Data-driven model reduction for the Bayesian solution of inverse problems

SummaryOne of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. This paper propose...

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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 102; no. 5; pp. 966 - 990
Main Authors: Cui, Tiangang, Marzouk, Youssef M., Willcox, Karen E.
Format: Journal Article
Language:English
Published: Bognor Regis Blackwell Publishing Ltd 04.05.2015
Wiley Subscription Services, Inc
Subjects:
adaptive Markov chain Monte Carlo
approximate Bayesian inference
Bayesian analysis
Computational efficiency
Construction costs
inverse problem
Inverse problems
Mathematical models
Model reduction
Partial differential equations
Sampling
ISSN:0029-5981, 1097-0207
Online Access:Get full text
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Summary:SummaryOne of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. This paper proposes a data‐driven projection‐based model reduction technique to reduce this computational cost. The proposed technique has two distinctive features. First, the model reduction strategy is tailored to inverse problems: the snapshots used to construct the reduced‐order model are computed adaptively from the posterior distribution. Posterior exploration and model reduction are thus pursued simultaneously. Second, to avoid repeated evaluations of the full‐scale numerical model as in a standard MCMC method, we couple the full‐scale model and the reduced‐order model together in the MCMC algorithm. This maintains accurate inference while reducing its overall computational cost. In numerical experiments considering steady‐state flow in a porous medium, the data‐driven reduced‐order model achieves better accuracy than a reduced‐order model constructed using the classical approach. It also improves posterior sampling efficiency by several orders of magnitude compared with a standard MCMC method. Copyright © 2014 John Wiley & Sons, Ltd.
Bibliography:ArticleID:NME4748
United States Department of Energy, Office of Advanced Scientific Computing Research (ASCR), Applied Mathematics Program - No. DE-FG02-08ER2585; No. DE-SC0009297
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.4748