Probability density adjoint for sensitivity analysis of the Mean of Chaos
Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quant...
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| Format: | Article |
| Language: | en_US |
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2016
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| Online Access: | http://hdl.handle.net/1721.1/103864 https://orcid.org/0000-0001-5552-6235 https://orcid.org/0000-0001-9669-2563 |
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| author | Blonigan, Patrick Joseph Wang, Qiqi |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Blonigan, Patrick Joseph Wang, Qiqi |
| author_sort | Blonigan, Patrick Joseph |
| collection | MIT |
| description | Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems.
This paper presents a new method for sensitivity analysis of ergodic chaotic dynamical systems, the density adjoint method. The method involves solving the governing equations for the system's invariant measure and its adjoint on the system's attractor manifold rather than in phase-space. This new approach is derived for and demonstrated on one-dimensional chaotic maps and the three-dimensional Lorenz system. It is found that the density adjoint computes very finely detailed adjoint distributions and accurate sensitivities, but suffers from large computational costs. |
| first_indexed | 2024-09-23T11:09:04Z |
| format | Article |
| id | mit-1721.1/103864 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:09:04Z |
| publishDate | 2016 |
| record_format | dspace |
| spelling | mit-1721.1/1038642022-10-01T01:38:27Z Probability density adjoint for sensitivity analysis of the Mean of Chaos Blonigan, Patrick Joseph Wang, Qiqi Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Blonigan, Patrick Joseph Wang, Qiqi Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. This paper presents a new method for sensitivity analysis of ergodic chaotic dynamical systems, the density adjoint method. The method involves solving the governing equations for the system's invariant measure and its adjoint on the system's attractor manifold rather than in phase-space. This new approach is derived for and demonstrated on one-dimensional chaotic maps and the three-dimensional Lorenz system. It is found that the density adjoint computes very finely detailed adjoint distributions and accurate sensitivities, but suffers from large computational costs. 2016-08-08T15:17:08Z 2016-08-08T15:17:08Z 2014-04 2014-02 Article http://purl.org/eprint/type/JournalArticle 00219991 http://hdl.handle.net/1721.1/103864 Blonigan, Patrick J., and Qiqi Wang. “Probability Density Adjoint for Sensitivity Analysis of the Mean of Chaos.” Journal of Computational Physics 270 (August 2014): 660–686. https://orcid.org/0000-0001-5552-6235 https://orcid.org/0000-0001-9669-2563 en_US http://dx.doi.org/10.1016/j.jcp.2014.04.027 Journal of Computational Physics Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf arXiv |
| spellingShingle | Blonigan, Patrick Joseph Wang, Qiqi Probability density adjoint for sensitivity analysis of the Mean of Chaos |
| title | Probability density adjoint for sensitivity analysis of the Mean of Chaos |
| title_full | Probability density adjoint for sensitivity analysis of the Mean of Chaos |
| title_fullStr | Probability density adjoint for sensitivity analysis of the Mean of Chaos |
| title_full_unstemmed | Probability density adjoint for sensitivity analysis of the Mean of Chaos |
| title_short | Probability density adjoint for sensitivity analysis of the Mean of Chaos |
| title_sort | probability density adjoint for sensitivity analysis of the mean of chaos |
| url | http://hdl.handle.net/1721.1/103864 https://orcid.org/0000-0001-5552-6235 https://orcid.org/0000-0001-9669-2563 |
| work_keys_str_mv | AT bloniganpatrickjoseph probabilitydensityadjointforsensitivityanalysisofthemeanofchaos AT wangqiqi probabilitydensityadjointforsensitivityanalysisofthemeanofchaos |