Data-driven model reduction for the Bayesian solution of inverse problems
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 dat...
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| Format: | Article |
| Language: | en_US |
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Wiley Blackwell
2015
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| Online Access: | http://hdl.handle.net/1721.1/96976 https://orcid.org/0000-0002-4840-8545 https://orcid.org/0000-0001-8242-3290 https://orcid.org/0000-0003-2156-9338 |
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| author | Cui, Tiangang Marzouk, Youssef M. Willcox, Karen E. |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Cui, Tiangang Marzouk, Youssef M. Willcox, Karen E. |
| author_sort | Cui, Tiangang |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T09:39:13Z |
| format | Article |
| id | mit-1721.1/96976 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:39:13Z |
| publishDate | 2015 |
| publisher | Wiley Blackwell |
| record_format | dspace |
| spelling | mit-1721.1/969762022-09-26T12:50:15Z Data-driven model reduction for the Bayesian solution of inverse problems Cui, Tiangang Marzouk, Youssef M. Willcox, Karen E. Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Cui, Tiangang Marzouk, Youssef M. Willcox, Karen E. 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. United States. Dept. of Energy. Office of Advanced Scientific Computing Research (Applied Mathematics Program Award DE-FG02-08ER2585) United States. Dept. of Energy. Office of Advanced Scientific Computing Research (Applied Mathematics Program Award DE-SC0009297) 2015-05-13T13:27:56Z 2015-05-13T13:27:56Z 2015-08 2014-06 Article http://purl.org/eprint/type/JournalArticle 00295981 1097-0207 http://hdl.handle.net/1721.1/96976 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. https://orcid.org/0000-0002-4840-8545 https://orcid.org/0000-0001-8242-3290 https://orcid.org/0000-0003-2156-9338 en_US http://dx.doi.org/10.1002/nme.4748 International Journal for Numerical Methods in Engineering Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Wiley Blackwell arXiv |
| spellingShingle | Cui, Tiangang Marzouk, Youssef M. Willcox, Karen E. Data-driven model reduction for the Bayesian solution of inverse problems |
| title | Data-driven model reduction for the Bayesian solution of inverse problems |
| title_full | Data-driven model reduction for the Bayesian solution of inverse problems |
| title_fullStr | Data-driven model reduction for the Bayesian solution of inverse problems |
| title_full_unstemmed | Data-driven model reduction for the Bayesian solution of inverse problems |
| title_short | Data-driven model reduction for the Bayesian solution of inverse problems |
| title_sort | data driven model reduction for the bayesian solution of inverse problems |
| url | http://hdl.handle.net/1721.1/96976 https://orcid.org/0000-0002-4840-8545 https://orcid.org/0000-0001-8242-3290 https://orcid.org/0000-0003-2156-9338 |
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