Multifidelity Dimension Reduction via Active Subspaces
© 2020 Remi Lam, Olivier Zahm, Youssef Marzouk, Karen Willcox. We propose a multifidelity dimension reduction method to identify a low-dimensional structure present in many engineering models. The structure of interest arises when functions vary primarily on a low-dimensional subspace of the high-di...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Society for Industrial & Applied Mathematics (SIAM)
2021
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| Online Access: | https://hdl.handle.net/1721.1/135339 |
| _version_ | 1826201885613228032 |
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| author | Lam, Remi R Zahm, Olivier 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 Lam, Remi R Zahm, Olivier Marzouk, Youssef M Willcox, Karen E |
| author_sort | Lam, Remi R |
| collection | MIT |
| description | © 2020 Remi Lam, Olivier Zahm, Youssef Marzouk, Karen Willcox. We propose a multifidelity dimension reduction method to identify a low-dimensional structure present in many engineering models. The structure of interest arises when functions vary primarily on a low-dimensional subspace of the high-dimensional input space, while varying little along the complementary directions. Our approach builds on the gradient-based methodology of active subspaces, and exploits models of different fidelities to reduce the cost of performing dimension reduction through the computation of the active subspace matrix. We provide a nonasymptotic analysis of the number of gradient evaluations sufficient to achieve a prescribed error in the active subspace matrix, both in expectation and with high probability. We show that the sample complexity depends on a notion of intrinsic dimension of the problem, which can be much smaller than the dimension of the input space. We illustrate the benefits of such a multifidelity dimension reduction approach using numerical experiments with input spaces of up to two thousand dimensions. |
| first_indexed | 2024-09-23T11:58:26Z |
| format | Article |
| id | mit-1721.1/135339 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:58:26Z |
| publishDate | 2021 |
| publisher | Society for Industrial & Applied Mathematics (SIAM) |
| record_format | dspace |
| spelling | mit-1721.1/1353392023-11-08T21:47:57Z Multifidelity Dimension Reduction via Active Subspaces Lam, Remi R Zahm, Olivier Marzouk, Youssef M Willcox, Karen E Massachusetts Institute of Technology. Department of Aeronautics and Astronautics © 2020 Remi Lam, Olivier Zahm, Youssef Marzouk, Karen Willcox. We propose a multifidelity dimension reduction method to identify a low-dimensional structure present in many engineering models. The structure of interest arises when functions vary primarily on a low-dimensional subspace of the high-dimensional input space, while varying little along the complementary directions. Our approach builds on the gradient-based methodology of active subspaces, and exploits models of different fidelities to reduce the cost of performing dimension reduction through the computation of the active subspace matrix. We provide a nonasymptotic analysis of the number of gradient evaluations sufficient to achieve a prescribed error in the active subspace matrix, both in expectation and with high probability. We show that the sample complexity depends on a notion of intrinsic dimension of the problem, which can be much smaller than the dimension of the input space. We illustrate the benefits of such a multifidelity dimension reduction approach using numerical experiments with input spaces of up to two thousand dimensions. 2021-10-27T20:23:02Z 2021-10-27T20:23:02Z 2020 2021-05-03T15:26:20Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/135339 en 10.1137/18M1214123 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 & Applied Mathematics (SIAM) SIAM |
| spellingShingle | Lam, Remi R Zahm, Olivier Marzouk, Youssef M Willcox, Karen E Multifidelity Dimension Reduction via Active Subspaces |
| title | Multifidelity Dimension Reduction via Active Subspaces |
| title_full | Multifidelity Dimension Reduction via Active Subspaces |
| title_fullStr | Multifidelity Dimension Reduction via Active Subspaces |
| title_full_unstemmed | Multifidelity Dimension Reduction via Active Subspaces |
| title_short | Multifidelity Dimension Reduction via Active Subspaces |
| title_sort | multifidelity dimension reduction via active subspaces |
| url | https://hdl.handle.net/1721.1/135339 |
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