may lead to diverging posteriors under sample data (2) any desired 124 UQ12 Abstracts posterior can be achieved by a prior satisfying pre-specified mechanisms via probability distributions, dynamical aver- finite-dimensional constraints (3) the measurement of sam- aging of random slow-fast microscopic mechanisms, ensem- ple data (in general) increases uncertainty instead of de- ble averaging of fluctuating driving forces, and especially, creasing it if the classical Bayesian framework is applied data-driven quantification of uncertain mechanisms in wa- (“as is’) to an infinite (possibly high-dimensional) space. ter vapor dynamics. Finally, we develop a (OUQ) variant of the Bayesian frame- work that (1) allows to work with incompletely specified Jinqiao Duan priors (2) remains consistent in infinite-dimensional spaces Institute for Pure and Applied Mathematics (whose posteriors converge towards the “true distribution’) UCLA (3) provides optimal bounds on posteriors (4) leads to [email protected] sharper estimates than those associated with the vanilla frequentist framework if the (incomplete) information on priors is accurate. This is a joint work with Clint Scovel MS62 (LANL) and Tim Sullivan (Caltech) and a sequel to an ear- Stochastic Integrable Dynamics of Optical Pulses lier work on Optimal Uncertainty Quantification (OUQ, Propagating through an Active Medium http://arxiv.org/abs/1009.0679, joint with C. Scovel, T. Sullivan, M. McKerns (Caltech) and M. Ortiz (Caltech)). Resonant interaction of light with a randomly-prepared, lambda-configuration active optical medium is described Houman Owhadi by exact solutions of a completely-integrable, stochastic Applied Mathematics partial differential equation, thus combining the opposing Caltech concepts of integrability and disorder. An optical pulse [email protected] passing through such a material will switch randomly be- tween left- and right-hand circular polarizations. Exact probability distributions of the electric-field envelope vari- MS61 ables describing the light polarization and their switching Conjugate Unscented Transformation – ”Optimal times will be presented . Quadrature” Gregor Kovacic This talk will introduce a recently developed Conju- Rensselaer Polytechnic Inst gate Unscented Transformation (CUT) to compute multi- Dept of Mathematical Sciences dimensional expectation integrals. An extension of pop- [email protected] ular unscented transformation will be presented to find a minimal number of quadrature points that is equivalent to Ethan Atkins the Gaussian quadrature rule of same order. Equivalent to Courant Institute same order implies that both the new reduced quadrature [email protected] point set and the Gaussian quadrature product rule exactly reproduce the expectation integral involving a polynomial Peter R. Kramer function of order d. Rensselaer Polytechnic Institute Department of Mathematical Sciences Nagavenkat Adurthi [email protected] MAE Deaprtment University at Buffalo [email protected] Ildar R. Gabitov Department of Mathematics, University of Arizona [email protected] Puneet Singla Mechanical & Aerospace Engineering University at Buffalo MS62 [email protected] Reduced Models for Mode-locked Lasers with Noise Tarunraj Singh Dept of Mechanical Engineering We explore the impact of spontaneous emissions noise on SUNY at Buffalo mode-locked laser linewidth by using a variational tech- tsingh@buffalo.edu nique to reduce the original model, a stochastic partial differential equation, to a low-dimensional stochastic ordi- nary differential equation. The joint distribution of the pa- MS62 rameters is mapped to a full-width half-maximum measure Perspectives on Quantifying Uncertain Mecha- of the output laser linewidth, i.e., frequency uncertainty. nisms in Dynamical Systems Events causing the linewidth to exceed a prescribed un- certainty level are rare, requiring the application of large Due to lack of scientific understanding, some mechanisms deviations theory or importance sampling approaches. are not always well-represented in mathematical models for complex systems. The impact of these uncertain mech- Richard O. Moore, Daniel S. Cargill anisms on the overall system evolution may be delicate New Jersey Institute of Technology or even profound. These uncertain mechanisms are some- [email protected], [email protected] times microscopic, and it is desirable to examine how they affect the system at the macroscopic level since we are often Tobias Schaefer mainly interested in macroscopic dynamics. The speaker Department of Mathematics presents an overview of several available analytical and The College of Staten Island, City University of New York computational techniques for extracting macroscopic dy- [email protected] namics, while taking uncertain microscopic mechanisms into account. The issues include quantifying uncertain UQ12 Abstracts 125

MS62 loss due to uncertainty in inflow conditions. The results Analysis and Simulations of a Perturbed Stochastic will be used to answer the following questions: Do we need Nonlinear Schr¨odinger Equation for Pulse Propa- new probabilistic algorithms to quantify the impact of un- gation in Broadband Optical Fiber Lines certainty? What is the optimal basis for standard per- formance metrics in turbomachinery? What are the com- We study the interplay between bit pattern randomness, putational and accuracy requirements of this probabilistic Kerr nonlinearity, and delayed Raman response in broad- approach? Are there alternate (more efficient) techniques? band multichannel optical fiber transmission lines. We We believe that the answers to the above questions will show that pulse propagation can be described by a per- provide a quantitative basis to assess the usefulness of non- turbed stochastic nonlinear Schr¨odinger equation, which intrusive (and possibly intrusive) probabilistic methods to takes into account changes in pulse amplitude, group veloc- analyze variability in engineering designs. ity, and position. Numerical simulations with the stochas- tic PDE along with analysis of the corresponding stochastic Sriram Shankaran reduced ODE model are used to calculate the bit-error-rate General Electric and to identify the major error-generating processes in the [email protected] fiber line. Avner Peleg MS64 State University of New York at Buffalo Prior Modelling for Inverse Problems Using Gaus- apeleg@buffalo.edu sian Markov Random Fields

Yeojin Chung In inverse problems, regularization functions are often cho- Southern Methodist University sen to incorporate prior information about a spatially dis- [email protected] tributed parameter, such as differentiability. In contrast, a standard Bayesian approach assumes that the value of each parameter is Gaussian with mean and variance dependent MS63 upon the values of its neighbors. This approach leads to Quantification of Uncertainty in Wind Energy a so-called Gaussian Markov random field prior. We will explore the interesting connections between these two ap- Abstract not available at time of publication. proaches, which in many cases yield equivalent variational problems. Karthik Duraisamy Stanford Johnathan M. Bardsley [email protected] University of Montana [email protected]

MS63 Uncertainty Quantification for Rayleigh-Taylor MS64 Turbulent Mixing Evaluation of Covariance Matrices and their use in Uncertainty Quantification We present two main results. First: a reformulation of con- vergence for simulations of turbulent flow, through binning Abstract not available at time of publication. solution values from neighboring points (in a ”supercell”) to define a finite approximation to a space-time dependent Eldad Haber probability density function. We thereby obtain conver- Department of Mathematics gence of fluctuations, and of nonlinear functions of the so- The University of British Columbia lution. Second: to reconstruct initial conditions (often not [email protected] recorded) from early time data with uncertainty bounds on the reconstruction and on the entire solution. MS64 Tulin Kaman Challenges in Uncertainty Quantification for Dy- SUNY Stony Brook namic History Matching [email protected] The inversion of large scale ill-posed problems introduces multiple challenges. Examples would be: how to prescribe James Glimm a suitable regularizer, design an informative experiment, State University of New York, Stony Brook quantify uncertainty, exploit supplementary information [email protected] from multiple sources, or even how to define an appropri- ate optimization scheme. In the context of flow in porous MS63 medium, subsurface parameters are inferred through in- version of oil production data in a process called history Case Studies in Uncertainty Quantification for matching. In this talk the inherent uncertainty of the prob- Aerodynamic Problems in Turbomachinery lem is tackled in terms of prior sampling. Despite meticu- In this study, we study the use of common UQ methods lous efforts to minimize the variability of the solution space, for problems of importance in practical engineering de- the distribution of the posterior may remain rather intru- signs. In particular, we assess the efficiency of common sive. In particular, geo-statisticians often propose large sets polynomial chaos basis functions and sampling techniques of prior samples that regardless of their apparent geologi- like Smolyak-grids. The computational frame-work will be cal distinction are almost entirely flow equivalent. As an first validated against Monte-Carlo simulations to assess antidote, a reduced space hierarchical clustering of flow- convergence of pdfs. It will then be used to assess the relevant indicators is proposed for aggregation of these variability in compressor blade efficiency and turbine vane samples. The effectiveness of the method is demonstrated both with synthetic and real field data. This research was 126 UQ12 Abstracts performed as part of IBM-Shell joint research project. chain models for neuron dynamics. Theories for predict- ing the size of synchronous firing events are presented, in Lior Horesh which the probabilistic dynamics between these events are Business Analytics and Mathematical Sciences taken into account. We use the theories to find different IBM TJ Watson Research Center model networks that preserve the global dynamics on these [email protected] networks.

Andrew R. Conn Katherine Newhall IBM T J Watson Research Ctr Rensselaer Polytechnic Institute [email protected] [email protected]

Gijs van Essen, Eduardo Jimenez MS65 Shell Innovation Research & Development [email protected], [email protected] Network Analysis of Anisotropic Electrical Prop- erties in Percolating Sheared Nanorod Dispersions

Sippe Douma Percolation in nanorod dispersions induces extreme prop- Shell erties, with large variability near the percolation thresh- [email protected] old. We investigate electrical properties across the dimen- sional percolation phase diagram of sheared nanorod dis- Ulisses Mello persions [Zheng et al., Adv. Mater. 19, 4038 (2007)]. We IBM Watson Research Center quantify bulk average properties and corresponding fluctu- [email protected] ations over Monte Carlo realizations, including finite size effects. We also identify fluctuations within realizations, with special attention on the tails of current distributions MS64 and other rare nanorod subsets which dominate the elec- Title Not Available at Time of Publication trical response. Abstract not available at time of publication. Feng B. Shi UNC,ChapelHill Luis Tenorio [email protected] Colorado School of Mines [email protected] Mark Forest University of North Carolina at Chapel Hill MS65 [email protected] The Influence of Topology on Sound Propagation in Granular Force Networks Peter J. Mucha University of North Carolina Granular materials have been modelled using both contin- [email protected] uum and particulate perspectives but neither approach can capture complex behaviours during sound propagation. A Simi Wang network representation provides an intermediate approach University of North Carolina at Chapel Hill that allows one to directly consider microscopic features [email protected] and longer-range interactions, e.g. force chains. In experi- ments on granular materials composed of photoelastic par- Xiaoyu Zheng ticles, we characterise the internal force structure and show Dept of Mathematics that weighted meso-scale network diagnostics are crucial Kent State University for quantifying sound propagation in this heterogeneous [email protected] medium.

Danielle S. Bassett Ruhai Zhou University of California Santa Barbara Old Dominion University [email protected] [email protected]

Eli Owens, Karen Daniels MS65 North Carolina State University Asymptotically Inspired Moment-Closure Approx- [email protected], [email protected] imation for Adaptive Networks Mason A. Porter Adaptive social networks, in which nodes and network University of Oxford structure co-evolve, are often described using a mean-field Oxford Centre for Industrial and Applied Mathematics system of equations for the density of node and link types. [email protected] These equations constitute an open system due to depen- dence on higher order topological structures. We propose a moment-closure approximation based on the analytical MS65 description of the system in an asymptotic regime. We Size of Synchronous Firing Events in Model Neu- show a good agreement between the improved mean-field ron Systems prediction and simulations of the full network system.

We investigate the interaction of synchronous dynamics Maxim S. Shkarayev and the network topology in simple pulse-coupled Markov Mathematical Science Department, Rensselaer Polytech UQ12 Abstracts 127

Inst. multiple climate model errors. We build a Bayesian hier- [email protected] archical model that ac- counts for the spatial dependence of individual models as well as cross-covariances across differ- Leah Shaw ent climate models. Our method allows for a non-separable College of William and Mary and non-stationary cross-covariance structure. We also Dept. of Applied Science present a covariance approximation approach to facilitate [email protected] the computation in the modeling and analysis of very large multivariate spatial data sets. The covariance approxima- tion consists of two parts: a reduced-rank part to capture MS66 the large-scale spatial dependence, and a sparse covariance Propagating Uncertainty from General Circulation matrix to correct the small-scale dependence error induced Models through Projected Local Impacts by the reduced rank approximation. Simulation results of model fitting and prediction show substantial improvement We develop statistical methodologies for impact analysis of the proposed approximation over the predictive process of climate change for economically important sectors, and approximation and the independent blocks analysis. We transfer this development to the design of decision-support then apply our computational approach to the joint statis- tools. Our approach is to implementin the context of spe- tical modeling of multiple climate model errors. cific regions and sensitive sectors of high economic and so- cial importancetools that allow a coherent characterization Huiyan Sang of the propagation of uncertainty all the way to projected Texas A&M University impacts, appropriately equipped with confidence or credi- [email protected] bility statements relevant to the quantification of risks. Peter Guttorp MS67 University of Washington Validation Experience for Stochastic Models of [email protected] Groundwater Flow and Radionuclide Transport at Underground Nuclear Test Sites and the Shift Away from Quantitative Measures and Toward It- MS66 erative Improvement Measures of Model Skill and Parametric Uncer- tainty Estimation for Climate Model Development Several groundwater models of underground nuclear tests, incorporating uncertainty, were subjected to validation Measures of model skill and parametric uncertainty esti- processes. There were failures in balancing readily quan- mation for climate model development. tifiable and measurable model attributes against harder- to-measure conceptual issues, in gaining decision-maker ac- Gabriel Huerta ceptance of statistically based conclusions, and ultimately Indiana University in the quality and quantity of data forming the foundation [email protected] of the original models. From this experience, the regulatory framework has shifted away from validation and toward a Charles Jackson modelevaluationapproachwithanemphasisoniterative UTIG improvement. University of Texas at Austin [email protected] Jenny Chapman Desert Research Institute [email protected] MS66 Optimal Parameter Estimation in Community At- Ahmed Hassan mosphere Models Irrigation and Hydraulics Department Cairo University The current tuning process of parameters in global climate [email protected] models is often performed subjectively or treated as an optimization procedure to minimize model biases based Karl Pohlmann on observations. In this study, a stochastic important- Desert Research Institute sampling algorithm, Multiple Very Fast Simulated Anneal- [email protected] ing (MVFSA) was employed to efficiently sample the input parameters in the KF scheme based on a skill score so that the algorithm progressively moved toward regions of the MS67 parameter space that minimize model errors. Validation and Data Assimilation of Shallow Water Guang Lin, Ben Yang, Yun Qian, Ruby Leung Models Pacific Northwest National Laboratory We will discuss the validation of large-scale coupled wave- [email protected], [email protected], current models for simulating hurricane storm surge. [email protected], [email protected] We will demonstrate that by including the appropriate physics, discretizations, and parameters, one can consis- MS66 tently match measured data from a wide range of hurri- canes. However, we will also point out where the mod- Covariance Approximation for Large Multivariate els have significant uncertainty and describe a new data- Spatial Datasets with An Application to Multiple assimilation framework for real-time hurricane surge fore- Climate Models casts. In this work we investigate the cross-correlations across Clint Dawson 128 UQ12 Abstracts

Institute for Computational Engineering and Sciences Albuquerque, New Mexico 87185 University of Texas at Austin [email protected] [email protected] Brian Williams, Rick Picard Jennifer Proft, J. Casey Dietrich Los Alamos National Laboratory University of Texas at Austin [email protected], [email protected] [email protected], [email protected]

Troy Butler MS68 Institute for Computational Engineering and Sciences Uncertainty Quantification and Model Validation University of Texas at Austin in Flight Control Applications [email protected] Models derived from physics or data are often too com- plicated for analysis or controller design. This is leads to Talea Mayo reduced order modeling. However, it is important to assess University of Texas at Austin the quality of such models. Often, for nonlinear systems [email protected] in particular, model validation is performed using Monte- Carlo simulations. Two systems are qualified to be similar Joannes Westerink if the variance of the trajectories are small. In this paper, Department of Civil Engineering and Geological Sciences we present a new paradigm where two systems are qualified University of Notre Dame to be similar if the density function of the output is simi- [email protected] lar, when excited by the same random input. This is more general than comparing few moments or the support of Ibrahim Hoteit the trajectories. We use Wasserstein distance to compare King Abdullah University of Science and Technology density functions and also argue why the commonly use (KAUST) Kullback-Liebler metric is unsuitable for model validation. [email protected] Examples based on flight control problems are presented to illustrate model validation in this framework. M.U. Altaf King Abdullah University of Science and Technology Raktim Bhattacharya [email protected] Texas A&M University College Station, Texas [email protected] MS67 Quantifying Long-Range Predictability and Model MS68 Error through Data Clustering and Information Theory New Positive-definite Random Matrix Ensembles for Stochastic Dynamical System with High Level We present a framework blending data clustering and in- of Heterogeneous Uncertainties formation theory to quantify long-range initial-value pre- dictability and forecast error with imperfect models in com- The scientific community has seen an increasing surge plex dynamical systems. With reference to wind-driven of applications of positive-definite random matrix ensem- ocean circulation, we demonstrate that the pertinent infor- bles in the fields of mechanics and multiscale mechan- mation for long-range forecasting can be represented via ics in recent years. These ensembles are employed to a coarse-grained partition of the set of initial data avail- directly model several positive-definite matrix-valued ob- able to a model. A related formalism is applied to assess jects, e.g., mass matrices, stiffness matrices, constitutive the forecast skill of Markov models of ocean circulation elasto-plasticity tensor, etc. Matrix variate distributions, regimes. e.g., Wishart/Gamma distribution, Beta Type 1 distribu- tion, Kummer-Beta distribution, or distributions derived Dimitris Giannakis from them, are currently considered for this modeling pur- New York University pose. These distributions are, however, parameterized such [email protected] that they induce specific mean and covariance structures that do not allow sufficient flexibility in modeling high level of uncertainties. The current work will discuss two new MS67 positive-definite random matrix ensembles that are likely Model Selection and Inference for a Nuclear Reac- to provide more flexibility in modeling high level of uncer- tor Application tainties. We compare statistical techniques for model selection, with Sonjoy Das, Sonjoy Das a focus on information theoretic approaches, applied in University at Buffalo a statistical framework for calibration of computer codes. sonjoy@buffalo.edu, sonjoy@buffalo.edu Additionally, we propose a sequential strategy for itera- tive refinement of importance distributions used to sample uncertain model inputs to estimate the probability that a MS68 calibrated model exceeds a fixed or random threshold. We Existence and Stability of Equilibria in Stochastic demonstrate these methods on a nuclear reactor applica- Galerkin Methods tion involving calculation of peak coolant temperature with the R7 code. We consider dynamical systems in form of nonlinear au- tonomous ordinary differential equations including random Laura Swiler parameters. Thus the corresponding solutions represent Sandia National Laboratories random processes. The existence of a unique stable equi- UQ12 Abstracts 129 librium is assumed for each sample of the parameters. the existence of a global compact random attractors for Thereby, the equilibria depend on the random parameters. general dynamical systems in weighted space of infinite se- We apply the polynomial chaos expansion of the unknown quences. We then apply the result to show the existence random process to solve the stochastic dynamical system. of a unique global compact random attractor for first or- The stochastic Galerkin method yields a larger coupled sys- der, second order and partly dissipative stochastic lattice tem of nonlinear ordinary differential equations satisfied by differential equations with random coupled coefficients and an approximation of the random process. The existence of multiplicative/additive white noise in weighted spaces. equilibria is investigated for the coupled system. More- over, we analyze the stability of these fixed points, where Xiaoying Han the spectrum of a Jacobian matrix has to be examined. Auburn University Numerical simulations of test examples are presented. [email protected] Roland Pulch University of Wuppertal MS69 [email protected] Unbiased Perturbations of the Navier-Stokes Equa- tion

MS68 We consider a new class of stochastic perturbations of the A Nonlinear Dimension Reduction Technique for Navier-Stokes equation. Its unique feature is the preserva- Random Fields Based on Topology-Preserving tion of the mean dynamics of the deterministic equation, Transformations hence it is an unbiased random perturbation of the equa- tion. We will discuss results for the steady state solutions The intrinsic dimensionality of a random field may be de- and the convergence to steady solutions, and show suffi- fined as the minimum number of degrees of freedom which cient conditions which are very similar to analogous results is neccessary to account for its relevant statistical informa- for the unperturbed equation. Numerical simulations com- tion. In this talk we will present a new nonlinear dimension paring this unbiased perturbation with the usual stochastic reduction technique for random fields based on latent vari- Navier-Stokes will be shown. able models and topology-preserving transformations. The low-dimensional embedding will be explicitly constructed Chia Ying Lee together with the probability measure associated with the Statistical and Applied Mathematical Sciences Institute reduced-order probability space. U. of North Carolina [email protected] Daniele Venturi Brown University Boris Rozovsky daniele [email protected] Brown University [email protected] Guang Lin Pacific Northwest National Laboratory [email protected] MS69 Generalized Malliavin Calculus and Spdes in George E. Karniadakis Higher-Order Chaos Spaces Brown University Division of Applied Mathematics The Malliavin derivative, divergence operator (Skorokhod george [email protected] integral), and the Ornstein-Uhlenbeck operator are ex- tended from the traditional Gaussian setting, or first-order chaos space, to nonlinear generalized functionals of white MS69 noise, which are elements of the full chaos space. These New Results for the Stochastic PDEs of Fluid Dy- extensions are then applied to study stochastic elliptic namics and parabolic equations driven by noise from higher-order chaos spaces. The addition of white noise driven terms to the fundamen- tal equations of physics and engineering are used to model Sergey Lototsky numerical and empirical uncertainties. In this talk we will Department of Mathematics discuss some recent results for the Stochastic Navier-Stokes University of Southern California and Euler Equations as well as for the Stochastic Primitive [email protected] Equations, a basic model in geophysical scale fluid flows. For all of the above systems our results cover the case of a Boris Rozovskii general nonlinear multiplicative stochastic forcing. Brown University boris [email protected] Nathan Glatt-Holtz Indiana University Dora Selesi [email protected] University of Novi Sad [email protected] MS69 Asymptotic Behavior of Stochastic Lattice Differ- MS69 ential Equations Stochastic-Integral Models for Propagation-of- Uncertainty Problems in Nondestructive Evalua- Random attractor is an important concept to describe long- tion term behavior of solutions for a given stochastic system. In this talk we will first provide sufficient conditions for Generalized polynomical chaos (gPC) and the probabilistic 130 UQ12 Abstracts collocation method (PCM) are finding considerable appli- ensemble Kalman filter data assimilation applied to the cation to problems of interest to engineers in which random Lorenz 40-variable model. The relevance of the technique, parame- ters are an essential feature of the mathematical as well as its utility, for operational data assimilation sys- model. So far the applications have been mainly to stochas- tems will be presented and discussed. tic partial differential equations, but we extend the method to volume-integral equations, which have met great suc- Humberto C. Godinez cess in electromagnetic nondestructive evaluation (NDE), Los Alamos National Laboratory especially with eddy-currents. The problems of main in- Applied Mathematics and Plasma Physics terest to the NDE community in this connection are con- [email protected] cerned with the issue of propagation of uncertainty when the relevant parameters are not well characterized, or are Dacian N. Daescu known simply as random variables. We demonstrate the Portland State University ideas by considering a metallic surface that has undergone Department of Mathematics and Statistics a shot-peening treatment to reduce residual stresses, and [email protected] has, therefore, become a random conductivity field. Elias Sabbagh MS70 Victor Technologies The Estimation of Functional Uncertainty using [email protected] Polynomial Chaos and Adjoint Equations

Kim Murphy, Harold Sabbagh The combined use of nonintrusive polynomial chaos (PC) Victor Technologies, LLC and adjoint equations (yielding the gradient) is addressed [email protected], [email protected] aimed at the estimation of uncertainty of a valuable func- tional subject to large errors in the input data. Random John Aldrin variables providing maximum impact on the result (leading Computationaltools values) may be found using the gradient information that [email protected] allows reduction of the problem dimension. The gradient may be also used for the calculation of PC coefficients, thus enabling further acceleration of the computations. Using Jeremy Knopp gradient information for the estimation of polynomial coef- Air Force Research Laboratory ficients (APC) also provides a significant reduction of the [email protected] computation time. The adjoint Monte VCarlo (AMC)is highly efficient from a computational viewpoint and accu- Mark Blodgett rate for moderate amplitude of errors. For a large number Air Forch Research Laboratory of random variables, the accuracy of AMC is close (or even [email protected] superior) to PC results even under large error. Michael Navon MS70 Florida State University Hybrid Methods for Data Assimilation [email protected] I present a theoretical comparison of two widely used data assimilation methods: the ensemble Kalman filter (EnKF) MS70 approach and the four dimensional variational (4D-Var) FATODE: A Library for Forward, Tangent Linear, approach. Then I propose a suboptimal hybridization and Adjoint ODE Integration scheme to combine the advantages of the EnKF and the 4D-Var. This new hybrid technique is computationally FATODE is a FORTRAN library for the integration of or- less expensive than the full 4D-Var and, in simulations, dinary differential equations with direct and adjoint sensi- performs better than EnKF for both linear and nonlinear tivity analysis capabilities. The paper describes the capa- test problems. bilities, implementation, code organization, and usage of this package. FATODE implements the forward, adjoint, Haiyan Cheng and tangent linear models for four families of methods — Willamette University ERK, FIRK, SDIRK, and Rosenbrock. A wide range of [email protected] applications are expected to benefit from its use; examples include parameter estimation, data assimilation, optimal Adrian Sandu control, and uncertainty quantification. Virginia Polytechnic Institute and State University Hong Zhang [email protected] Virginia Tech [email protected]

MS70 Adrian Sandu Model Covariance Sensitivity as a Guidance for Lo- Virginia Polytechnic Institute and calization in Data Assimilation State University [email protected] In this talk we present how to use model covariance sen- sitivity information to guide, in a more precise manner, the selection of appropriate cross-correlation length-scale MS71 parameters for model covariance localization techniques. Upscaling Covariance sensitivities are obtained using adjoint-based Micro-scale Material Variability Through the use methods. Numerical experiments are presented for the UQ12 Abstracts 131 of Random Voronoi Tessellations criterion is reliable owing to the accurate and conservative error estimate, and that the refinement measures outper- A randomly seeded Voronoi tessellation is used to model form uniform refinement. the microscale grain structure of a thin ductile ring. Each grain is assigned an elastic stiffness tensor with cubic sym- Gianluca Iaccarino metry but with randomly oriented principal directions. Stanford University The ring is subjected to internal pressure loading and de- [email protected] formed elastically. The displacement and stress response of the ring is studied from the perspective of homogeniza- Jeroen Witteveen tion theory as the ratio of the grain size to ring diameter Stanford University is varied. Center for Turbulence Research [email protected] Joseph Bishop Sandia National Laboratory [email protected] MS71 Random Poisson-Disk Samples and Meshes MS71 Maximal Poisson-disk sampling produces random point Discrete Models of Fracture and Mass Transport clouds of uniform density. Every part of the domain is in Cement-based Composites within distance r of a sample, yet no two samples are closer than r to each other. I will describe an optimal algorithm The life-cycle performance of structural concrete is af- for generating samples, and how we sample the domain fected by material features and internal processes that span boundary differently to get a Delaunay triangle or Voronoi several length scales. This presentation regards the dis- polyhedral mesh. These meshes have provable quality sim- crete lattice modeling of such features, fracture, and crack- ilar to determinist meshes, but with uniform random ori- assisted mass transport in concrete. Domain discretization entations. is based on Voronoi/Delaunay tessellations of semi-random point sets. Lack of scale separation complicates the model- Scott A. Mitchell, Mohamed S. Ebeida ing efforts. Variability is quantified by simulating multiple, Sandia National Laboratories random realizations of nominally identical structures. [email protected], [email protected] John Bolander UC Davis MS72 [email protected] Quantile Emulation for Non-Gaussian Stochastic Models Peter Grassl School of Engineering Stochastic models often require a large number of expensive University of Glasgow runs for practical applications. In the emulator framework, [email protected] the model is replaced with a faster surrogate (a Gaussian process) which captures prediction uncertainty under the assumption of Gaussianity. If the simulator response is MS71 non-Gaussian however, alternative approaches have to be Maximal Poisson-disk Sampling for UQ Purposes sought. We investigate emulation of quantiles and discuss how to perform Bayesian inference for this class of models. We describe a new approach to solve the maximal Poisson- A real world example application is provided. disk sampling in d-dimensional spaces for UQ purposes. In contrast to existing methods, our technique tracks the Remi Barillec remaining voids after a classical dart throwing phase by University of Aston, UK constructing the associated convex hulls. This provides a Non-linearity and Complexity Research Group mechanism for termination with bounded time complex- [email protected] ity. We also show how to utilize this sampling techniques to achieve better estimations of probability of failure and Alexis Boukouvalas, Dan Cornford detection of discontinuities. We demonstrate application University of Aston, UK examples. [email protected], [email protected] Mohamed S. Ebeida Sandia National Laboratories MS72 [email protected] Methods for Assessing Chances of Rare, High- Consequence Events in Groundwater Monitoring MS71 This talk looks at multiple approaches for assessing uncer- Simplex Stochastic Collocation Approach tainty in high-consequence, low probability events related to groundwater monitoring. We consider Monte Carlo, The Simplex Stochastic Collocation method is introduced Markov chain Monte Carlo, and null-space Monte Carlo, as an non-intrusive, adaptive un- certainty quantification all of which have difficulty estimating the chance of low method for computational problems with random inputs. probability events. We also look at modifications to these The effectiveness of adaptive formulation is determined by approaches that help address this issue. We focus on a both h- and p-refinement measures and a stopping crite- synthetic application in 3d solute transport. rion derived from an error estimate based on hierarchical surpluses. A p-criterion for the polynomial degree p is for- Dave Higdon mulated to achieves a constant order of convergence with Los Alamos National Laboratory dimensionality. Numerical results show that the stopping 132 UQ12 Abstracts

Statistical Sciences challenges lie and outline future research. [email protected] Peter Challenor Elizabeth Keating, Zhenxue Dai, James Gattiker National Oceanography Centre, Southampton, UK Los Alamos National Laboratory [email protected] [email protected], [email protected], [email protected] MS73 MS72 Calibration of Gravity Waves in WACCM Sensitivity Analysis and Estimation of Extreme The Whole Atmosphere Community Climate Model Tail Behaviour in Two-dimensional Monte Carlo (WACCM) is a comprehensive numerical model, span- Simulation (2DMC) ning the range of altitude from the Earth’s surface to Two-dimensional Monte Carlo simulation is frequently the thermosphere. Gravity waves are a key component used to implement risk models, comprising mechanistic and of the dynamics, and are parametrized. However, the cur- probabilistic components, to separately quantify uncer- rent parametrization does not result in fully realistic fea- tainty and variability within a population. Risk managers tures such as the period of the quasi-biennial oscillation. must assess the proportion exceeding a critical threshold, We carry out a Bayesian calibration of the gravity waves and the levels of exceedence. We describe an efficient scheme using efficient sequential design of experiments. method combining Bayesian model emulation and extreme Serge Guillas value theory, which can also be used to quickly identify University College London those model parameters having the greatest impact on the [email protected] probabilities of rare events. Marc C. Kennedy, Victoria Roelofs Hanli Liu The Food and Environment Research Agency NCAR [email protected], [email protected] [email protected] MS73 MS72 Uncertainty in Modeled Upper Ocean Heat Con- An Investigation of the Pineapple Express Phe- tent Change using a Large Ensemble nomenon via Bivariate Extreme Value Theory We evaluate the uncertainty in the heat content change We apply bivariate extreme value methods in an examina- (∆Q) in the top 700 meters in the ocean component of tion of extreme winter precipitation events produced by a the CCSM3.0 model using an emulator created from a regional climate model. We first assess the model’s ability large member ensemble. A large ensemble of the CCSM3.0 to reproduce these events in the US Pacific coast region. ocean/ice system at a 3 degree resolution was created by We then link these events to large-scale process dynamics, varying parameters related to ocean mixing and advection. with a particular focus on the pineapple express (PE), a The outcomes are compared to four estimates using obser- special type of winter event. Finally, we examine extreme vational data. We explore how other modeled estimates of events produced by the model in a future climate scenario. ∆Q from the CMIP3 ensemble can be understood in the context of this large ensemble.

Grant Weller Robin Tokmakian Department of Statistics, Naval Postgraduate School Colorado State University [email protected] [email protected] MS73 Dan Cooley Colorado State University Emulating Time Series Output of Climate Models [email protected] The RAPIT project is concerned with the risk, probability and impacts of future changes to the Atlantic Meridional Stephan Sain Overturning Circulation (AMOC) under anthropogenic Institute for Mathematics Applied to Geosciences forcing. Our principle resource is an unprecedented per- National Center for Atmospheric Research turbed parameter ensemble, (order 10,000 runs), of the [email protected] fully coupled, un-flux-adjusted climate model, HadCM3. We present dynamic methods for emulating the AMOC time series output by the model and explore the use of MS73 these emulators in helping to constrain future AMOC pro- An Introduction to Emulators and Climate Models jections using different data sources and ocean monitoring systems. State of the art climate simulators pose particular prob- lems for UQ methods. They have very large state spaces Danny Williamson 12 (o10 ) and are computationally expensive. In this talk Durham University I will introduce climate models, what they do, how they [email protected] work and the problems that arise when we quantify their uncertainty, identify its source and use data to reduce it. I will outline some solutions to these , where the current MS74 A Non-intrusive Alternative to a Computational UQ12 Abstracts 133

Measure Theoretic Inverse recipe applicable in virtually any situation. We demon- strate this fiducial recipe on examples of varying complex- We develop a non-intrusive technique for extending the ity. We also investigate, by simulation and by theoreti- computational measure-theoretic methodology to problems cal considerations, some properties of the statistical pro- where it is either infeasible or impractical to obtain deriva- cedures derived by the fiducial recipe showing they often tive information from the map. We discuss various sources posses good repeated sampling, frequentist properties. As of errors in the methodology and how to address these. an example we apply the recipe to interval observed mixed linear model. Portions of this talk are based on a joined Troy Butler work with Hari Iyer, Thomas C.M. Lee and Jessi Cisewski Institute for Computational Engineering and Sciences University of Texas at Austin [email protected] Jan Hannig Department of Statistics, University of North Carolina [email protected] MS74 Inverse Function-based Methodology for UQ MS75 There is a growing need of statistical methodology for Variable Selection and Sensitivity Analysis via Dy- problems addressing inverse sensitivity analysis in which namic Trees with an application to Computer Code there are one or multiple quantities of interest connected Performance Tuning to the input space through a system of partial differen- tial equations. Though Bayesian methodology has become We introduce a new response surface methodology, dy- quite popular in this setting, we explore potential non- namic trees, with an application to variable selection and Bayesian solutions using some newer ideas related to in- an input sensitivity analysis. These methods are used to verse function-based inference. The goal is to understand analyze automatic computer code tuning that combines the distribution on the parameter space without use of pri- classification and regression elements on large data sets. ors. The talk will also highlight an R package implementing the methods, called dynaTree, which is available on CRAN. Jessi Cisewski Department of Statistics and Operations Research Robert Gramacy University of North Carolina at Chapel Hill University of Chicago [email protected] [email protected]

MS74 MS75 A Computational Approach for Inverse Sensitivity Bayesian Filtering in Large-Scale Geophysical Sys- Problems using Set-valued Inverses and Measure tems and Uncertainty Quantification Theory Bayesian filters compute the probability distribution of the We discuss a numerical method for inverse sensitivity anal- system, thus readily provide a framework for uncertainty ysis of a deterministic map from a set of parameters to quantification and reduction. In geophysical applications, a randomly perturbed quantity of interest. The solution filtering techniques are designed to produce a small sample method has two stages: (1) approximate the unique set- of state estimates, as a way to reduce computational bur- valued solution to the inverse problem and (2) apply mea- den. This, coupled with poorly known model-observation sure theory to compute the approximate probability mea- deficiencies, would lead to distribution estimates that are sure on the parameter space that solves the inverse prob- far from optimal, yet still provide meaningful estimates. lem. We discuss convergence and analysis of the method. We present this problem and discuss possible approaches to produce improved uncertainty estimates. Donald Estep Ibrahim Hoteit Colorado State University King Abdullah University of Science and Technology [email protected] or [email protected] (KAUST) [email protected] MS74 Bruce Cornuelle Inverse Problem and Fisher’s View of Statistical University of California, San Diego Inference [email protected] R. A. Fisher’s fiducial inference has been the subject of many discussions and controversies ever since he intro- Aneesh Subramanian duced the idea during the 1930’s. The idea experienced University of California, San Diego, USA a bumpy ride, to say the least, during its early years [email protected] and one can safely say that it eventually fell into disfavor among mainstream statisticians. However, it appears to Hajoon Song have made a resurgence recently under various guises. For University of California, Santa Cruz, USA example under the new name generalized inference fiducial [email protected] inference has proved to be a useful tool for deriving sta- tistical procedures for problems where frequentist methods Xiaodong Luo with good properties were previously unavailable. There- 1King Abdullah University of Science and Technology fore we believe that the fiducial argument of R.A. Fisher (KAUST), deserves a fresh look from a new angle. In this talk we first [email protected] generalize Fisher’s fiducial argument and obtain a fiducial 134 UQ12 Abstracts

MS75 School for Engineering of Matter On Data Partitioning for Model Validation Arizona State University [email protected], [email protected] Validation processes usually require that experimental data be split into calibration and validation datasets. As this choice is often subjective, we introduce an approach based MS76 on the concept of cross-validation. The proposed method Toward Analysis of Uncertainty in Chaotic Systems allows one to systematically determine the optimal par- tition and to address fundamental issues in validation, Due to the exponential growth of small disturbances, un- namely that the model 1) be evaluated with respect to certainty analysis in chaotic systems is challenging. For the data and to predictions of quantities of interest; 2) be example, even for mean quantities, sensitivity analysis us- highly challenged by the validation set. ing a standard adjoint-based approach fails because the adjoint variables diverge. In this talk, recent work on un- Rebecca Morrison certainty quantification for chaotic systems is described. In UT Austin particular, several methods, including polynomial chaos ex- [email protected] pansions, are evaluated for capturing uncertainty in mean quantities using the Lorenz equations as a model problem. Corey Bryant The University of Texas at Austin Eleanor Deram Institute for Computational Engineering and Sciences University of Texas at Austin [email protected] [email protected]

Gabriel A. Terejanu Todd Oliver Institute for Computational Engineering and Sciences PECOS/ICES, The University of Texas at Austin University of Texas at Austin [email protected] [email protected] Robert D. Moser Serge Prudhomme University of Texas at Austin ICES [email protected] The University of Texas at Austin [email protected] MS76 A Dynamically Weighted Particle Filter for Sea Kenji Miki Surface Temperature Modeling Institute for Computational Engineering and Sciences University of Texas at Austin The sea surface temperature (SST) is an important factor [email protected] of the earth climate system. We analyze the SST data of Caribbean Islands area after a hurricane using the radial basis function network-based dynamic model. Comparing MS75 to the traditional grid-based approach, our approach re- Validation of a Random Matrix Model for quires much less CPU time and makes the real-time fore- Mesoscale Elastic Description of Materials with cast of SST doable on a personal computer. Microstructures Faming Liang We present validation of a bounded random matrix model Texas A&M University defining the constitutive elastic behavior of heterogeneous College Station, Texas material. Using an experimental database of microstruc- fl[email protected] tures, we first construct a surrogate model in order to fur- ther the data, required for calibration and validation. We Duchwan Ryu then recall the construction of the random matrix model Department of Biostatistics characterizing the mesoscale apparent elasticity tensor of Medical College of Georgia the material. Finally a procedure is presented to validate [email protected] the model using observations resulting from fine scale sim- ulations. Bani Mallick Arash Noshadravan Department of Statistics University of Southern California Texas A&M University [email protected] [email protected]

Roger Ghanem MS76 University of Southern California Aerospace and Mechanical Engineering and Civil Characterization of the Effect of Uncertainty in Engineering Terrain Representations for Modeling Geophysical [email protected] Mass Flows In modeling flow on natural terrains a persistent and diffi- Johann Guilleminot cult problem is the effect of errors and uncertainties in the Laboratoire de Modelisation et Simulation Multi Echelle representation of the terrain. In this talk we will discuss Universite Paris-Est the effect of such uncertainty on outputs from a geophysi- [email protected] cal mass flow model. We will then introduce methodology to systematically account for these uncertainties by using Ikshwaku Atodaria, Pedro Peralta a model of the error and sampling it to create ensembles UQ12 Abstracts 135 of possible elevations. (S)PDE for this estimate in the continuous-time limit.

Ramona Stefanescu Kody Law University at Buffalo Mathematics Institute ers32@buffalo.edu University of Warwick [email protected] Abani K. Patra SUNY at Buffalo Dept of Mechanical Engineering MS77 [email protected]ffalo.edu Adaptive Construction of Surrogates for Bayesian Inference Marcus Bursik Surrogate models are often used to accelerate Bayesian in- Dept. of Geology ference in statistical inverse problems. Yet the construction SUNY at Buffalo of globally accurate surrogates for complex models can be mib@buffalo.edu prohibitive and in a sense unnecessary, as the posterior dis- tribution typically concentrates on a small fraction of the MS77 prior support. We present a new adaptive approach that uses stochastic optimization (the cross-entropy method) to Statistical Inference Problems for Nonlinear construct surrogates that are accurate over the support SPDEs of the posterior distribution. Efficiency and accuracy are We consider a parameter estimation problem to determine demonstrated via parameter inference in nonlinear PDEs. the drift coefficient for a large class of parabolci Stochastic Jinglai Li,YoussefM.Marzouk PDEs driven by additive or multiplicative noise. We derive Massachusetts Institute of Technology several different classes of estimators based on the first N [email protected], [email protected] Fourier modes of a sample path observed continuously on a finite time interval. We study the consistency and asymp- totic normality of these estimators as number of Fourier MS77 coefficients increases, and we present some numerical sim- Reimagining Diffusion Monte Carlo for Quantum ulation results. Monte Carlo, Sequential Importance Sampling, Igor Cialenco Rare Event Simulation and More Illinois Institute of Technology Diffusion Monte Carlo was developed forty years ago within [email protected] the Quantum Monte Carlo community to compute ground state energies of the Schrodinger operator. Since then the MS77 basic birth/death strategy of DMC has found its way into a wide variety of application areas. For example efficient Filtering the Navier Stokes Equations resampling strategies used in sequential importance sam- Data assimilation refers to methodologies for the incorpo- pling algorithms (e.g. particle filters) are based on DMC. ration of noisy observations of a physical system into an un- As I will demonstrate, some tempting generalizations of the derlying model in order to infer the properties of the state basic DMC framework lead to an instability in the time of the system (possibly including parameters). The model discretization parameter. This instability has important itself is typically subject to uncertainties, in the input data consequences in, for example, applications of DMC in se- and in the physical laws themselves. This leads naturally quential importance sampling and rare event simulation. to a Bayesian formulation in which the posterior probabil- We suggest a modification of the basic DMC algorithm ity distribution of the system state, given the observations, that eliminates this instability. In fact, the new algorithm plays a central conceptual role. The aim of this paper is is more efficient than DMC under any condition (parame- to use this Bayesian posterior probability distribution as ter regime). We prove this as well as show numerically and a gold standard against which to evaluate various com- analytically that it is stable in unstable regimes for DMC. monly used data assimilation algorithms. We study the 2D Jonathan Weare Navier-Stokes equations in a periodic geometry and eval- University of Chicago uate a variety of sequential filtering approximations based Department of Mathematics on 3DVAR and on extended and ensemble Kalman filters. [email protected] The performance of these data assimilation algorithms is quantified by comparing the relative error in reproducing moments of the posterior probability distribution. The pri- Martin Hairer mary conclusions of the study are that: (i) with appropri- The University of Warwick ate parameter choices, approximate filters can perform well [email protected] in reproducing the mean of the desired probability distri- bution; (ii) however these filters typically perform poorly MS78 when attempting to reproduce information about covari- ance; (iii) this poor performance is compounded by the Computing and Using Observation Impact in 4D- need to modify the filters, and their covariance in particu- Var Data Assimilation lar, in order to induce filter stability and avoid divergence. Data assimilation combines information from an imperfect Thus, whilst filters can be a useful tool in predicting mean model, sparse and noisy observations, and error statistics, behaviour, they should be viewed with caution as predic- to produce a best estimate of the state of a physical system. tors of uncertainty. We complement this study with (iv) a Different observational data points have different contribu- theoretical analysis of the ability of the filters to estimate tions to reducing the uncertainty with which the state is the mean state accurately, and we derive a non-autonomous estimated. In this paper we present a computational ap- 136 UQ12 Abstracts proach to quantify the observation impact for analyzing the Nathanial Burch effectiveness of the assimilation system, for data pruning, SAMSI and for designing future sensor networks. [email protected]

Alexandru Cioaca Virginia Tech MS79 [email protected] Analyzing Predictive Uncertainty using Paired Complex and Simple Models Adrian Sandu Virginia Polytechnic Institute and In analyzing the uncertainty of environmental model pre- State University dictions a tension exists between the prior information and [email protected] likelihood terms of Bayes Equation. The first requires a complex model that reflects the complexity of earth pro- cesses. The second requires a simple, fast-running model MS78 that can capture information from historical data. Use of Error Covariance Sensitivity and Impact Estima- a single model to achieve both erodes its ability to achieve tion with Adjoint 4D-Var either. A paired model approach can achieve the same ends with fewer compromises. The adjoint-data assimilation system (DAS) is presented as a feasible approach to evaluate the forecast sensitivity with John Doherty respect to the specification of the observation and back- Flinders University and ground error covariances in a four-dimensional variational Watermark Numerical Computing DAS. A synergistic link is established between various tech- [email protected] niques to analyze the DAS performance: observation sen- sitivity, error covariance sensitivity and impact estimation, and a posteriori diagnosis. Applications to atmospheric MS79 modeling and the current status of implementation at nu- Modeling Spatial Variability as Measurement Un- merical weather prediction centers are discussed. certainty

Dacian N. Daescu Direct evaluation of uncertainty in models, parameters and Portland State University measurements will be viewed through an ill-posed inverse Department of Mathematics and Statistics problem and we will demonstrate how incorporating un- [email protected] certainty can regularize the problem. In particular, we will estimate soil hydraulic properties using two different types of measurements, and incorporate uncertainty due MS78 to spatial variation. These estimates can be used over Lagrangian Data Assimilation larger scales than those that were measured, and their cor- responding uncertainty indicates areas where measurement Abstract not available at time of publication. uncertainty needs to be reduced.

Christopher Jones Jodi Mead University of North Carolina and University of Warwick Boise State University [email protected] Department of Mathematics [email protected] MS78 Uncertainty Quantification and Data Assimilation MS79 Issues for Macro-Fiber Composite Actuators Using Electrochemical Impedance Spectroscopy for Studying Respiration of Anode Respiring Bacteria Macro-fiber composites (MFC) are being considered for a for Solid Oxide Fuel Cells range of present and emerging applications, such as flow control and remote configuration of large space structures, Electrochemical impedance spectroscopy (EIS) is a power- due to their large bandwidth, moderate power require- ful diagnostic technique that involves applying a small AC ments, and moderate stain capabilities. However, they voltage to an electrode for a range of frequencies. EIS for also exhibit hysteresis and constitutive nonlinearities due estimating anode resistances in the study of anode bacteria to their PZT components. In this presentation, we will dis- respiration is of interest. Respiration of the bacteria leads cuss uncertainty quantification and data assimilation tech- to an electrical current that can be used for various bioen- niques for these actuators within the context of the homog- ergy applications. Here the focus is on the inverse problem enized energy modeling framework. This will utilize data for practical data obtained in solid-oxide fuel cell research. collected under a variety of operating regimes. Ralph C. Smith Rosemary A. Renaut North Carolina State Univ Arizona State University Dept of Mathematics, CRSC School of Mathematical and Statistical Sciences [email protected] [email protected]

Zhengzheng Hu Department of Mathematics MS79 North carolina State University Quantifying Simplification-induced Error using [email protected] Subspace Techniques All geophysical models represent a simplification of real- UQ12 Abstracts 137 ity. As a result, the history-matching process can lead to tim [email protected] surrogate parameters that compensate for model simplifi- cation. This parameter surrogacy may or may not create David Mokrauer predictive bias, depending on prediction sensitivity to null Dept of Mathematics and solution space parameter components. The potential NC State University for bias indicates the role of history matching is predic- [email protected] tion dependent. History-matching-induced predictive bias is analyzed and quantified from a subspace perspective for a physics-based water resource model. MS80 Intrusive Analysis for Uncertainty Quantification Jeremy White of Simulation Models U.S. Geological Survey Florida Water Science Center We develop intrusive, hybrid uncertainty quantification [email protected] methods applicable to modern, high-resolution simulation models. We seek to construct surrogate models of un- Joseph Hughes certainty by augmenting knowledge of the model with re- US Geological Survey sults of intrusive analysis, such as Automatic Differenti- Florida Water Science Center ation. Our toolset now includes a gradient-enhanced re- [email protected] gression, stochastic-processes based analysis that provides error bounds and statistical metrics for the prior regres- sion model, and a framework for the use of reduced, lower- MS80 fidelity approximations to effectively describe uncertainties Hybrid Reduced order Modeling for Uncertainty in the model. Management in Nuclear Modeling Oleg Roderick The speaker will overview reduced order modeling tech- Argonne National Laboratory niques currently used in nuclear reactor design calculations. [email protected] Reactor calculations are very complex given that nature of the physics governing their behavior and their heteroge- neous design. Reduced order modeling is therefore required PP1 to allow engineers to carry out design calculations on a rou- A Statistical Decision-Theoretic Approach to Dy- tine basis. In doing so, the fidelity of the calculations must namic Resource Allocation for a Self-Aware Un- be preserved. When used to perform uncertainty quan- manned Aerial Vehicle tification, sensitivity analysis, or data assimilation, addi- tional reduction is necessary since these analyses require For inference and prediction tasks, it is typical for decision- many executions of the models. The speaker has devel- makers to have available to them several different numer- oped hybrid statistical deterministic reduction techniques ical models as well as experimental data. Our statistical to enable the execution of these analysis on a routine basis. decision-theoretic approach to dynamic resource allocation He will give a quick overview of reduction techniques used seeks to exploit optimally all available information by se- in best-estimate reaction calculations, then focus in depth lecting models and data with the appropriate fidelity for on reduction algorithms he developed to perform sensitiv- the task at hand. We demonstrate our approach on the ity and uncertainty analyses. online prediction of flight capabilities for a self-aware un- manned aerial vehicle. Hany S. Abdel-Khalik North Carolina State Univ. Doug Allaire, Karen E. Willcox [email protected] Massachusetts Institute of Technology [email protected], [email protected]

MS80 Sparse Interpolatory Reduced-Order Models for PP1 Simulation of Light-Induced Molecular Transfor- Computational Reductions in Stochas- mations tically Driven Neuronal Models with Adaptation Currents We describe an efficient algorithm for using a quantum- chemistry simulator to drive a gradient descent algorithm. The complexity of stochastic, conductance-based neuronal Our objective is to model light-induced molecular trans- network dynamics has motivated several computational re- formations. The simulator is far too expensive and the ductions to the Hodgkin-Huxley neuron model. These re- design space too high-dimensional for the simulator to be ductions, however, rarely generalize to neurons containing used directly to drive the dynamics. We begin by applying realistic adaptive ionic currents. Using several measures of domain-specific knowledge to reduce the dimension of the robustness and network simulations, we show the model- design space. Then we use sparse interpolation to model ing algorithm described in this talk achieves the goals of the energy from the quantum code on hyper-cubes in con- attaining accuracy and efficiency while producing a mod- figuration space, controlling the volume of the hyper-cubes eling scheme general enough for modeling a wide array of both to maintain accuracy and to avoid failure of the quan- specialized neuronal dynamics. tum codes internal optimization. We will conclude the presentation with some examples that illustrate the algo- Victor Barranca rithm’s effectiveness. Rensselaer Polytechnic Institute [email protected] Carl T. Kelley North Carolina State Univ Gregor Kovacic Department of Mathematics Rensselaer Polytechnic Inst 138 UQ12 Abstracts

Dept of Mathematical Sciences in the Sar Induced by a Mobile Phone [email protected] A reduced basis method is introduced to deal with a David Cai stochastic problem in a numerical dosimetry application New York University in which the field solutions are computed using an itera- Courant institute tive solver. More precisely, the computations already per- [email protected] formed are used to build an initial guess for the iterative solver. It is shown that this approach significantly reduces the computational cost. PP1 Mohammed Amine Drissaoui Propagating Arbitrary Uncertainties Through Laboratoire AMPERE Models Via the Probabilistic Collocation Method [email protected] Nonintrusive methods for propagating uncertainty in simu- lations have been introduced in recent times. Some of these PP1 methods use polynomial chaos expansions which can be used with many standard statistical distributions based on Uncertainty Quantification for Hydromechanical the Askey scheme. This work describes an efficient method Coupling in Three Dimensional Discrete Fracture for propagating arbitrary distributions through forward Network models based on application of the standard recurrence re- Fractures and fracture networks are the principle pathways lation for generating orthogonal polynomials. The method for migration of water, heat and mass in geothermal sys- is demonstrated in the context of eddy-current nondestruc- tems, oil/gas reservoirs, sequestrated CO2 leakages. We tive evaluation. investigate the impact of parameter uncertainties of the Matthew Cherry PDFs that characterize discrete fracture networks on the University of Dayton Research Institute hydromechanical response of the system. Numerical results [email protected] of first, second and third moments, normalized to a base case scenario, are presented and integrated into a prob- abilistic risk assessment framework. (Prepared by LLNL Jeremy Knopp under Contract DE-AC52-07NA27344) Air Force Research Laboratory [email protected] Souheil M. Ezzedine, Frederick Ryerson LLNL [email protected], [email protected] PP1 A Predictive Model for Geographic Statistical Data PP1 Any planar map may be transformed into a graph. If we Random and Regular Dynamics of Stochastically consider each country to be represented by a vertex (or Driven Neuronal Networks node), if they are adjacent they will be joined by an edge. To consider how trends migrate across boundaries, we ob- Dynamical properties of and uncertainty quantification in tain relevant measures of the statistic we want to consider; Integrate-and-Fire neuronal networks with multiple time namely, the index of prevalence, and the index of incidence. scales of excitatory and inhibitory neuronal conductances We define a cycle by a given unit of time, usually a year. driven by random Poisson trains of external spikes will be We then propose various alternate equations whereby, by discussed. Both the asynchronous regime in which the net- parametrizing various variables, such as population size, work spikes arrive at completely random times and the birth rate, death rate, and rate of immigration/emigration, synchronous regime in which network spikes arrive within we calculate a new index of prevalence/index of incidence, periodically repeating, well-separated time periods, even for the next cycle. For a given data set, each statistic we though individual neurons spike randomly will be pre- consider may propagate by a different equation, and/or a sented. different set of parameters; this will be determined empiri- cally. What we are proposing is, technically, to model how Pamela B. Fuller a discrete stochastic process propagates geographically, ac- Rensselaer Polytechnic Institute cording to geographical proximity. Very often, statistics [email protected] that depend on geographical proximity are tabulated by variables that are not; i.e., alphabetically. Such a predic- tive model would be relevant in areas such as public health; PP1 and/or crime mapping, for law enforcement purposes. We Calibration of Computer Models for Radiative present an application using a GIS (geographic information Shock Experiments system). POLAR experiments aimed to mimic the astrophysical ac- Jorge Diaz-Castro cretion shock formation in laboratory using high-power University of P.R. School of Law laser facilities. The dynamics and the main physical prop- University of P.R. at Rio Piedras erties of the radiative shock produced by the collision of [email protected] the heated plasma with a solid obstacle have been charac- terised on recent experiments and compared to radiation hydrodynamic simulations. This poster will present the PP1 statistical method based on Bayesian inference used to cal- A Stochastic Collocation Method Combined with a ibrate the main unknown parameters of the simulation and Reduced Basis Method to Compute Uncertainties to quantify the model uncertainty. Jean Giorla UQ12 Abstracts 139

Commissariat `a l’Energie Atomique, France National Center for Atmospheric Research [email protected] [email protected]

E. Falize, C. Busschaert, B. Loupias Stephan Sain CEA/DAM/DIF, F-91297, Arpajon, France Institute for Mathematics Applied to Geosciences [email protected], [email protected], National Center for Atmospheric Research [email protected] [email protected]

M.Koenig,A.Ravasio,A.Dizi`ere William Kleiber, Michael Wiltberger Laboratoire LULI, Ecole Polytechnique, Palaiseau, France National Center for Atmospheric Research [email protected], [email protected], [email protected] [email protected], [email protected] Derek Bingham Dept. of Statistics and Actuarial Science Josselin Garnier Simon Fraser University Universite Paris 7 [email protected] [email protected] Shane Reese C. Michaut Brigham Young University LUTH, Observatoire de Paris, Meudon, France [email protected] [email protected]

PP1 PP1 Variance Based Sensitivity Analysis of Epidemic Regional Climate Model Ensembles and Uncer- Size to Network Structure tainty Quantification I demonstrate the use of global sensitivity analysis to study One goal of the North American Regional Climate Change the dependence of epidemic growth on the structure of the Assessment Program (NARCCAP) is to better under- underlying network. These networks model the social in- stand regional climate model output and the impact of the teractions and migration patterns of individuals susceptible boundary conditions provided by the global climate model, to a disease. Variance based sensitivity indices are shown the regional climate model itself, and interaction between to indicate quantities in the structure of these networks the two. This poster will outline a statistical framework that determine the behaviour of epidemics. for quantifying temperature output and the associated un- certainty both spatially and temporally. The aim is to Kyle S. Hickmann, James (Mac) Hyman, John E. understand the contributions of each model type and how Ortmann those contributions vary over space. Tulane University [email protected], [email protected], Tamara A. Greasby [email protected] National Center for Atmospheric Research [email protected] PP1 Autoregressive Model for Real-Time Weather Pre- PP1 diction and Detecting Climate Sensitivity Multiple Precision, Spatio-Temporal Computer Model Validation using Predictive Processes We propose reduced stochastic models with nonlinear terms replaced by autoregressive linear stochastic model in The Lyon-Fedder-Mobarry (LFM) global magnetosphere Fourier space for filtering and for climate modeling. Using model is a computer model used to study physical processes the Lorenz-96 model as a test bed, we show that this re- in the magnetosphere and ionosphere. Given a set of input duced filtering strategy is computationally cheap and pro- values and solar wind data, the LFM model numerically vides more accurate filtered solutions than current meth- solves the magnetohydrodynamic equations and outputs ods. The potential of application of this autoregressive a spatio-temporal field of ionospheric energy. The LFM model to study climate sensitivity using the Fluctuation- model has the benefit of being able to be run at multiple Dissipation Theorem (FDT) is also addresses. precisions (with higher precisions more closely represent- ing true ionospheric conditions at the cost of computation). Emily L. Kang This work focuses on relating the multiple precision output Department of Mathematical Sciences from the LFM model to field observations of ionospheric en- University of Cincinnati ergy. Of particular interest here are the input settings (and [email protected] their uncertainties) of the LFM model which most closely match the field observations. A low rank spatio-temporal John Harlim statistical LFM model emulator is constructed using pre- Department of Mathematics dictive processes. The emulator borrows strength across North Carolina State University the multiple precisions of the LFM model to calibrate the [email protected] input variables to field observations. In this way, the less computationally demanding yet lower precision models are leveraged to provide estimates of the higher precision LFM PP1 model output. A Split Step Adams Moulton Milstein Method for

Matthew J. Heaton 140 UQ12 Abstracts

Stiff Stochastic Differential Equations fied approach. This method could pave the way for effi- cient Markov chain Monte Carlo in the high-dimensional A split-step method for solving It¯o stochastic differen- parameter setting. tial equations (SDEs) is presented. The method is based on Adams Moulton Formula for stiff ordinary differential Chad E. Lieberman equations and modified for use on stiff SDEs which are MIT stiff in both the deterministic and stochastic components. [email protected] Its order of convergence is proved and stability regions are displayed. Numerical results show the effectiveness of the Karen E. Willcox method in the path-wise approximation of SDEs and its’ Massachusetts Institute of Technology capability to deal with uncertainty. [email protected] Abdul M. Khaliq Middle Tennessee State University PP1 Department of Mathematical Sciences Uncertainty in Model Selection in Remote Sensing [email protected] The model choice problem arise in the context of estimat- David A. Voss ing the total amount of atmospheric aerosols using satellite Western Illinois University measurements. Modeling uncertainty related to unknown [email protected] aerosol type is taken into account when assessing uncer- tainty in aerosol products using Bayesian model selection tools. In this work, uncertainty modeling is comprised of PP1 measurement uncertainty estimates, uncertainty in aerosol Computer Model Calibration with High and Low models, and uncertainty in model selection. Illustrating Resolution Model Output for Spatio-Temporal and quantifying modeling uncertainty gives valuable infor- Data mation to algorithm developers and users.

We discuss a framework for computer model calibration Anu M¨a¨att¨a, Marko Laine, Johanna Tamminen based on low and high resolution model output for large Finnish Meteorological Institute spatio-temporal datasets. The physical model in use is anu.maatta@fmi.fi, marko.laine@fmi.fi, a coupled magnetohydrodynamical model for solar storms johanna.tamminen@fmi.fi occurring in Earth’s upper atmosphere. The statistical model is informed by known physical equations and is tai- lored to large datasets. Given initial runs of the computer PP1 model, we propose a sequential design based on Expected Multifidelity Approach to Variance Reduction in Improvement. Monte Carlo Simulation William Kleiber Engineers often have a suite of numerical models at their National Center for Atmospheric Research disposal to simulate a physical phenomenon. For uncer- [email protected] tainty propagation, we present an approach that utilizes information from inexpensive, low-fidelity models to reduce Stephan Sain the variance of the Monte Carlo estimator of an expensive, Institute for Mathematics Applied to Geosciences high-fidelity model. For a given computational budget, we National Center for Atmospheric Research demonstrate that our approach can produce more accurate [email protected] estimation of the statistics of interest than regular Monte Carlo simulation. Michael Wiltberger Leo Ng, Karen E. Willcox National Center for Atmospheric Research Massachusetts Institute of Technology [email protected] leo [email protected], [email protected] Derek Bingham Dept. of Statistics and Actuarial Science PP1 Simon Fraser University Local Sensitivity Analysis of Stochastic Systems [email protected] with Few Samples

Shane Reese We estimate local sensitivity of predicted quantities in Brigham Young University stochastic models with respect to input parameters by min- [email protected] imizing the Lp residual of linear hyperplanes fit through sparse multidimensional output. We analyze how the number of function evaluations necessary for reliable esti- PP1 mates for the sensitivity indices depends upon the Lp norm Goal-Oriented Statistical Inference (0

PP1 PP1 Worst Case Scenario Analysis Applied to Uncer- Visualization of Uncertainty: Standard Deviation tainty Quantification in Electromagnetic Simula- and Pdf’s tions Uncertainty can be expressed as an error bar (ie stan- The input parameters of models used for the simulation dard deviation) or a distribution. Except for the simplest of technical devices exhibit uncertainties, e.g., due to the cases, concurrent visualization of uncertainty and underly- manufacturing process. Whenever their probability distri- ing value, uncertainty remains un-visualized. We present a bution is unknown, a worst case scenario analysis [Babuˇska method to display scalar uncertainty based on tessellating et al. (2005)] is appealing, potentially requiring little nu- the field of uncertainty density into cells containing nearly merical effort. Based on sensitivity analysis techniques, the equal uncertainty. We present a method for segmenting a quantification of uncertainty due to variations in geometry, field of node based probability distributions into meaning- material distribution and sources will be discussed for elec- ful features. We use climate data to illustrate the concepts. tromagnetic problems within the finite element method. Richard A. Strelitz Ulrich Roemer Los Alamos Naitional Laboratory Technische Universitaet Darmstadt Los Alamos National Laboratory Institut fuer Theorie Elektromagnetischer Felder [email protected] [email protected]

Stephan Koch PP1 Institut fuer Theorie Elektromagnetischer Felder How Typical Is Solar Energy? A 6 Year Evaluation Technische Universitaet Darmstadt of Typical Meteorological Year Data (TMY3) [email protected] The US solar industry makes bets on system performance using NRELs typical meteorological year data (TMY3). Thomas Weiland TMY3 is a 1-year dataset of typical solar irradiance and Institut fuer Theorie Elektromagnetischer Felder, TEMF other meteorological elements used for simulation of solar Technische Universitaet Darmstadt power production. Irradiance naturally varies from TMY3 [email protected] temporally and geographically, thus creating risk. Using data from NOAAs Surface Radiation Network (SurfRad), PP1 6-years of irradiance observations were analyzed. Statisti- cally comparing SurfRad against TMY3 quantified tempo- Constructive and Destructive Correlation Dynam- ral and geographic uncertainty in typical solar irradiance. ics in Simple Stochastic Swimmer Models

Micro-swimming organisms usually can be classified into Matthew K. Williams, Shawn Kerrigan two groups based on their method of propulsion: push- Locus Energy ers and pullers. Experimental data as well as numerical [email protected], simulations point towards much larger orientational corre- [email protected] lations for suspensions of pushers compared to pullers. I will discuss an analytical mean field theory for a simplified swimmer model that captures two body interactions and PP1 can help lead to an understanding of the above observa- Second-Order Probability for Error Analysis in Nu- tions. merical Computation Kajetan Sikorski It is difficult to quantify the uncertainty for numerical com- Rensselaer Polytechnic Institute putation because computational error are deeply affected Department of Mathematical Sciences by many epistemic uncertainty variables. The best known [email protected] methods for estimating computational error are Richard- son extrapolation(RE) and generalized RE. However, it PP1 only estimate descretization error. In this paper we pro- pose second-order probability method for error analysis Preserving Positivity in Pc Approximations Via in numerical computation. This method can provide in- Weighted Pc Expansions tegrated error analysis for all error sources and quantify The preservation of the positivity of the solution in dy- measurement uncertainty of numerical computation error. namical systems is important in a wide range of applica- tions. When working with polynomial chaos (PC) approx- Hua Chen, Yingyan Wu, Shudao Zhang, Haibing Zhou, imations, the positivity can be lost after the truncation Jun Xiong of the PC expansion. We show that the introduction of Institute of Applied Physics and Computational weights in the PC approximations solves this problem for Mathematics a wide range of polynomial systems. We present sufficient chen [email protected], wu [email protected], conditions for the weights and an algorithm that allows zhang [email protected], zhou [email protected], determining these weights. xiong [email protected] Faidra Stavropoulou, Josef Obermaier Helmholtz Zentrum Muenchen [email protected], [email protected] 14262 2012 SIAM Conference on Uncertainty Quantification

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Or­ganizer and Speaker Index 14464 2012 SIAM Conference on Uncertainty Quantification

A Becker, Dirk-Alexander, CP8, 3:20 Tue Carnes, Brian, CP4, 5:50 Mon Abdel-Khalik, Hany S., MS80, 1:00 Thu Bellsky, Thomas, MS36, 2:00 Tue Chakraborty, Debananda, CP20, 1:40 Thu Abdel-Khalik, Hany S., MS80, 1:00 Thu Bellsky, Thomas, MS36, 2:00 Tue Chakravarty, Sourish, CP1, 2:00 Mon Abdollahzadeh, Asaad, CP13, 10:30 Berger, James, MS16, 2:00 Mon Wed Berliner, Mark, IP6, 8:15 Thu Chakravorty, Suman, MS61, 5:30 Wed Abgrall, Remi, MS56, 3:00 Wed Bernstein, Dennis, MS54, 2:30 Wed Challenor, Peter, MT2, 2:00 Mon Adams, Brian M., MS35, 3:00 Tue Bhat, K. Sham, MS45, 10:30 Wed Challenor, Peter, MT5, 2:00 Tue Adams, Marvin, PD1, 8:00 Tue Bhattacharya, Raktim, MS68, 10:00 Thu Challenor, Peter, MT8, 2:00 Wed Adler, Pierre, MS43, 5:00 Tue Bingham, Derek, IP2, 1:00 Mon Challenor, Peter, MS73, 1:00 Thu Albert, Carlo, CP9, 3:20 Tue Birman, Jessie, CP6, 10:10 Tue Challenor, Peter, MS73, 1:00 Thu Alexanderian, Alen, MS41, 4:30 Tue Bishop, Joseph, MS71, 10:00 Thu Chapman, Jenny, MS67, 10:00 Thu Allaire, Doug, PP1, 6:00 Sun Bolander, John, MS71, 11:00 Thu Chaturantabut, Saifon, MS58, 3:30 Wed Andrianakis, Yiannis, MS1, 11:00 Mon Booth, Richard, CP10, 4:30 Tue Chen, Jie, MS21, 4:30 Mon Anitescu, Mihai, MS55, 2:00 Wed Borgonovo, Emanuele, MS3, 11:00 Mon Chen, Ray-Bing, CP3, 4:30 Mon Anitescu, Mihai, MS55, 3:00 Wed Bozdog, Dragos, CP15, 2:40 Wed Chen, Xiao, MS9, 10:00 Mon Antil, Harbir, MS58, 3:00 Wed Branicki, Michal, MS20, 5:30 Mon Chen, Xiaoxiao, MS38, 4:30 Tue Archibald, Rick, MS5, 10:00 Mon Branicki, Michal, MS45, 11:00 Wed Chen, Yi, MS38, 6:00 Tue Archibald, Rick, MS17, 5:30 Mon Bronkhorst, Curt, MS48, 9:30 Wed Cheng, Haiyan, MS70, 11:00 Thu Arnst, Maarten, CP3, 4:50 Mon Brunel, Nicolas J-B, MS15, 3:00 Mon Chernov, Alexey, MS10, 2:30 Mon Augenbroe, Godfried, MS28, 11:00 Tue Bryant, Corey, MS14, 3:00 Mon Cherry, Matthew, PP1, 6:00 Sun Auvinet-Guichard, Gabriel, MS33, 2:30 Brynjarsdottir, Jenny, CP2, 2:40 Mon Chevreuil, Mathilde, MS18, 5:00 Mon Tue Bui, Tan, MS15, 2:30 Mon Chipman, Hugh, MS21, 5:00 Mon Burkardt, John, MT1, 9:30 Mon Cho, Heyrim, MS61, 5:00 Wed B Choudhary, Ruchi, MS44, 4:30 Tue Bal, Guillaume, MS26, 10:30 Tue Burkardt, John, MT4, 9:30 Tue Choudhary, Ruchi, MS44, 4:30 Tue Barajas-Solano, David A., MS43, 6:00 Butler, Troy, MS5, 9:30 Mon Tue Butler, Troy, MS14, 2:00 Mon Chowdhary, Kenny, MS23, 10:00 Tue Bardsley, Johnathan M., MS40, 4:30 Tue Butler, Troy, MS14, 2:00 Mon Chung, Moo, MS6, 10:30 Mon Bardsley, Johnathan M., MS40, 4:30 Butler, Troy, MS74, 1:30 Thu Cialenco, Igor, MS77, 1:30 Thu Tue Cioaca, Alexandru, MS78, 2:00 Thu Bardsley, Johnathan M., MS47, 9:30 Wed C Cisewski, Jessi, MS74, 2:30 Thu Campanelli, Mark, MS35, 2:00 Tue Bardsley, Johnathan M., MS64, 4:30 Clément, Alexandre, MS32, 3:30 Tue Wed Campanelli, Mark, MS42, 4:30 Tue Clément, Chevalier, MS4, 10:30 Mon Barillec, Remi, MS72, 10:30 Thu Campanelli, Mark, MS42, 4:30 Tue Connors, Jeffrey M., MS14, 2:30 Mon Barnes, Andrew, CP4, 5:10 Mon Cao, Yanzhao, MS46, 9:30 Wed Conrad, Patrick R., CP13, 10:10 Wed Barranca, Victor, PP1, 6:00 Sun Cao, Yanzhao, MS46, 10:00 Wed Constantine, Paul, MS22, 4:30 Mon Bassett, Danielle S., MS65, 5:00 Wed Cao, Yanzhao, MS53, 2:00 Wed Carlberg, Kevin T., MS58, 2:00 Wed Constantine, Paul, MS49, 11:00 Wed Bayarri, M.J., MS16, 2:00 Mon Constantine, Paul, MS58, 2:00 Wed Bayarri, M.J., MS37, 2:00 Tue Carlberg, Kevin T., MS58, 2:30 Wed Constantinescu, Emil M., MS20, 4:30 Mon

Italicized names indicate session organizers. 2012 SIAM Conference on Uncertainty Quantification 14565

Cooley, Dan, MT7, 9:30 Wed E Gibson, Nathan L., MS43, 4:30 Tue Crowell, Sean, MS36, 3:00 Tue Ebeida, Mohamed S., MS71, 11:30 Thu Gibson, Nathan L., CP14, 3:00 Wed Cui, Tiangang, CP11, 5:30 Tue Efendiev, Yalchin, MS50, 9:30 Wed Ginting, Victor E., MS43, 5:30 Tue Cyr, Eric C., MS5, 10:30 Mon Efendiev, Yalchin, MS54, 3:00 Wed Giorla, Jean, PP1, 6:00 Sun Ehrlacher, Virginie, MS18, 6:00 Mon Gittelson, Claude, MS46, 11:00 Wed D Glatt-Holtz, Nathan, MS69, 10:30 Thu Da Veiga, Sebastien, CP5, 5:10 Mon Eisenhower, Bryan, MS28, 9:30 Tue Gleich, David F., MS22, 4:30 Mon Daescu, Dacian N., MS70, 9:30 Thu Eisenhower, Bryan, MS28, 9:30 Tue Gleich, David F., MS22, 4:30 Mon Daescu, Dacian N., MS78, 1:00 Thu El Moselhy, Tarek, MS2, 9:30 Mon Glimm, James G., MS49, 9:30 Wed Daescu, Dacian N., MS78, 1:00 Thu El Moselhy, Tarek, MS10, 3:00 Mon Glimm, James G., MS49, 9:30 Wed Dalbey, Keith, MS1, 10:30 Mon Eldred, Michael S., MS10, 3:30 Mon Glimm, James G., MS56, 2:00 Wed Das, Sonjoy, MS54, 2:00 Wed ElSheikh, Ahmed H., CP9, 3:00 Tue Glimm, James G., MS63, 4:30 Wed Das, Sonjoy, MS61, 4:30 Wed Ernst, Oliver G., MS24, 10:30 Tue Glover, Nina, MS44, 5:30 Tue Das, Sonjoy, MS68, 9:30 Thu Esmailzadeh, Saba S., CP10, 5:10 Tue Godinez, Humberto C., MS70, 9:30 Thu Das, Sonjoy, MS68, 9:30 Thu Estep, Donald, MS74, 1:00 Thu Godinez, Humberto C., MS70, 10:30 Das, Sonjoy, MS76, 1:00 Thu Estep, Donald, MS74, 1:00 Thu Thu Dawson, Clint, MS67, 4:30 Mon Ezzedine, Souheil M., PP1, 6:00 Sun Godinez, Humberto C., MS78, 1:00 Thu Debusschere, Bert J., MS26, 9:30 Tue Gorodetsky, Alex A., CP5, 4:30 Mon Debusschere, Bert J., MS41, 4:30 Tue F Fan, Ya Ju, CP20, 1:20 Thu Gosling, John Paul, MS8, 10:30 Mon Debusschere, Bert J., MS48, 9:30 Wed Flath, H. Pearl, CP11, 5:50 Tue Gramacy, Robert, MS75, 1:00 Thu Debusschere, Bert J., MS48, 10:00 Wed Fonoberov, Vladimir, MS7, 9:30 Mon Greasby, Tamara A., PP1, 6:00 Sun Debusschere, Bert J., MT3, 4:30 Mon Fox, Colin, MS2, 10:30 Mon Grigoriu, Mircea, CP7, 9:30 Tue Debusschere, Bert J., MT6, 4:30 Tue Fox, Colin, MS47, 9:30 Wed Guillas, Serge, MS73, 2:00 Thu Debusschere, Bert J., MT9, 4:30 Wed Freitag, Steffen, CP1, 2:40 Mon Gulati, Sneh, MS25, 10:00 Tue Deram, Eleanor, MS76, 1:30 Thu French, Joshua P., CP13, 11:10 Wed Gunzburger, Max, MS12, 2:00 Mon Diaz-Castro, Jorge, PP1, 6:00 Sun Fuller, Pamela B., PP1, 6:00 Sun Gunzburger, Max, MS19, 4:30 Mon Diez, Matteo, CP3, 5:50 Mon Guttorp, Peter, MS66, 9:30 Thu Doherty, John, MS79, 1:30 Thu G Doostan, Alireza, MS10, 2:00 Mon Galagali, Nikhil, CP11, 4:30 Tue H Doostan, Alireza, MS17, 4:30 Mon Garcke, Jochen, MS6, 10:00 Mon Haario, Heikki, MS47, 10:00 Wed Doostan, Alireza, MS17, 4:30 Mon Gattiker, James, MS59, 6:00 Wed Haber, Eldad, MS64, 4:30 Wed Doostan, Alireza, MS23, 9:30 Tue George, Jemin, CP18, 9:50 Thu Haber, Eldad, MS64, 6:00 Wed Doostan, Alireza, MS31, 2:00 Tue Ghanem, Roger, MT3, 4:30 Mon Hall, Timothy, CP6, 9:50 Tue Doostan, Alireza, MS38, 4:30 Tue Han, Xiaoying, MS62, 9:30 Wed Ghanem, Roger, MS23, 9:30 Tue Drissaoui, Mohammed Amine, PP1, Han, Xiaoying, MS69, 9:30 Thu Ghanem, Roger, MT6, 4:30 Tue 6:00 Sun Han, Xiaoying, MS69, 9:30 Thu Ghanem, Roger, MS53, 2:00 Wed Duan, Jinqiao, MS62, 9:30 Wed Han, Xiaoying, MS77, 1:00 Thu Ghanem, Roger, MT9, 4:30 Wed Dudley Ward, Nicholas, CP10, 5:30 Tue Hannig, Jan, MS74, 2:00 Thu Ghattas, Omar, MS2, 11:00 Mon Duraisamy, Karthik, MS63, 5:00 Wed He, Jincong, MS58, 2:00 Wed Ghattas, Omar, MS57, 2:00 Wed Dwight, Richard, CP2, 2:20 Mon Giannakis, Dimitris, MS67, 11:00 Thu

Italicized names indicate session organizers. 14666 2012 SIAM Conference on Uncertainty Quantification

He, Xiaoming, MS53, 3:30 Wed Jackson, Charles, MS57, 3:00 Wed Lazarov, Boyan S., CP14, 2:00 Wed Heaton, Matthew J., PP1, 6:00 Sun Jackson, Charles, MS59, 4:30 Wed Le Gratiet, Loic, MS4, 9:30 Mon Heimbach, Patrick, MS45, 10:00 Wed Jackson, Charles, MS66, 9:30 Thu Le Gratiet, Loic, MS4, 9:30 Mon Heimbach, Patrick, MS57, 2:30 Wed Jacobson, Clas, MS28, 9:30 Tue Lee, Barry, MS9, 11:00 Mon Heinkenschloss, Matthias, MS19, 4:30 Jakeman, John D., MS5, 11:00 Mon Lee, Chia Ying, MS62, 9:30 Wed Mon Janon, Alexandre, CP5, 5:50 Mon Lee, Chia Ying, MS69, 9:30 Thu Heinkenschloss, Matthias, MS51, 4:30 Wed Jones, Christopher, MS78, 2:30 Thu Lee, Chia Ying, MS69, 11:30 Thu Helbert, Celine, CP3, 5:10 Mon Lee, Chia Ying, MS77, 1:00 Thu Helbert, Celine, CP5, 6:10 Mon K Lee, Hyung B., MS34, 3:30 Tue Kaman, Tulin, MS63, 5:30 Wed Hengartner, Nicolas, MS21, 5:30 Mon Lee, Hyung-Chun, MS12, 2:00 Mon Kamath, Chandrika, MS22, 6:00 Mon Henze, Gregor, MS28, 11:30 Tue Lee, Hyung-Chun, MS12, 2:00 Mon Kamojjala, Krishna, MS39, 5:30 Tue Hickmann, Kyle S., PP1, 6:00 Sun Lee, Hyung-Chun, MS19, 4:30 Mon Kang, Emily L., PP1, 6:00 Sun Hickmann, Kyle S., CP8, 2:00 Tue Lee, Jangwoon, MS19, 6:00 Mon Kang, Emily L., MS52, 2:00 Wed Higdon, David, PD1, 8:00 Tue Lee, Lindsay, MS8, 10:00 Mon Kaufman, Cari, MS52, 3:30 Wed Higdon, Dave, MS60, 5:30 Wed Leemis, Lawrence, MS35, 2:00 Tue Kelley, Carl T., MS80, 2:00 Thu Higdon, Dave, MS72, 10:00 Thu LeMaitre, Olivier, MS2, 9:30 Mon Kennedy, John, MS28, 10:00 Tue Hill, Mary, MS25, 11:00 Tue LeMaitre, Olivier, MS11, 2:00 Mon Kennedy, Marc C., MS72, 9:30 Thu LeMaitre, Olivier, MS18, 4:30 Mon Hittinger, Jeffrey A., MS39, 4:30 Tue Kennedy, Marc C., MS72, 9:30 Thu LeMaitre, Olivier, MS24, 9:30 Tue Horesh, Lior, MS64, 4:30 Wed Ketelsen, Christian, MS43, 6:30 Tue LeMaitre, Olivier, MS24, 9:30 Tue Horesh, Lior, MS64, 5:00 Wed Khaliq, Abdul M., PP1, 6:00 Sun LeMaitre, Olivier, MS32, 2:00 Tue Hoteit, Ibrahim, MS75, 2:30 Thu Kleiber, William, PP1, 6:00 Sun Lemaître, Paul, CP8, 3:00 Tue Hough, Patricia D., MS27, 9:30 Tue Klein, Thierry, CP18, 10:30 Thu Lemaître, Paul, MS35, 3:30 Tue Howard, Marylesa, CP20, 1:00 Thu Knio, Omar M., IP3, 8:15 Tue Leung, Ruby, MS52, 2:30 Wed Huan, Xun, MS11, 2:30 Mon Knupp, Patrick M., MS34, 2:30 Tue Li, Jinglai, MS77, 1:00 Thu Huerta, Gabriel, MS66, 10:30 Thu Kolehmainen, Ville P., MS40, 5:00 Tue Liang, Faming, MS76, 2:00 Thu Huzurbazar, Aparna V., CP15, 2:00 Wed Koltakov, Sergey, CP11, 4:50 Tue Lieberman, Chad E., PP1, 6:00 Sun Hwang, Youngdeok, MS31, 2:30 Tue Konecny, Franz, CP14, 2:20 Wed Lin, Guang, MS45, 9:30 Wed I Konomi, Bledar, MS20, 5:00 Mon Lin, Guang, MS52, 2:00 Wed Iaccarino, Gianluca, MS9, 9:30 Mon Kouri, Drew, MS51, 5:00 Wed Lin, Guang, MS59, 4:30 Wed Iaccarino, Gianluca, MS49, 9:30 Wed Koutsourelakis, Phaedon S., CP12, 9:30 Lin, Guang, MS66, 9:30 Thu Iaccarino, Gianluca, MS56, 2:00 Wed Wed Lin, Guang, MS66, 11:00 Thu Iaccarino, Gianluca, MS56, 2:00 Wed Kovacic, Gregor, MS62, 10:00 Wed Ling, You, CP2, 3:00 Mon Iaccarino, Gianluca, MS63, 4:30 Wed Kramer, Peter R., MS16, 3:30 Mon Litvinenko, Alexander, MS31, 3:30 Tue Iaccarino, Gianluca, MS71, 10:30 Thu Kreutz, Clemens, CP14, 2:40 Wed Lockwood, Brian, MS55, 2:00 Wed Israel, Daniel, MS39, 5:00 Tue Kucerova, Anna, CP13, 9:50 Wed Lopes, Danilo, MS16, 2:30 Mon J L Lototsky, Sergey, MS69, 10:00 Thu Jackson, Charles, MS45, 9:30 Wed Laine, Marko, MS47, 10:30 Wed Lucas, Donald D., MS45, 9:30 Wed Jackson, Charles, MS52, 2:00 Wed Law, Kody, MS77, 2:00 Thu Lucas, Donald D., MS45, 9:30 Wed

Italicized names indicate session organizers. 2012 SIAM Conference on Uncertainty Quantification 14767

Lucas, Donald D., MS52, 2:00 Wed Morrison, Rebecca, MS75, 1:30 Thu O’Hagan, Anthony, MT8, 2:00 Wed Lucas, Donald D., MS59, 4:30 Wed Morzfeld, Matthias, MS29, 9:30 Tue O’Hagan, Anthony, MS60, 5:00 Wed Lucas, Donald D., MS66, 9:30 Thu Morzfeld, Matthias, MS29, 10:00 Tue Ortmann, John E., PP1, 6:00 Sun Motamed, Mohammad, MS24, 10:00 Ossiander, Mina E., MS43, 4:30 Tue M Tue Määttä, Anu, PP1, 6:00 Sun Ossiander, Mina E., MS43, 4:30 Tue Mueller, Michael, MS49, 10:30 Wed Madankan, Reza, CP7, 9:50 Tue Ostoja-Starzewski, Martin, CP1, 3:20 Muhanna, Rafi L., CP17, 9:30 Thu Mon Mahadevan, Sankaran, MS26, 11:00 Tue Mullen, Robert, CP17, 10:30 Thu Owhadi, Houman, MS61, 6:00 Wed Mahadevan, Sankaran, MS42, 5:00 Tue Muñoz, Facundo, MS44, 6:00 Tue Malaya, Nicholas, MS34, 3:00 Tue P Mallick, Bani, MS50, 9:30 Wed N Packard, Andrew, CP7, 10:10 Tue Marzouk, Youssef M., MS2, 9:30 Mon Nadim, Farrokh, MS33, 3:00 Tue Pajonk, Oliver, CP9, 2:40 Tue Marzouk, Youssef M., MS11, 2:00 Mon Nair, Prasanth B., CP13, 10:50 Wed Pal Choudhury, Pabitra, CP20, 2:00 Thu Marzouk, Youssef M., MS18, 4:30 Mon Najm, Habib N., MS26, 9:30 Tue Panaretos, Victor M., MS6, 11:00 Mon Marzouk, Youssef M., MS24, 9:30 Tue Najm, Habib N., MS41, 4:30 Tue Papanicolaou, George C., IP4, 8:15 Wed Marzouk, Youssef M., MS32, 2:00 Tue Najm, Habib N., MS48, 9:30 Wed Papaspiliopoulos, Omiros, MS15, 2:00 Mcdougall, Damon, MS36, 3:30 Tue Narayan, Akil, MS10, 2:00 Mon Mon McKenna, Sean A, MS25, 9:30 Tue Narayanan, Satish, MS28, 9:30 Tue Parks, Jean, MS35, 2:30 Tue McKenna, Sean A, MS25, 9:30 Tue Navon, Michael, MS70, 9:30 Thu Parno, Matthew, CP3, 5:30 Mon McKenna, Sean A, MS33, 2:00 Tue Newhall, Katherine, MS65, 4:30 Wed Patra, Abani K., MS54, 2:00 Wed Mead, Jodi, MS47, 11:00 Wed Newhall, Katherine, MS65, 4:30 Wed Patra, Abani K., MS54, 2:00 Wed Mead, Jodi, MS79, 1:00 Thu Ng, Leo, PP1, 6:00 Sun Patra, Abani K., MS61, 4:30 Wed Mead, Jodi, MS79, 1:00 Thu Nobile, Fabio, MS2, 9:30 Mon Patra, Abani K., MS68, 9:30 Thu Medina-Cetina, Zenon, MS25, 9:30 Tue Nobile, Fabio, MS6, 9:30 Mon Patra, Abani K., MS76, 1:00 Thu Medina-Cetina, Zenon, MS33, 2:00 Tue Nobile, Fabio, MS11, 2:00 Mon Pätz, Torben, CP1, 2:20 Mon Medina-Cetina, Zenon, MS33, 2:00 Tue Nobile, Fabio, MS15, 2:00 Mon Peleg, Avner, MS62, 11:00 Wed Mehta, Prashant G., MS54, 3:30 Wed Nobile, Fabio, MS18, 4:30 Mon Peles, Slaven, MS7, 11:00 Mon Meidani, Hadi, CP19, 1:00 Thu Nobile, Fabio, MS18, 4:30 Mon Peri, Daniele, CP4, 4:30 Mon Miller, Robert, MS29, 10:30 Tue Nobile, Fabio, MS24, 9:30 Tue Perrin, Guillaume, MS11, 3:00 Mon Ming, Ju, MS19, 5:30 Mon Nobile, Fabio, MS32, 2:00 Tue Peszynska, Malgorzata, MS43, 4:30 Tue Minvielle-Larrousse, Pierre, CP10, 4:50 Noble, Patrick R., CP1, 3:40 Mon Peterson, Elmor L., CP17, 10:50 Thu Tue Noshadravan, Arash, MS75, 2:00 Thu Petra, Noemi, MS57, 2:00 Wed Mitchell, Lewis, MS36, 2:00 Tue Nouy, Anthony, MS17, 6:00 Mon Petra, Noemi, MS57, 2:00 Wed Mitchell, Lewis, MS36, 2:30 Tue Nunes, Vitor Leite, CP18, 10:10 Thu Pettersson, Mass Per, MS56, 2:30 Wed Mitchell, Scott A., MS71, 9:30 Thu Pham, Khanh D., CP6, 9:30 Tue Mitchell, Scott A., MS71, 9:30 Thu O Oakley, Jeremy, MS8, 9:30 Mon Phipps, Eric, MS9, 10:30 Mon Mittal, Akshay, MS9, 9:30 Mon Oakley, Jeremy, MS8, 9:30 Mon Picheny, Victor, MS4, 10:00 Mon Mondal, Anirban, MS50, 11:00 Wed Oakley, Jeremy, MS8, 11:00 Mon Pineda, Angel R., CP17, 9:50 Thu Moore, Richard O., MS62, 10:30 Wed O’Hagan, Anthony, MT2, 2:00 Mon Pitman, E. Bruce, MS37, 2:30 Tue Morgan, Eugene, MS44, 5:00 Tue O’Hagan, Anthony, MT5, 2:00 Tue Poczos, Barnabas, MS22, 5:30 Mon

Italicized names indicate session organizers. 14868 2012 SIAM Conference on Uncertainty Quantification

Powell, Catherine, MS18, 5:30 Mon Romero, Vicente J., MS60, 6:00 Wed Simoen, Ellen, CP12, 10:30 Wed Pratola, Matt, MS27, 10:00 Tue Rosic, Bojana V., MS11, 3:30 Mon Singla, Puneet, MS54, 2:00 Wed Pratola, Matthew, MS57, 3:30 Wed Routray, Aurobinda, CP19, 1:20 Thu Singla, Puneet, MS61, 4:30 Wed Prieur, Clémentine, MS3, 9:30 Mon Royset, Johannes O., MS51, 4:30 Wed Singla, Puneet, MS61, 4:30 Wed Prieur, Clémentine, MS3, 9:30 Mon Rozovski, Boris, MS46, 9:30 Wed Singla, Puneet, MS68, 9:30 Thu Prudencio, Ernesto E., MS13, 2:00 Mon Singla, Puneet, MS76, 1:00 Thu Prudencio, Ernesto E., MS13, 2:00 Mon S Sloan, Ian H., MS17, 5:00 Mon Sabbagh, Harold, MS69, 11:00 Thu Prudencio, Ernesto E., MS20, 4:30 Mon Smarslok, Benjamin P., CP12, 9:50 Wed Sacks, Jerry, MS16, 2:00 Mon Prudencio, Ernesto E., MS27, 10:30 Tue Smith, Ralph C., MS70, 9:30 Thu Saetrom, Jon, CP9, 2:20 Tue Prudencio, Ernesto E., MS60, 4:30 Wed Smith, Ralph C., MS78, 1:00 Thu Safta, Cosmin, MS59, 5:00 Wed Prudencio, Ernesto E., MS67, 9:30 Thu Smith, Ralph C., MS78, 1:30 Thu Sahai, Tuhin, MS7, 9:30 Mon Prudencio, Ernesto E., MS75, 1:00 Thu Solonen, Antti, MS40, 6:00 Tue Sahai, Tuhin, MS7, 10:30 Mon Pulch, Roland, MS68, 10:30 Thu Song, Song, CP19, 2:00 Thu Sain, Stephan, MS59, 4:30 Wed Spiller, Elaine, MS37, 2:00 Tue Q Salloum, Maher, MS26, 9:30 Tue Spiller, Elaine, MS37, 3:00 Tue Qian, Peter, MS21, 4:30 Mon Sandu, Adrian, MS55, 2:30 Wed Srinivasan, Gowri, MS50, 10:00 Wed Qian, Peter, MS21, 6:00 Mon Sandu, Adrian, MS70, 9:30 Thu Stadler, Georg, MS57, 2:00 Wed Qian, Peter, MS27, 9:30 Tue Sandu, Adrian, MS78, 1:00 Thu Stavropoulou, Faidra, PP1, 6:00 Sun Quagliarella, Domenico, MS49, 10:00 Sang, Huiyan, MS66, 10:00 Thu Wed Stavropoulou, Faidra, CP7, 10:30 Tue Sangalli, Laura M., MS6, 9:30 Mon Stefanescu, Ramona, MS76, 1:00 Thu Sangalli, Laura M., MS6, 9:30 Mon R Steinberg, David M., MS4, 11:00 Mon Rabitz, Herschel, MS3, 10:00 Mon Sangalli, Laura M., MS15, 2:00 Mon Sternfels, Raphael, CP6, 10:30 Tue Rahrovani, Sadegh, CP2, 3:40 Mon Sankararaman, Shankar, CP2, 3:20 Mon Stoyanov, Miroslav, MS32, 3:00 Tue Rajasekharan, Ajaykumar, CP2, 2:00 Sapsis, Themistoklis, MS20, 6:00 Mon Strelitz, Richard A., PP1, 6:00 Sun Mon Sargsyan, Khachik, MS23, 10:30 Tue Stripling, Hayes, MS55, 3:30 Wed Ranganathan, Shivakumar I., CP1, 3:00 Scheichl, Robert, CP18, 9:30 Thu Mon Stuart, Andrew, MS2, 10:00 Mon Schick, Michael, MS24, 11:00 Tue Rahunanthan, Arunasalam, CP12, 10:10 Su, Heng, MS27, 11:00 Tue Schieche, Bettina, CP4, 5:30 Mon Wed Sudret, Bruno, MS3, 10:30 Mon Schillings, Claudia, MS51, 6:00 Wed Ray, Jaideep, MS33, 3:30 Tue Sullivan, Tim, MS41, 5:30 Tue Schultz, Ruediger, MS51, 5:30 Wed Razi, Mani, CP4, 6:10 Mon Sun, Yan, CP16, 4:50 Wed Schwab, Christoph, IP1, 8:15 Mon Reichert, Peter, MS16, 3:00 Mon Swiler, Laura, MS67, 9:30 Thu Secchi, Piercesare, MS6, 9:30 Mon Renaut, Rosemary A., MS79, 2:30 Thu Sykora, Jan, CP11, 5:10 Tue Secchi, Piercesare, MS15, 2:00 Mon Ricciuto, Daniel, MS59, 5:30 Wed Seppanen, Aku, MS40, 5:30 Tue Rizzi, Francesco, MS26, 10:00 Tue T Sergienko, Ekaterina, CP5, 5:30 Mon Tenorio, Luis, MS11, 2:00 Mon Robinson, Allen C., MS26, 9:30 Tue Shankaran, Sriram, MS63, 4:30 Wed Tenorio, Luis, MS50, 10:30 Wed Robinson, Allen C., MS41, 4:30 Tue Shi, Feng B., MS65, 6:00 Wed Tenorio, Luis, MS64, 5:30 Wed Robinson, Allen C., MS41, 5:00 Tue Tenorio, Luis, MT10, 9:30 Thu Robinson, Allen C., MS48, 9:30 Wed Shkarayev, Maxim S., MS65, 5:30 Wed Terejanu, Gabriel A., MS13, 2:00 Mon Roderick, Oleg, MS80, 1:30 Thu Shvartsman, Mikhail M., CP16, 4:30 Wed Terejanu, Gabriel A., MS20, 4:30 Mon Roemer, Ulrich, PP1, 6:00 Sun Sikorski, Kajetan, PP1, 6:00 Sun

Italicized names indicate session organizers. 2012 SIAM Conference on Uncertainty Quantification 14969

Terejanu, Gabriel A., MS60, 4:30 Wed Webster, Clayton G., MS19, 4:30 Mon Yousefpour, Negin, CP17, 11:10 Thu Terejanu, Gabriel A., MS60, 4:30 Wed Webster, Clayton G., MS31, 2:00 Tue Yu, Dan, MS13, 2:30 Mon Terejanu, Gabriel A., MS67, 9:30 Thu Webster, Clayton G., MS46, 9:30 Wed Terejanu, Gabriel A., MS75, 1:00 Thu Webster, Clayton G., MS53, 2:00 Wed Z Zabaras, Nicholas, MS13, 3:00 Mon Tissot, Jean-Yves, CP8, 2:40 Tue Webster, Clayton G., MS53, 2:30 Wed Zabaras, Nicholas, MS12, 3:30 Mon Togawa, Kanali, MS7, 10:00 Mon Weirs, V. Gregory, MS34, 2:00 Tue Zabaras, Nicholas, MS32, 2:00 Tue Tokmakian, Robin, MS73, 1:30 Thu Weirs, V. Gregory, MS39, 4:30 Tue Zabaras, Nicholas, MS38, 5:00 Tue Tong, Charles, MS9, 9:30 Mon Weirs, V. Gregory, MS39, 6:00 Tue Tong, Charles, MS28, 10:30 Tue Weller, Grant, MS72, 11:00 Thu Zabaras, Nicholas, MS41, 6:00 Tue Trenchea, Catalin S., MS12, 2:30 Mon Wever, Utz, MS38, 5:30 Tue Zeng, Xiaoyan, MS52, 3:00 Wed Trenchea, Catalin S., MS13, 3:30 Mon White, Jeremy, MS79, 2:00 Thu Zhang, Guannan, MS19, 5:00 Mon Tu, Xuemin, MS29, 9:30 Tue Wildey, Tim, MS5, 9:30 Mon Zhang, Guannan, MS53, 3:00 Wed Wildey, Tim, MS5, 9:30 Mon Zhang, Hong, MS70, 10:00 Thu U Wildey, Tim, MS14, 2:00 Mon Zhang, Zhongqiang, MS23, 11:00 Tue Ullmann, Elisabeth, CP13, 9:30 Wed Willcox, Karen E., IP5, 1:00 Wed Zhou, Haibing, PP1, 6:00 Sun V Williams, Cranos M., CP10, 5:50 Tue Zuev, Konstantin M., CP15, 2:20 Wed van Wyk, Hans-Werner, MS12, 3:00 Williams, Matthew K., PP1, 6:00 Sun Mon Williamson, Danny, MS73, 2:30 Thu Vasile, Massimilian, MS56, 3:30 Wed Witteveen, Jeroen, CP4, 4:50 Mon Veneziani, Alessandro, MS15, 3:30 Mon Wojtkiewicz, Steven F., CP8, 2:20 Tue Venturi, Daniele, MS68, 11:00 Thu Wolpert, Robert, MS37, 3:30 Tue Vernon, Ian, MS1, 9:30 Mon Woodward, Carol S., MS34, 2:00 Tue Vernon, Ian, MS1, 9:30 Mon Woodward, Carol S., MS34, 2:00 Tue Vernon, Ian, MT2, 2:00 Mon Woodward, Carol S., MS39, 4:30 Tue Vernon, Ian, MT5, 2:00 Tue Wu, Jeff, MS21, 4:30 Mon Vernon, Ian, MT8, 2:00 Wed Wu, Jeff, MS27, 9:30 Tue Vishwajeet, Kumar, CP19, 1:40 Thu Wu, Jeff, MS31, 3:00 Tue Viswanathan, Hari, MS25, 10:30 Tue Wu, Yuefeng, CP9, 2:00 Tue W X Wahl, Francois, CP5, 4:50 Mon Xiu, Dongbin, MS10, 2:00 Mon Wan, Jiang, MS48, 10:30 Wed Xiu, Dongbin, MS17, 4:30 Mon Wan, Xiaoliang, MS46, 10:30 Wed Xiu, Dongbin, MS23, 9:30 Tue Wang, Liping, CP14, 3:20 Wed Xiu, Dongbin, MS31, 2:00 Tue Wang, Qiqi, MS22, 5:00 Mon Xiu, Dongbin, MS32, 2:30 Tue Wang, Yan, MS42, 5:30 Tue Xiu, Dongbin, MS38, 4:30 Tue Weare, Jonathan, MS29, 11:00 Tue Y Weare, Jonathan, MS77, 2:30 Thu Yannello, Vincent, CP17, 10:10 Thu Webster, Clayton G., MT1, 9:30 Mon Yoshimura, Akiyoshi, CP7, 10:50 Tue Webster, Clayton G., MT4, 9:30 Tue Youngman, Ben, MS1, 10:00 Mon Webster, Clayton G., MS12, 2:00 Mon Yousefpour, Negin, CP10, 6:10 Tue 15070 2012 SIAM Conference on Uncertainty Quantification

Notes 2012 SIAM Conference on Uncertainty Quantification 1517151

UQ12 Budget

Conference Budget SIAM Conference on Uncertainty Quantification April 2 - 5, 2012 Raleigh, NC

Expected Paid Attendance: 400

Revenue Registration $130,780 Total $130,780

Direct Expenses Printing $2,700 Organizing Committee $2,100 Invited Speaker $12,750 Food and Beverage $22,000 Telecomm $1,500 AV and Equipment (rental) $17,325 Room (rental) $5,500 Advertising $3,800 Conference Staff Labor $23,600 Other (supplies, staff travel, freight, exhibits, misc.) $3,200 Total Direct Expenses: $94,475 Support Services: * Services covered by Revenue $36,305 Services covered by SIAM $33,014 Total Support Services: $69,319

Total Expenses: $163,794

* Support services includes customer service, accounting, computer support, shipping, marketing and other SIAM support staff. It also includes a share of the computer systems and general items (building expenses in the SIAM HQ).

72 Raleigh Marriott City 2012Center SIAM Conference Hotel onMap Uncertainty Quantification

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