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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];  [2];  [2]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Office of Scientific and Technical Information (OSTI)
  2. 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) (SC-21)
Grant/Contract Number:
SC0009297
OSTI ID:
1557833
Journal Information:
International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering Journal Issue: 5 Vol. 102; ISSN 0029-5981
Publisher:
WileyCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (17)

An adaptive and efficient greedy procedure for the optimal training of parametric reduced-order models: ADAPTIVE GREEDY PROCEDURE FOR THE OPTIMAL TRAINING OF PARAMETRIC ROMS journal September 2014
A posteriori stochastic correction of reduced models in delayed-acceptance MCMC, with application to multiphase subsurface inverse problems: Stochastic correction of reduced models in delayed-acceptance MCMC
  • Cui, Tiangang; Fox, Colin; O'Sullivan, Michael J.
  • International Journal for Numerical Methods in Engineering, Vol. 118, Issue 10 https://doi.org/10.1002/nme.6028
journal March 2019
Adaptive multi‐index collocation for uncertainty quantification and sensitivity analysis
  • Jakeman, John D.; Eldred, Michael S.; Geraci, Gianluca
  • International Journal for Numerical Methods in Engineering, Vol. 121, Issue 6 https://doi.org/10.1002/nme.6268
journal November 2019
Adaptive multi‐index collocation for uncertainty quantification and sensitivity analysis
  • Jakeman, John D.; Eldred, Michael S.; Geraci, Gianluca
  • International Journal for Numerical Methods in Engineering, Vol. 121, Issue 19 https://doi.org/10.1002/nme.6450
journal August 2020
The Use of Radial Basis Function Surrogate Models for Sampling Process Acceleration in Bayesian Inversion book April 2019
Multilevel model reduction for uncertainty quantification in computational structural dynamics journal October 2016
Fast model updating coupling Bayesian inference and PGD model reduction journal April 2018
A transport-based multifidelity preconditioner for Markov chain Monte Carlo journal November 2019
Bayesian Estimation for Stochastic Gene Expression Using Multifidelity Models journal February 2019
Surrogate accelerated Bayesian inversion for the determination of the thermal diffusivity of a material journal January 2019
Adaptive multi-index collocation for uncertainty quantification and sensitivity analysis report November 2019
Statistical Inference Method for Liner Impedance Eduction with a Shear Grazing Flow journal March 2019
Adaptivity in Bayesian Inverse Finite Element Problems: Learning and Simultaneous Control of Discretisation and Sampling Errors journal February 2019
A transport-based multifidelity preconditioner for Markov chain Monte Carlo preprint January 2018
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data text January 2019
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data posted_content April 2019
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data journal January 2019

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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Related Subjects

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