An Introduction to Statistical Learning Theory

Introduction to Compact Dynamical Modeling - References Luca Daniel, Massachusetts Institute of Technology

ASSEMBLING MODELS FROM FUNDAMENTAL LAWS AND PDEs 1. Book: L. O. Chua and P. Lin, Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques, Prentice-Hall Series in Electrical and Computer Engineering, Englewood Cliffs, NJ: Prentice-Hall, 1975. 2. L. Daniel, "Simulation and Modelling Techniques for Signal Integrity and Electromagnetic Interference on High Frequency Electronic Systems," Ph.D. Thesis, University of California at Berkeley, May 2003. [Chapters 2, 3, 7, 8, 9, 10.] 3. J. C. Willems, “Dissipative dynamical systems,” Arch. Rational Mechanics Anal., vol. 45, pp. 321–393, 1972.

STEADY STATE AND TIME DOMAIN SIMULATION 4. Book: Numerical Linear Algebra by Lloyd N. Trefethen and David Bau Society for Industrial and Applied Math © 1997 (361 pages) Citation ISBN:9780898713619 5. Book: Introduction to numerical analysis. By: Stoer, Josef. New York : Springer, c2002 6. Book: Introduction to linear algebra Strang, Gilbert. Wellesley, MA : Wellesley-Cambridge Press, c2009. 7. Book: Computer solution of large sparse positive definite systems By: George, Alan. Englewood Cliffs, N.J. : Prentice-Hall, c1981. 8. Book: Direct Methods for Sparse Matrices, I. Duff, A. Erisman and J. Reid Clarendon Press, 1986. 9. Book: Numerical continuation methods By: Allgower, E. L.. Berlin ; New York : Springer-Verlag, c1990 10. Book: Iterative Solution of Nonlinear Equations in Several Variables, Ortega and Rheinboldt. Society for Industrial and Applied Mathematics, 2000.

MODEL ORDER REDUCTION OF LINEAR DYNAMICAL SYSTEMS 11. B. Moore, “Principal component analysis in linear systems: Controllability, observability, and model reduction,” IEEE Trans. Automat. Contr., vol. AC-26, pp. 17–32, Feb. 1981. 12. K. Glover, “All optimal Hankel-norm approximations of linear multi-variable systems and their L -error bounds,” Int. J. Control, vol. 39, no. 6, pp. 1115–1193, June 1984. 13. J.-R Li, F. Wang, J. White, “Efficient model reduction of interconnect via approximate system Gramians,” in Int. Conf. Computer Aided-Design, San Jose, CA, November 1999, pp. 380–383. 14. J. Phillips, L. Daniel, L. M. Silveira, "Guaranteed Passive Balancing Transformations for Model Order Reduction", IEEE Transaction on Computer Aided Design of Integrated Circuits and Systems, vol. 22, no. 8, p. 1027-41, August 2003. 15. Liang,Y.C.,Lee,H.P.,Lim,S.P.,Lin,W.Z.,Lee,K.H.and Wu, C.G.,“Proper Orthogonal Decomposition and its Applications-Part I: Theory ”,Journal of Sound and Vibration (2002)252(3),page 527-544. 16. P. Feldmann, R. W. Freund, “Efficient linear circuit analysis by Padé approximation via the Lanczos process,” IEEE Trans. Computer-Aided Design, vol. 14, pp. 639–649, May 1995. 17. E. Grimme, “Krylov projection methods for model reduction,” Ph.D. dissertation, Coordinated-Science Laboratory, Univ. of Illinois at Urbana-Champaign, IL, 1997. 18. A. Odabasioglu, M. Celik, and L. T. Pileggi, “PRIMA: Passive reduced-order interconnect macromodeling algorithm,” IEEE Trans. Computer-Aided Design, vol. 17, pp. 645–654, Aug. 1998. 19. J. R. Phillips, “Model reduction of time-varying linear systems using approximate multipoint Krylov- subspace projectors,” in Int. Conf. on Computer Aided-Design, Santa Clara, CA, Nov. 1998, pp. 96–102. 20. L. Daniel, A. Sangiovanni-Vincentelli, J. White, "Techniques for Including Dielectrics when Extracting Low-Order Models of High Speed Interconnect". IEEE/ACM International Conference on Computer Aided Design, San Jose, CA, p. 240-4, November 2001. 21. L. Daniel, J. Phillips, "Model Order Reduction for Strictly Passive and Causal Distributed Systems", IEEE/ACM 39th Design Automation Conference, New Orleans, LA, p. 46-51, June 2002. 22. J. M. Wang, C..C. Chu, Q. Yu, E. S. Kuh, “On Projection-Based Algorithms for Model-Order Reduction of Interconnects”, IEEE Trans. on Circuit and Systems-I, Vol 49, no 11, Nov 2002. 23. B. Bond and L. Daniel, "Guaranteed Stable Projection-Based Model Reduction for Indefinite and Unstable Linear Systems" Proceedings of the IEEE Conference on Computer-Aided Design, San Jose, p. 728-35, November 2008. (IEEE/ACM William J. McCalla ICCAD Best Paper Award). 24. Z. Zhang, Q. Wang, N. Wong and L. Daniel, “A moment-matching scheme for the passivity-preserving model order reduction of indefinite descriptor systems with possible polynomial parts,” in Proc. Asia and South Pacific Design Automation Conference (ASP-DAC), pp. 49-55, Yokohama, Japan , Jan. 2011. (Best Paper Candidate) 25. A. Hochman, J. Fernandez Villena, A. G. Polimeridis, L.M. Silveira, J. K. White, and L. Daniel. “Reduced-Order Models for Electromagnetic Scattering Problems”. In IEEE Trans. on Antennas and Propagation, vol: PP, issue: 99, April 2014. 26. Mahmood, Z.; Grivet-Talocia, S.; Chinea, A.; Calafiore, G.C.; Daniel, L., "Efficient Localization Methods for Passivity Enforcement of Linear Dynamical Models". Accepted for publication IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems (TCAD), 2014.**

MODEL ORDER REDUCTION OF NON-LINEAR DYNAMICAL SYSTEMS 27. J. R. Phillips, “Projection frameworks for model reduction of weakly nonlinear systems,” in 37th ACM/IEEE Design Automation Conf., 2000, pp. 184–189. 28. M. Rewienski and J. White, "A Trajectory Piecewise-linear Approach to Model Order Reduction and Fast Simulation of Nonlinear Circuits and Micromachined devices," IEEE Transactions on Computer- Aided Design of Integrated Circuits and Systems, Vol. 22, No. 2, pp. 155--170, Feb. 2003. 29. N. Dong and J. Roychowdhury, “Piecewise polynomial nonlinear model reduction.” ACM/IEEE Design Automation Conference, June 2003. 30. K. C. Sou, A. Megretski, L. Daniel, "Bounding L2 Gain System Error Due to Approximations of the Nonlinear Vector Field", Proceedings of the IEEE Conference on Computer-Aided Design, San Jose, p. 879-86, November 2007. 31. Sou, K. C., A. Megretski, and L. Daniel, “Convex Relaxation Approach to the Identification of the Wiener-Hammerstein Model,” in Proceedings of the 47th IEEE/ACM Conference on Decision and Control, Cancun Mexico, p. 1375-82, December 2008.** 32. B. N. Bond, L. Daniel, "Stable Macromodels for Nonlinear Descriptor Systems through Piecewise-Linear Approximation and Projection", IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 28, no. 10, p. 1467-1480, October 2009. 33. B. Bond, Z. Mahmood, R. Sredojevic, Y. Li, A. Megretski, V. Stojanovic, Y. Avniel, L. Daniel, “Compact Stable Modeling of Nonlinear Analog Circuits using System Identification via Semi-Definite Programming and Robustness Certification,” IEEE Trans. on Computer Aided Design of Integrated Circuits and Systems, vol. 29,no 8, p. 1149-1162, August 2010. 34. Bond, B., T. Moselhy, and L. Daniel, “System Identification Techniques for Modeling of the Human Arterial System,” SIAM Conference on the Life Sciences, Pittsburgh, PA, p. 12-15, July 2010 35. Bond, B., and L. Daniel, “Model Order Reduction for Analog Integrated Circuits”, Proceedings of the IEEE/ACM 47th Design Automation Conference, Anaheim, CA, pp. 415-420, June 2010. 36. Y.-C. Hsiao and L. Daniel, “Sparse Basis Pursuit on Automatic Nonlinear Circuit Modeling,” in Proceedings of the IEEE 10th International Conference on ASIC, Hong Kong, October 2013. (Invited Paper).**

MODEL ORDER REDUCTION OF PARAMETERIZED DYNAMICAL SYSTEMS 37. P. Rabiei and M. Pedram, “Model reduction of variable-geometry interconnects using variational spectrally-weighted balanced truncation,” in Int. Conf. Computer Aided-Design, San Jose, CA, Nov. 2001, pp. 586–591. 38. L. Daniel, C. S. Ong, S. C. Low, K. H. Lee, J. White, "Geometrically Parameterized Interconnect Performance Models for Interconnect Synthesis", IEEE/ACM International Symposium on Physical Design, San Diego, CA, p. 202-7, May 2002. 39. L. Daniel, C. S. Ong, S. C. Low, K. H. Lee, J. White, "A Multiparameter Moment Matching Model Reduction Approach for Generating Geometrically Parameterized Interconnect Performance Models", IEEE Transaction on Computer Aided Design of Integrated Circuits and Systems, vol. 23, no. 5, p. 678- 93, May 2004. 40. P. Li, F. Liu, S. Nassif, and L. Pileggi. “Modelling interconnect variability using efficient parametric model order reduction”. In Design, Automation and Test Conference in Europe, March 2005. 41. J. H. Lee, D. Vasilyev, A. Vithayathil, L. Daniel, and J. White, "Accelerated Optical Topography Inspection Using Parameterized Model Order Reduction", IEEE International Microwave Symposium, Los Angeles, CA, p. 4, June 2005. 42. B. N. Bond, L. Daniel, "A Piecewise-Linear Moment-Matching Approach to Parameterized Model- Order Reduction for Highly Nonlinear Systems", IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 26, no. 12, p. 2116–2129, December 2007. 43. K. C. Sou, A. Megretski, L. Daniel, "A Quasi-Convex Optimization Approach to Parameterized Model Order Reduction", IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 27, no. 3, p. 456-469, March 2008. 44. Moselhy, T., and L. Daniel, “Variation-Aware Interconnect Extraction using Statistical Moment Preserving Model Order Reduction,” IEEE Design, Automation and Test in Europe Conference, Dresden, Germany, pp.453-458, March 2010.(Best Paper Award Nomination) 45. Z. Zhang, I. M. Elfadel and L. Daniel, “Model order reduction of fully parameterized systems by recursive least square optimization,” Intl. Conf. Computer-Aided Design (ICCAD), pp. 523-530, San Jose, CA, Nov. 2011. (William J. McCalla ICCAD Best Paper Candidate.) 46. Z Mahmood and L Daniel, Passivity-preserving Algorithm for Multiport Parameterized Modeling in the Frequency Domain, In the proceedings of SIAM Conf. on Computational Science and Engineering, Boston, MA, February 2013

OPEN DOMAIN MODEL ORDER REDUCTION TOOLS FROM OUR GROUP AT MIT 1. August 2009. Squid. Open source Matlab tool for the generation of reduced order linear system models from available transfer function data points. Based on quasi-convex relaxation of a system identification problem subject to stability and passivity constraints. http://www.mit.edu/~dluca/squid/ 2. February 2010, SMORES: Simulation and Model Order Reduction of Electrical Systems. Public domain Matlab circuit simulator that reads spice-like netlists and performs several types of analysis. http://bnbond.com/software/smores/ 3. March 2010, STPWL: Stabilized Trajectory Piece-Wise Linear model reduction. This is a Matlab toolbox for stable trajectory piecewise linear model order reduction of nonlinear systems. http://bnbond.com/software/stpwl/stpwl.zip 4. March 2010, public domain open source Matlab code for generating guaranteed stable compact models of nonlinear analog circuit blocks from input/output data (e.g. low noise amplifiers, mixers, or power amplifiers). http://bnbond.com/software/stins/ 5. June 2010, Matlab compact modeling code. The tool takes a S-parameter or Z-parameter file in `.snp' touchstone format or .mat file in Matlab and generates a compact dynamical model in verilogA. The code incorporates binary search to find the minimum system order for a given error bound. Key contribution: using sum of squares to enforce stability and passivity constraints allowing an order of magnitude faster performance than our previous quasi-convex based tool. http://web.mit.edu/zohaib/www/#software 6. December 2013, Spectral projector computation, index checking and system decomposition for linear DAEs (or linear time-invariant descriptor systems). http://web.mit.edu/z_zhang/www/codes_data.htm