Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS)
© 2017 Elsevier Inc. This paper develops the Non-Intrusive Least Squares Shadowing (NILSS) method, which computes the sensitivity for long-time averaged objectives in chaotic dynamical systems. In NILSS, we represent a tangent solution by a linear combination of one inhomogeneous tangent solution an...
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| Format: | Article |
| Language: | English |
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Elsevier BV
2021
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| Online Access: | https://hdl.handle.net/1721.1/133931 |
| _version_ | 1826206525932175360 |
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| author | Ni, Angxiu Wang, Qiqi |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Ni, Angxiu Wang, Qiqi |
| author_sort | Ni, Angxiu |
| collection | MIT |
| description | © 2017 Elsevier Inc. This paper develops the Non-Intrusive Least Squares Shadowing (NILSS) method, which computes the sensitivity for long-time averaged objectives in chaotic dynamical systems. In NILSS, we represent a tangent solution by a linear combination of one inhomogeneous tangent solution and several homogeneous tangent solutions. Next, we solve a least squares problem using this representation; thus, the resulting solution can be used for computing sensitivities. NILSS is easy to implement with existing solvers. In addition, for chaotic systems with many degrees of freedom but few unstable modes, NILSS has a low computational cost. NILSS is applied to two chaotic PDE systems: the Lorenz 63 system and a CFD simulation of flow over a backward-facing step. In both cases, the sensitivities computed by NILSS reflect the trends in the long-time averaged objectives of dynamical systems. |
| first_indexed | 2024-09-23T13:33:59Z |
| format | Article |
| id | mit-1721.1/133931 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:33:59Z |
| publishDate | 2021 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1339312023-11-07T19:14:08Z Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS) Ni, Angxiu Wang, Qiqi Massachusetts Institute of Technology. Department of Aeronautics and Astronautics © 2017 Elsevier Inc. This paper develops the Non-Intrusive Least Squares Shadowing (NILSS) method, which computes the sensitivity for long-time averaged objectives in chaotic dynamical systems. In NILSS, we represent a tangent solution by a linear combination of one inhomogeneous tangent solution and several homogeneous tangent solutions. Next, we solve a least squares problem using this representation; thus, the resulting solution can be used for computing sensitivities. NILSS is easy to implement with existing solvers. In addition, for chaotic systems with many degrees of freedom but few unstable modes, NILSS has a low computational cost. NILSS is applied to two chaotic PDE systems: the Lorenz 63 system and a CFD simulation of flow over a backward-facing step. In both cases, the sensitivities computed by NILSS reflect the trends in the long-time averaged objectives of dynamical systems. 2021-10-27T19:57:16Z 2021-10-27T19:57:16Z 2017 2019-09-26T16:24:29Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/133931 Sensitivity Analysis on Chaotic Dynamical System by Non-Intrusive Least Square Shadowing (Ni-Lss). 46th AIAA Fluid Dynamics Conference, 13-17 June 2016. 2016. AIAA - American Institute of Aeronautics and Astronautics. en 10.1016/J.JCP.2017.06.033 Journal of Computational Physics Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Ni, Angxiu Wang, Qiqi Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS) |
| title | Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS) |
| title_full | Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS) |
| title_fullStr | Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS) |
| title_full_unstemmed | Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS) |
| title_short | Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS) |
| title_sort | sensitivity analysis on chaotic dynamical systems by non intrusive least squares shadowing nilss |
| url | https://hdl.handle.net/1721.1/133931 |
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