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Title: Data–driven model reduction for the Bayesian solution of inverse problems

Journal Article · · International Journal for Numerical Methods in Engineering
DOI: https://doi.org/10.1002/nme.4748 · OSTI ID:1557833
 [1];  [1];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
+ Show Author Affiliations

One of the prime 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 presents a data-driven projection-based model reduction technique to reduce this computational cost. The proposed technique has two distinctive features. To begin, 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.

Research Organization:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
SC0009297; FG02‐08ER2585
OSTI ID:
1557833
Journal Information:
International Journal for Numerical Methods in Engineering, Vol. 102, Issue 5; ISSN 0029-5981
Publisher:
WileyCopyright Statement
Country of Publication:
United States
Language:
English

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  • International Journal for Numerical Methods in Engineering, Vol. 121, Issue 19 https://doi.org/10.1002/nme.6450
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Figures / Tables (12)

Figure 1(p. 3)figure Figure 1
Algorithm 1(p. 9)figure Algorithm 1
Algorithm 2(p. 15)figure Algorithm 2
Figure 2(p. 17)figure Figure 2
Figure 3(p. 18)figure Figure 3
Table I(p. 19)table Table I
Figure 4(p. 20)figure Figure 4
Figure 5(p. 21)figure Figure 5
Figure 6(p. 21)figure Figure 6
Figure 7(p. 22)figure Figure 7
Table II(p. 22)table Table II
Figure 8(p. 23)figure Figure 8

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97 MATHEMATICS AND COMPUTING
model reduction
inverse problem
adaptive Markov chain Monte Carlo
approximate Bayesian inference