Efficient Localization of Discontinuities in Complex Computational Simulations
Surrogate models for computational simulations are input-output approximations that allow computationally intensive analyses, such as uncertainty propagation and inference, to be performed efficiently. When a simulation output does not depend smoothly on its inputs, the error and convergence rate of...
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2015
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| Online Access: | http://hdl.handle.net/1721.1/94534 https://orcid.org/0000-0003-3152-8206 https://orcid.org/0000-0001-8242-3290 |
| _version_ | 1826203591825686528 |
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| author | Gorodetsky, Alex Arkady Marzouk, Youssef M. |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Gorodetsky, Alex Arkady Marzouk, Youssef M. |
| author_sort | Gorodetsky, Alex Arkady |
| collection | MIT |
| description | Surrogate models for computational simulations are input-output approximations that allow computationally intensive analyses, such as uncertainty propagation and inference, to be performed efficiently. When a simulation output does not depend smoothly on its inputs, the error and convergence rate of many approximation methods deteriorate substantially. This paper details a method for efficiently localizing discontinuities in the input parameter domain, so that the model output can be approximated as a piecewise smooth function. The approach comprises an initialization phase, which uses polynomial annihilation to assign function values to different regions and thus seed an automated labeling procedure, followed by a refinement phase that adaptively updates a kernel support vector machine representation of the separating surface via active learning. The overall approach avoids structured grids and exploits any available simplicity in the geometry of the separating surface, thus reducing the number of model evaluations required to localize the discontinuity. The method is illustrated on examples of up to eleven dimensions, including algebraic models and ODE/PDE systems, and demonstrates improved scaling and efficiency over other discontinuity localization approaches. |
| first_indexed | 2024-09-23T12:39:43Z |
| format | Article |
| id | mit-1721.1/94534 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:39:43Z |
| publishDate | 2015 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/945342022-09-28T09:16:03Z Efficient Localization of Discontinuities in Complex Computational Simulations Gorodetsky, Alex Arkady Marzouk, Youssef M. Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Gorodetsky, Alex Arkady Marzouk, Youssef M. Surrogate models for computational simulations are input-output approximations that allow computationally intensive analyses, such as uncertainty propagation and inference, to be performed efficiently. When a simulation output does not depend smoothly on its inputs, the error and convergence rate of many approximation methods deteriorate substantially. This paper details a method for efficiently localizing discontinuities in the input parameter domain, so that the model output can be approximated as a piecewise smooth function. The approach comprises an initialization phase, which uses polynomial annihilation to assign function values to different regions and thus seed an automated labeling procedure, followed by a refinement phase that adaptively updates a kernel support vector machine representation of the separating surface via active learning. The overall approach avoids structured grids and exploits any available simplicity in the geometry of the separating surface, thus reducing the number of model evaluations required to localize the discontinuity. The method is illustrated on examples of up to eleven dimensions, including algebraic models and ODE/PDE systems, and demonstrates improved scaling and efficiency over other discontinuity localization approaches. BP (Firm) 2015-02-13T19:38:00Z 2015-02-13T19:38:00Z 2014-11 2014-07 Article http://purl.org/eprint/type/JournalArticle 1064-8275 1095-7197 http://hdl.handle.net/1721.1/94534 Gorodetsky, Alex, and Youssef Marzouk. “Efficient Localization of Discontinuities in Complex Computational Simulations.” SIAM Journal on Scientific Computing 36, no. 6 (January 2014): A2584–A2610. © 2014, Society for Industrial and Applied Mathematics https://orcid.org/0000-0003-3152-8206 https://orcid.org/0000-0001-8242-3290 en_US http://dx.doi.org/10.1137/140953137 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 | Gorodetsky, Alex Arkady Marzouk, Youssef M. Efficient Localization of Discontinuities in Complex Computational Simulations |
| title | Efficient Localization of Discontinuities in Complex Computational Simulations |
| title_full | Efficient Localization of Discontinuities in Complex Computational Simulations |
| title_fullStr | Efficient Localization of Discontinuities in Complex Computational Simulations |
| title_full_unstemmed | Efficient Localization of Discontinuities in Complex Computational Simulations |
| title_short | Efficient Localization of Discontinuities in Complex Computational Simulations |
| title_sort | efficient localization of discontinuities in complex computational simulations |
| url | http://hdl.handle.net/1721.1/94534 https://orcid.org/0000-0003-3152-8206 https://orcid.org/0000-0001-8242-3290 |
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