Dakota, a Multilevel Parallel Object-Oriented Framework For
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SAND2014-4633 Unlimited Release July 2014 Updated May 15, 2019 Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.10 User’s Manual Brian M. Adams, Michael S. Eldred, Gianluca Geraci, Russell W. Hooper, John D. Jakeman, Kathryn A. Maupin, Jason A. Monschke, Ahmad A. Rushdi, J. Adam Stephens, Laura P. Swiler, Timothy M. Wildey Optimization and Uncertainty Quantification Department William J. Bohnhoff Radiation Effects Theory Department Keith R. Dalbey Software Simulation and Analysis Department Mohamed S. Ebeida Discrete Math and Optimization Department John P. Eddy Mathematical Analysis and Decision Sciences Department Patricia D. Hough, Mohammad Khalil Quantitative Modeling and Analysis Department Kenneth T. Hu W76-1 System Life Extension Department Elliott M. Ridgway, Dena M. Vigil Software Engineering and Research Department Justin G. Winokur V&V, UQ, Credibility Processes Department Sandia National Laboratories P.O. Box 5800 Albuquerque, New Mexico 87185 4 Abstract The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate- based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user’s manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies. Dakota Version 6.10 User’s Manual generated on May 15, 2019 Contents Preface 19 1 Introduction 21 1.1 Motivation for Dakota Development................................. 21 1.2 Dakota Capabilities.......................................... 21 1.3 Coupling Dakota to a Simulation................................... 23 1.4 User’s Manual Organization..................................... 24 1.5 Files Referenced in this Manual................................... 25 1.6 Summary............................................... 25 2 Dakota Tutorial 27 2.1 Quickstart............................................... 27 2.1.1 Acquiring and Installing Dakota............................... 27 2.1.2 Running Dakota with a simple input file........................... 28 2.1.3 Examples of Dakota output.................................. 29 2.2 Dakota Input File Format....................................... 31 2.3 Examples............................................... 33 2.3.1 Rosenbrock Test Problem.................................. 34 2.3.2 Two-Dimensional Grid Parameter Study........................... 35 2.3.3 Gradient-based Unconstrained Optimization......................... 36 2.3.4 Uncertainty Quantification with Monte Carlo Sampling................... 36 2.3.5 User Supplied Simulation Code Examples.......................... 39 2.3.5.1 Optimization with a User-Supplied Simulation Code - Case 1.......... 39 2.3.5.2 Optimization with a User-Supplied Simulation Code - Case 2.......... 44 2.4 Dakota Command-Line Options................................... 44 2.5 Next Steps............................................... 46 6 CONTENTS 2.5.1 Problem Exploration and Method Selection......................... 46 2.5.2 Key Getting Started References............................... 46 3 Parameter Study Capabilities 49 3.1 Overview............................................... 49 3.1.1 Initial Values......................................... 50 3.1.2 Bounds............................................ 50 3.2 Vector Parameter Study........................................ 51 3.3 List Parameter Study......................................... 52 3.4 Centered Parameter Study...................................... 53 3.5 Multidimensional Parameter Study.................................. 54 3.6 Parameter Study Usage Guidelines.................................. 56 3.7 Example: Vector Parameter Study with Rosenbrock......................... 56 4 Design of Experiments Capabilities 59 4.1 Overview............................................... 59 4.2 Design of Computer Experiments.................................. 60 4.3 DDACE................................................ 61 4.3.1 Central Composite Design.................................. 61 4.3.2 Box-Behnken Design..................................... 62 4.3.3 Orthogonal Array Designs.................................. 63 4.3.4 Grid Design.......................................... 64 4.3.5 Monte Carlo Design..................................... 64 4.3.6 LHS Design.......................................... 64 4.3.7 OA-LHS Design....................................... 64 4.4 FSUDace............................................... 64 4.5 PSUADE MOAT........................................... 65 4.6 Sensitivity Analysis.......................................... 66 4.6.1 Sensitivity Analysis Overview................................ 66 4.6.2 Assessing Sensitivity with DACE.............................. 68 4.7 DOE Usage Guidelines........................................ 69 5 Uncertainty Quantification Capabilities 71 5.1 Overview............................................... 71 5.1.1 Summary of Dakota UQ Methods.............................. 71 Dakota Version 6.10 User’s Manual generated on May 15, 2019 CONTENTS 7 5.1.2 Variables and Responses for UQ............................... 74 5.2 Sampling Methods.......................................... 74 5.2.1 Uncertainty Quantification Example using Sampling Methods............... 76 5.2.2 Incremental Sampling.................................... 80 5.2.3 Principal Component Analysis................................ 81 5.2.4 Wilks-based Sample Sizes.................................. 81 5.3 Reliability Methods.......................................... 81 5.3.1 Local Reliability Methods.................................. 83 5.3.1.1 Method mapping.................................. 83 5.3.2 Global Reliability Methods.................................. 84 5.3.3 Uncertainty Quantification Examples using Reliability Analysis.............. 85 5.3.3.1 Mean-value Reliability with Textbook...................... 85 5.3.3.2 FORM Reliability with Lognormal Ratio..................... 86 5.4 Stochastic Expansion Methods.................................... 91 5.4.1 Uncertainty Quantification Examples using Stochastic Expansions............. 92 5.4.1.1 Polynomial Chaos Expansion for Rosenbrock.................. 92 5.4.1.2 Uncertainty Quantification Example using Stochastic Collocation........ 92 5.5 Importance Sampling Methods.................................... 97 5.5.1 Importance Sampling Method based on Reliability Approach................ 98 5.5.2 Gaussian Process Adaptive Importance Sampling Method................. 98 5.6 Adaptive Sampling Methods..................................... 99 5.6.1 Adaptive sampling based on surrogates........................... 99 5.6.2 Adaptive sampling based on dart throwing.......................... 100 5.7 Epistemic Nondeterministic Methods................................. 101 5.7.1 Interval Methods for Epistemic Analysis.......................... 102 5.7.2 Dempster-Shafer Theory of Evidence............................ 102 5.8 Bayesian Calibration Methods.................................... 107 5.8.1 QUESO............................................ 108 5.8.2 DREAM........................................... 109 5.8.3 GPMSA............................................ 110 5.8.4 WASABI........................................... 110 5.8.5 Feature Comparison..................................... 110 5.8.6 Bayesian Calibration Example................................ 111 5.8.7 Chain Diagnostics...................................... 113 Dakota Version 6.10 User’s Manual generated on May 15, 2019 8 CONTENTS 5.8.8 Calibrating the Observation Error Model.......................... 114 5.8.9 Scaling and Weighting of Residuals............................. 114 5.8.10 Model Evidence....................................... 114 5.8.11 Model Discrepancy...................................... 116 5.8.12 Bayesian Experimental Design................................ 118 5.8.12.1 One-at-a-time Implementation.......................... 121 5.9 Uncertainty Quantification Usage Guidelines............................ 122 6 Optimization Capabilities 125 6.1 Optimization Formulations...................................... 125 6.1.1 Constraint Considerations.................................. 127 6.2 Optimizing with Dakota: Choosing a Method............................ 127 6.2.1 Gradient-Based Local Methods............................... 128 6.2.1.1 Methods for Unconstrained Problems....................... 128 6.2.1.2 Methods for Bound-Constrained Problems.................... 128 6.2.1.3 Methods for Constrained Problems........................ 129 6.2.1.4 Example...................................... 130 6.2.2 Derivative-Free Local