Adaptive Construction of Surrogates for the Bayesian Solution of Inverse Problems
The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or forward model. When these evaluations are computationally inte...
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2014
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| Online Access: | http://hdl.handle.net/1721.1/89467 https://orcid.org/0000-0001-8242-3290 |
| _version_ | 1826206923496620032 |
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| author | Li, Jinglai Marzouk, Youssef M. |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Li, Jinglai Marzouk, Youssef M. |
| author_sort | Li, Jinglai |
| collection | MIT |
| description | The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or forward model. When these evaluations are computationally intensive, approximations of the forward model are essential to accelerating sample-based inference. Yet the construction of globally accurate approximations for nonlinear forward models can be computationally prohibitive and in fact unnecessary, as the posterior distribution typically concentrates on a small fraction of the support of the prior distribution. We present a new approach that uses stochastic optimization to construct polynomial approximations over a sequence of distributions adaptively determined from the data, eventually concentrating on the posterior distribution. The approach yields substantial gains in efficiency and accuracy over prior-based surrogates, as demonstrated via application to inverse problems in partial differential equations. |
| first_indexed | 2024-09-23T13:40:42Z |
| format | Article |
| id | mit-1721.1/89467 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:40:42Z |
| publishDate | 2014 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/894672022-10-01T16:25:38Z Adaptive Construction of Surrogates for the Bayesian Solution of Inverse Problems Li, Jinglai Marzouk, Youssef M. Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Marzouk, Youssef M. The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or forward model. When these evaluations are computationally intensive, approximations of the forward model are essential to accelerating sample-based inference. Yet the construction of globally accurate approximations for nonlinear forward models can be computationally prohibitive and in fact unnecessary, as the posterior distribution typically concentrates on a small fraction of the support of the prior distribution. We present a new approach that uses stochastic optimization to construct polynomial approximations over a sequence of distributions adaptively determined from the data, eventually concentrating on the posterior distribution. The approach yields substantial gains in efficiency and accuracy over prior-based surrogates, as demonstrated via application to inverse problems in partial differential equations. United States. Dept. of Energy. Office of Advanced Scientific Computing Research (Grant DE-SC0002517) 2014-09-12T17:12:05Z 2014-09-12T17:12:05Z 2014-06 2013-09 Article http://purl.org/eprint/type/JournalArticle 1064-8275 1095-7197 http://hdl.handle.net/1721.1/89467 Li, Jinglai, and Youssef M. Marzouk. “Adaptive Construction of Surrogates for the Bayesian Solution of Inverse Problems.” SIAM Journal on Scientific Computing 36, no. 3 (January 2014): A1163–A1186. © 2014, Society for Industrial and Applied Mathematics https://orcid.org/0000-0001-8242-3290 en_US http://dx.doi.org/10.1137/130938189 SIAM Journal on Scientific Computing Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics |
| spellingShingle | Li, Jinglai Marzouk, Youssef M. Adaptive Construction of Surrogates for the Bayesian Solution of Inverse Problems |
| title | Adaptive Construction of Surrogates for the Bayesian Solution of Inverse Problems |
| title_full | Adaptive Construction of Surrogates for the Bayesian Solution of Inverse Problems |
| title_fullStr | Adaptive Construction of Surrogates for the Bayesian Solution of Inverse Problems |
| title_full_unstemmed | Adaptive Construction of Surrogates for the Bayesian Solution of Inverse Problems |
| title_short | Adaptive Construction of Surrogates for the Bayesian Solution of Inverse Problems |
| title_sort | adaptive construction of surrogates for the bayesian solution of inverse problems |
| url | http://hdl.handle.net/1721.1/89467 https://orcid.org/0000-0001-8242-3290 |
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