Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems
A greedy algorithm for the construction of a reduced model with reduction in both parameter and state is developed for an efficient solution of statistical inverse problems governed by partial differential equations with distributed parameters. Large-scale models are too costly to evaluate repeatedl...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Society of Industrial and Applied Mathematics (SIAM)
2011
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| Online Access: | http://hdl.handle.net/1721.1/60569 https://orcid.org/0000-0003-2156-9338 |
| _version_ | 1811082335423037440 |
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| author | Lieberman, Chad E. Willcox, Karen E. Ghattas, O. |
| author2 | Massachusetts Institute of Technology. Aerospace Controls Laboratory |
| author_facet | Massachusetts Institute of Technology. Aerospace Controls Laboratory Lieberman, Chad E. Willcox, Karen E. Ghattas, O. |
| author_sort | Lieberman, Chad E. |
| collection | MIT |
| description | A greedy algorithm for the construction of a reduced model with reduction in both parameter and state is developed for an efficient solution of statistical inverse problems governed by partial differential equations with distributed parameters. Large-scale models are too costly to evaluate repeatedly, as is required in the statistical setting. Furthermore, these models often have high-dimensional parametric input spaces, which compounds the difficulty of effectively exploring the uncertainty space. We simultaneously address both challenges by constructing a projection-based reduced model that accepts low-dimensional parameter inputs and whose model evaluations are inexpensive. The associated parameter and state bases are obtained through a greedy procedure that targets the governing equations, model outputs, and prior information. The methodology and results are presented for groundwater inverse problems in one and two dimensions. |
| first_indexed | 2024-09-23T12:01:30Z |
| format | Article |
| id | mit-1721.1/60569 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:01:30Z |
| publishDate | 2011 |
| publisher | Society of Industrial and Applied Mathematics (SIAM) |
| record_format | dspace |
| spelling | mit-1721.1/605692022-09-27T23:34:03Z Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems Lieberman, Chad E. Willcox, Karen E. Ghattas, O. Massachusetts Institute of Technology. Aerospace Controls Laboratory Willcox, Karen E. Lieberman, Chad E. Willcox, Karen E. A greedy algorithm for the construction of a reduced model with reduction in both parameter and state is developed for an efficient solution of statistical inverse problems governed by partial differential equations with distributed parameters. Large-scale models are too costly to evaluate repeatedly, as is required in the statistical setting. Furthermore, these models often have high-dimensional parametric input spaces, which compounds the difficulty of effectively exploring the uncertainty space. We simultaneously address both challenges by constructing a projection-based reduced model that accepts low-dimensional parameter inputs and whose model evaluations are inexpensive. The associated parameter and state bases are obtained through a greedy procedure that targets the governing equations, model outputs, and prior information. The methodology and results are presented for groundwater inverse problems in one and two dimensions. United States. Dept. of Energy (DE-FG02-08ER25858) United States. Dept. of Energy (DE-FG02-08ER25860) United States. Air Force Office of Sponsored Research (grant FA9550-06-0271) MIT-Singapore Alliance. Computational Engineering Programme 2011-01-14T14:57:45Z 2011-01-14T14:57:45Z 2010-08 2009-11 Article http://purl.org/eprint/type/JournalArticle 1064-8275 http://hdl.handle.net/1721.1/60569 Lieberman, Chad, Karen Willcox, and Omar Ghattas. “Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems.” SIAM Journal on Scientific Computing 32.5 (2010): 2523-2542. © 2010 SIAM https://orcid.org/0000-0003-2156-9338 en_US http://dx.doi.org/10.1137/090775622 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 of Industrial and Applied Mathematics (SIAM) SIAM |
| spellingShingle | Lieberman, Chad E. Willcox, Karen E. Ghattas, O. Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems |
| title | Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems |
| title_full | Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems |
| title_fullStr | Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems |
| title_full_unstemmed | Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems |
| title_short | Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems |
| title_sort | parameter and state model reduction for large scale statistical inverse problems |
| url | http://hdl.handle.net/1721.1/60569 https://orcid.org/0000-0003-2156-9338 |
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