Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems [Chapter 7]
Solution of statistical inverse problems via the frequentist or Bayesian approaches described in earlier chapters can be a computationally intensive endeavor, particularly when faced with large-scale forward models characteristic of many engineering and science applications. High computational cost...
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| Format: | Article |
| Language: | en_US |
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John Wiley & Sons
2016
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| Online Access: | http://hdl.handle.net/1721.1/105500 https://orcid.org/0000-0001-8242-3290 https://orcid.org/0000-0003-2156-9338 |
| _version_ | 1826193938819579904 |
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| author | van Bloemen Waanders, B. Frangos, Michalis 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 van Bloemen Waanders, B. Frangos, Michalis Marzouk, Youssef M Willcox, Karen E |
| author_sort | van Bloemen Waanders, B. |
| collection | MIT |
| description | Solution of statistical inverse problems via the frequentist or Bayesian approaches described in earlier chapters can be a computationally intensive endeavor, particularly when faced with large-scale forward models characteristic of many engineering and science applications. High computational cost arises in several ways. First, thousands or millions of forward simulations may be required to evaluate estimators of interest or to characterize a posterior distribution. In the large-scale setting, performing so many forward simulations is often computationally intractable. Second, sampling may be complicated by the large dimensionality of the input space--as when the inputs are fields represented with spatial discretizations of high dimension--and by nonlinear forward dynamics that lead to multimodal, skewed, and/or strongly correlated posteriors. In this chapter, we present an overview of surrogate and reduced order modeling methods that address these computational challenges. For illustration, we consider a Bayesian formulation of the inverse problem. Though some of the methods we review exploit prior information, they largely focus on simplifying or accelerating evaluations of a stochastic model for the data, and thus are also applicable in a frequentist context. |
| first_indexed | 2024-09-23T09:47:39Z |
| format | Article |
| id | mit-1721.1/105500 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:47:39Z |
| publishDate | 2016 |
| publisher | John Wiley & Sons |
| record_format | dspace |
| spelling | mit-1721.1/1055002022-09-30T16:53:48Z Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems [Chapter 7] van Bloemen Waanders, B. Frangos, Michalis Marzouk, Youssef M Willcox, Karen E Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Massachusetts Institute of Technology. Department of Mechanical Engineering Willcox, Karen E Frangos, Michalis Marzouk, Youssef M Willcox, Karen E Solution of statistical inverse problems via the frequentist or Bayesian approaches described in earlier chapters can be a computationally intensive endeavor, particularly when faced with large-scale forward models characteristic of many engineering and science applications. High computational cost arises in several ways. First, thousands or millions of forward simulations may be required to evaluate estimators of interest or to characterize a posterior distribution. In the large-scale setting, performing so many forward simulations is often computationally intractable. Second, sampling may be complicated by the large dimensionality of the input space--as when the inputs are fields represented with spatial discretizations of high dimension--and by nonlinear forward dynamics that lead to multimodal, skewed, and/or strongly correlated posteriors. In this chapter, we present an overview of surrogate and reduced order modeling methods that address these computational challenges. For illustration, we consider a Bayesian formulation of the inverse problem. Though some of the methods we review exploit prior information, they largely focus on simplifying or accelerating evaluations of a stochastic model for the data, and thus are also applicable in a frequentist context. Sandia National Laboratories (Laboratory Directed Research and Development (LDRD) program) United States. Dept. of Energy (Contract DE-AC04-94AL85000) Singapore-MIT Alliance Computational Engineering Programme United States. Dept. of Energy (Award Number DE-FG02-08ER25858 ) United States. Dept. of Energy (Award Number DESC00025217) 2016-12-01T19:55:14Z 2016-12-01T19:55:14Z 2010-01 Article http://purl.org/eprint/type/BookItem 9780470697436 9780470685853 http://hdl.handle.net/1721.1/105500 Frangos, M., Y. Marzouk, K. Willcox, and B. van Bloemen Waanders (2010). Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems. In Lorenz Biegler, George Biros, Omar Ghattas, Matthias Heinkenschloss, David Keyes, Bani Mallick, Youssef Marzouk, Luis Tenorio, Bart van Bloemen Waanders, and Karen Willcox, eds., Large-scale inverse problems and quantification of uncertainty (pp. 123-149) New York: Wiley. https://orcid.org/0000-0001-8242-3290 https://orcid.org/0000-0003-2156-9338 en_US http://dx.doi.org/10.1002/9780470685853 Computational Methods for Large-Scale Inverse Problems and Quantification of Uncertainty , Biegler et al. (Eds.) Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf John Wiley & Sons Prof. Willcox via Barbara Williams |
| spellingShingle | van Bloemen Waanders, B. Frangos, Michalis Marzouk, Youssef M Willcox, Karen E Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems [Chapter 7] |
| title | Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems [Chapter 7] |
| title_full | Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems [Chapter 7] |
| title_fullStr | Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems [Chapter 7] |
| title_full_unstemmed | Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems [Chapter 7] |
| title_short | Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems [Chapter 7] |
| title_sort | surrogate and reduced order modeling a comparison of approaches for large scale statistical inverse problems chapter 7 |
| url | http://hdl.handle.net/1721.1/105500 https://orcid.org/0000-0001-8242-3290 https://orcid.org/0000-0003-2156-9338 |
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