Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces
Many multivariate functions in engineering models vary primarily along a few directions in the space of input parameters. When these directions correspond to coordinate directions, one may apply global sensitivity measures to determine the most influential parameters. However, these methods perform...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2014
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| Online Access: | http://hdl.handle.net/1721.1/92546 https://orcid.org/0000-0001-9669-2563 |
| _version_ | 1826188242030952448 |
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| author | Constantine, Paul G. Wang, Qiqi Dow, Eric A. |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Constantine, Paul G. Wang, Qiqi Dow, Eric A. |
| author_sort | Constantine, Paul G. |
| collection | MIT |
| description | Many multivariate functions in engineering models vary primarily along a few directions in the space of input parameters. When these directions correspond to coordinate directions, one may apply global sensitivity measures to determine the most influential parameters. However, these methods perform poorly when the directions of variability are not aligned with the natural coordinates of the input space. We present a method to first detect the directions of the strongest variability using evaluations of the gradient and subsequently exploit these directions to construct a response surface on a low-dimensional subspace---i.e., the active subspace---of the inputs. We develop a theoretical framework with error bounds, and we link the theoretical quantities to the parameters of a kriging response surface on the active subspace. We apply the method to an elliptic PDE model with coefficients parameterized by 100 Gaussian random variables and compare it with a local sensitivity analysis method for dimension reduction. |
| first_indexed | 2024-09-23T07:56:42Z |
| format | Article |
| id | mit-1721.1/92546 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T07:56:42Z |
| publishDate | 2014 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/925462022-09-30T01:10:54Z Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces Constantine, Paul G. Wang, Qiqi Dow, Eric A. Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Dow, Eric A. Wang, Qiqi Many multivariate functions in engineering models vary primarily along a few directions in the space of input parameters. When these directions correspond to coordinate directions, one may apply global sensitivity measures to determine the most influential parameters. However, these methods perform poorly when the directions of variability are not aligned with the natural coordinates of the input space. We present a method to first detect the directions of the strongest variability using evaluations of the gradient and subsequently exploit these directions to construct a response surface on a low-dimensional subspace---i.e., the active subspace---of the inputs. We develop a theoretical framework with error bounds, and we link the theoretical quantities to the parameters of a kriging response surface on the active subspace. We apply the method to an elliptic PDE model with coefficients parameterized by 100 Gaussian random variables and compare it with a local sensitivity analysis method for dimension reduction. 2014-12-29T22:22:45Z 2014-12-29T22:22:45Z 2014-07 2014-04 Article http://purl.org/eprint/type/JournalArticle 1064-8275 1095-7197 http://hdl.handle.net/1721.1/92546 Constantine, Paul G., Eric Dow, and Qiqi Wang. “Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces.” SIAM Journal on Scientific Computing 36, no. 4 (January 2014): A1500–A1524. © 2014 Society for Industrial and Applied Mathematics https://orcid.org/0000-0001-9669-2563 en_US http://dx.doi.org/10.1137/130916138 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 | Constantine, Paul G. Wang, Qiqi Dow, Eric A. Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces |
| title | Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces |
| title_full | Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces |
| title_fullStr | Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces |
| title_full_unstemmed | Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces |
| title_short | Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces |
| title_sort | active subspace methods in theory and practice applications to kriging surfaces |
| url | http://hdl.handle.net/1721.1/92546 https://orcid.org/0000-0001-9669-2563 |
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