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.
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September 2016
Research-Article
Computationally Efficient Variational Approximations for Bayesian Inverse Problems
Panagiotis Tsilifis,
Panagiotis Tsilifis
Department of Mathematics,
University of Southern California,
Los Angeles, CA 90089-2532
e-mail: tsilifis@usc.edu
University of Southern California,
Los Angeles, CA 90089-2532
e-mail: tsilifis@usc.edu
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Ilias Bilionis,
Ilias Bilionis
Assistant Professor
School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47906-2088
e-mail: ibilion@purdue.edu
School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47906-2088
e-mail: ibilion@purdue.edu
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Ioannis Katsounaros,
Ioannis Katsounaros
Leiden Institute of Chemistry,
Leiden University,
Einsteinweg 55, P.O. Box 9502,
Leiden 2300 RA, The Netherlands
e-mail: katsounaros@anl.gov
Leiden University,
Einsteinweg 55, P.O. Box 9502,
Leiden 2300 RA, The Netherlands
e-mail: katsounaros@anl.gov
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Nicholas Zabaras
Nicholas Zabaras
Professor
Warwick Centre for Predictive Modeling,
University of Warwick,
Coventry CV4 7AL, UK
e-mail: nzabaras@gmail.com
Warwick Centre for Predictive Modeling,
University of Warwick,
Coventry CV4 7AL, UK
e-mail: nzabaras@gmail.com
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Panagiotis Tsilifis
Department of Mathematics,
University of Southern California,
Los Angeles, CA 90089-2532
e-mail: tsilifis@usc.edu
University of Southern California,
Los Angeles, CA 90089-2532
e-mail: tsilifis@usc.edu
Ilias Bilionis
Assistant Professor
School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47906-2088
e-mail: ibilion@purdue.edu
School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47906-2088
e-mail: ibilion@purdue.edu
Ioannis Katsounaros
Leiden Institute of Chemistry,
Leiden University,
Einsteinweg 55, P.O. Box 9502,
Leiden 2300 RA, The Netherlands
e-mail: katsounaros@anl.gov
Leiden University,
Einsteinweg 55, P.O. Box 9502,
Leiden 2300 RA, The Netherlands
e-mail: katsounaros@anl.gov
Nicholas Zabaras
Professor
Warwick Centre for Predictive Modeling,
University of Warwick,
Coventry CV4 7AL, UK
e-mail: nzabaras@gmail.com
Warwick Centre for Predictive Modeling,
University of Warwick,
Coventry CV4 7AL, UK
e-mail: nzabaras@gmail.com
Manuscript received September 15, 2015; final manuscript received July 5, 2016; published online July 26, 2016. Editor: Ashley F. Emery.
J. Verif. Valid. Uncert. Sep 2016, 1(3): 031004 (13 pages)
Published Online: July 26, 2016
Article history
Received:
September 15, 2015
Revised:
July 5, 2016
Citation
Tsilifis, P., Bilionis, I., Katsounaros, I., and Zabaras, N. (July 26, 2016). "Computationally Efficient Variational Approximations for Bayesian Inverse Problems." ASME. J. Verif. Valid. Uncert. September 2016; 1(3): 031004. https://doi.org/10.1115/1.4034102
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