Computationally Efficient Variational Approximations for Bayesian Inverse Problems

被引：3

作者：

Tsilifis P. ^{[1
]}

Bilionis I. ^{[2
]}

Katsounaros I. ^{[3
]}

Zabaras N. ^{[4
]}

机构：

[1] Department of Mathematics, University of Southern California, Los Angeles, 90089-2532, CA

[2] School of Mechanical Engineering, Purdue University, West Lafayette, 47906-2088, IN

[3] Leiden Institute of Chemistry, Leiden University, Einsteinweg 55, P.O. Box 9502, Leiden

[4] Warwick Centre for Predictive Modeling, University of Warwick, Coventry

来源：

| 1600年 / American Society of Mechanical Engineers (ASME)卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Bayesian - Bayesian approaches - Computational burden - Computationally efficient - Forward modeling - Markov chain Monte Carlo - Markov Chain Monte-Carlo - Model calibration - Posterior distributions - Variational approximation;

D O I：

10.1115/1.4034102

中图分类号：

学科分类号：

摘要：

The major drawback of the Bayesian approach to model calibration is the computational burden involved in describing the posterior distribution of the unknown model parameters arising from the fact that typical Markov chain Monte Carlo (MCMC) samplers require thousands of forward model evaluations. In this work, we develop a variational Bayesian approach to model calibration which uses an information theoretic criterion to recast the posterior problem as an optimization problem. Specifically, we parameterize the posterior using the family of Gaussian mixtures and seek to minimize the information loss incurred by replacing the true posterior with an approximate one. Our approach is of particular importance in underdetermined problems with expensive forward models in which both the classical approach of minimizing a potentially regularized misfit function and MCMC are not viable options. We test our methodology on two surrogate-free examples and show that it dramatically outperforms MCMC methods. Copyright © 2016 by ASME

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