Data-driven model reduction for the Bayesian solution of inverse problems
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Marzouk_Data-driven model.pdf
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Author(s)
Cui, Tiangang
Marzouk, Youssef M.
Willcox, Karen E.
Date Issued
August 2015
Journal
International Journal for Numerical Methods in Engineering
Publisher
Wiley Blackwell
Citation
Cui, Tiangang, Youssef M. Marzouk, and Karen E. Willcox. “Data-Driven Model Reduction for the Bayesian Solution of Inverse Problems.” Int. J. Numer. Meth. Engng 102, no. 5 (August 15, 2014): 966–990.
Version
Author's final manuscript
Abstract
One 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.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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DOI of Published Version
https://doi.org/10.1002/nme.4748
