Forward and adjoint sensitivity computation of chaotic dynamical systems
This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged “statistical” quantities to infinitesimal perturbations of the system parame...
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| Format: | Article |
| Language: | en_US |
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Elsevier
2015
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| Online Access: | http://hdl.handle.net/1721.1/99452 https://orcid.org/0000-0001-9669-2563 |
| _version_ | 1811095665994891264 |
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| author | Wang, Qiqi |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Wang, Qiqi |
| author_sort | Wang, Qiqi |
| collection | MIT |
| description | This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged “statistical” quantities to infinitesimal perturbations of the system parameters. The algorithms are demonstrated on the Lorenz attractor. We show that sensitivity derivatives of statistical quantities can be accurately estimated using a single, short trajectory (over a time interval of 20) on the Lorenz attractor. |
| first_indexed | 2024-09-23T16:23:30Z |
| format | Article |
| id | mit-1721.1/99452 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:23:30Z |
| publishDate | 2015 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/994522022-10-02T07:51:43Z Forward and adjoint sensitivity computation of chaotic dynamical systems Wang, Qiqi Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Wang, Qiqi This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged “statistical” quantities to infinitesimal perturbations of the system parameters. The algorithms are demonstrated on the Lorenz attractor. We show that sensitivity derivatives of statistical quantities can be accurately estimated using a single, short trajectory (over a time interval of 20) on the Lorenz attractor. 2015-10-26T16:09:33Z 2015-10-26T16:09:33Z 2012-10 2012-02 Article http://purl.org/eprint/type/JournalArticle 00219991 1090-2716 http://hdl.handle.net/1721.1/99452 Wang, Qiqi. “Forward and Adjoint Sensitivity Computation of Chaotic Dynamical Systems.” Journal of Computational Physics 235 (February 2013): 1–13. https://orcid.org/0000-0001-9669-2563 en_US http://dx.doi.org/10.1016/j.jcp.2012.09.007 Journal of Computational Physics Creative Commons Attribution-Noncommercial-NoDerivatives http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier Arxiv |
| spellingShingle | Wang, Qiqi Forward and adjoint sensitivity computation of chaotic dynamical systems |
| title | Forward and adjoint sensitivity computation of chaotic dynamical systems |
| title_full | Forward and adjoint sensitivity computation of chaotic dynamical systems |
| title_fullStr | Forward and adjoint sensitivity computation of chaotic dynamical systems |
| title_full_unstemmed | Forward and adjoint sensitivity computation of chaotic dynamical systems |
| title_short | Forward and adjoint sensitivity computation of chaotic dynamical systems |
| title_sort | forward and adjoint sensitivity computation of chaotic dynamical systems |
| url | http://hdl.handle.net/1721.1/99452 https://orcid.org/0000-0001-9669-2563 |
| work_keys_str_mv | AT wangqiqi forwardandadjointsensitivitycomputationofchaoticdynamicalsystems |