Optimal Model Management for Multifidelity Monte Carlo Estimation
This work presents an optimal model management strategy that exploits multifidelity surrogate models to accelerate the estimation of statistics of outputs of computationally expensive high-fidelity models. Existing acceleration methods typically exploit a multilevel hierarchy of surrogate models tha...
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2017
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| Online Access: | http://hdl.handle.net/1721.1/108618 https://orcid.org/0000-0002-5045-046X https://orcid.org/0000-0003-2156-9338 |
| _version_ | 1826216402778849280 |
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| author | Gunzburger, Max Peherstorfer, Benjamin Willcox, Karen E |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Gunzburger, Max Peherstorfer, Benjamin Willcox, Karen E |
| author_sort | Gunzburger, Max |
| collection | MIT |
| description | This work presents an optimal model management strategy that exploits multifidelity surrogate models to accelerate the estimation of statistics of outputs of computationally expensive high-fidelity models. Existing acceleration methods typically exploit a multilevel hierarchy of surrogate models that follow a known rate of error decay and computational costs; however, a general collection of surrogate models, which may include projection-based reduced models, data-fit models, support vector machines, and simplified-physics models, does not necessarily give rise to such a hierarchy. Our multifidelity approach provides a framework to combine an arbitrary number of surrogate models of any type. Instead of relying on error and cost rates, an optimization problem balances the number of model evaluations across the high-fidelity and surrogate models with respect to error and costs. We show that a unique analytic solution of the model management optimization problem exists under mild conditions on the models. Our multifidelity method makes occasional recourse to the high-fidelity model; in doing so it provides an unbiased estimator of the statistics of the high-fidelity model, even in the absence of error bounds and error estimators for the surrogate models. Numerical experiments with linear and nonlinear examples show that speedups by orders of magnitude are obtained compared to Monte Carlo estimation that invokes a single model only. |
| first_indexed | 2024-09-23T16:47:06Z |
| format | Article |
| id | mit-1721.1/108618 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:47:06Z |
| publishDate | 2017 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/1086182022-10-03T08:18:14Z Optimal Model Management for Multifidelity Monte Carlo Estimation Gunzburger, Max Peherstorfer, Benjamin Willcox, Karen E Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Peherstorfer, Benjamin Willcox, Karen E This work presents an optimal model management strategy that exploits multifidelity surrogate models to accelerate the estimation of statistics of outputs of computationally expensive high-fidelity models. Existing acceleration methods typically exploit a multilevel hierarchy of surrogate models that follow a known rate of error decay and computational costs; however, a general collection of surrogate models, which may include projection-based reduced models, data-fit models, support vector machines, and simplified-physics models, does not necessarily give rise to such a hierarchy. Our multifidelity approach provides a framework to combine an arbitrary number of surrogate models of any type. Instead of relying on error and cost rates, an optimization problem balances the number of model evaluations across the high-fidelity and surrogate models with respect to error and costs. We show that a unique analytic solution of the model management optimization problem exists under mild conditions on the models. Our multifidelity method makes occasional recourse to the high-fidelity model; in doing so it provides an unbiased estimator of the statistics of the high-fidelity model, even in the absence of error bounds and error estimators for the surrogate models. Numerical experiments with linear and nonlinear examples show that speedups by orders of magnitude are obtained compared to Monte Carlo estimation that invokes a single model only. 2017-05-02T20:44:01Z 2017-05-02T20:44:01Z 2016-10 2015-11 Article http://purl.org/eprint/type/JournalArticle 1064-8275 1095-7197 http://hdl.handle.net/1721.1/108618 Peherstorfer, Benjamin, Karen Willcox, and Max Gunzburger. “Optimal Model Management for Multifidelity Monte Carlo Estimation.” SIAM Journal on Scientific Computing 38.5 (2016): A3163–A3194. © 2016 Society for Industrial and Applied Mathematics https://orcid.org/0000-0002-5045-046X https://orcid.org/0000-0003-2156-9338 en_US http://dx.doi.org/10.1137/15M1046472 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 SIAM |
| spellingShingle | Gunzburger, Max Peherstorfer, Benjamin Willcox, Karen E Optimal Model Management for Multifidelity Monte Carlo Estimation |
| title | Optimal Model Management for Multifidelity Monte Carlo Estimation |
| title_full | Optimal Model Management for Multifidelity Monte Carlo Estimation |
| title_fullStr | Optimal Model Management for Multifidelity Monte Carlo Estimation |
| title_full_unstemmed | Optimal Model Management for Multifidelity Monte Carlo Estimation |
| title_short | Optimal Model Management for Multifidelity Monte Carlo Estimation |
| title_sort | optimal model management for multifidelity monte carlo estimation |
| url | http://hdl.handle.net/1721.1/108618 https://orcid.org/0000-0002-5045-046X https://orcid.org/0000-0003-2156-9338 |
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