Ergodic sensitivity analysis of one-dimensional chaotic maps
© 2020 The Authors. Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view. In this work, we present a numerical investigation of a novel approach, know...
| Main Authors: | , , |
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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/1721.1/134415 |
| _version_ | 1826192412161081344 |
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| author | Śliwiak, Adam A Chandramoorthy, Nisha Wang, Qiqi |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Śliwiak, Adam A Chandramoorthy, Nisha Wang, Qiqi |
| author_sort | Śliwiak, Adam A |
| collection | MIT |
| description | © 2020 The Authors. Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view. In this work, we present a numerical investigation of a novel approach, known as the space-split sensitivity or S3 algorithm. The S3 algorithm is an ergodic-averaging method to differentiate statistics in ergodic, chaotic systems, rigorously based on the theory of hyperbolic dynamics. We illustrate S3 on one-dimensional chaotic maps, revealing its computational advantage over naïve finite difference computations of the same statistical response. In addition, we provide an intuitive explanation of the key components of the S3 algorithm, including the density gradient function. |
| first_indexed | 2024-09-23T09:11:32Z |
| format | Article |
| id | mit-1721.1/134415 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:11:32Z |
| publishDate | 2021 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1344152023-02-22T21:04:21Z Ergodic sensitivity analysis of one-dimensional chaotic maps Śliwiak, Adam A Chandramoorthy, Nisha Wang, Qiqi Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Massachusetts Institute of Technology. Center for Computational Science and Engineering Massachusetts Institute of Technology. Department of Mechanical Engineering © 2020 The Authors. Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view. In this work, we present a numerical investigation of a novel approach, known as the space-split sensitivity or S3 algorithm. The S3 algorithm is an ergodic-averaging method to differentiate statistics in ergodic, chaotic systems, rigorously based on the theory of hyperbolic dynamics. We illustrate S3 on one-dimensional chaotic maps, revealing its computational advantage over naïve finite difference computations of the same statistical response. In addition, we provide an intuitive explanation of the key components of the S3 algorithm, including the density gradient function. 2021-10-27T20:04:54Z 2021-10-27T20:04:54Z 2020 2021-05-04T18:07:07Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/134415 en 10.1016/j.taml.2020.01.058 Theoretical and Applied Mechanics Letters Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV Elsevier |
| spellingShingle | Śliwiak, Adam A Chandramoorthy, Nisha Wang, Qiqi Ergodic sensitivity analysis of one-dimensional chaotic maps |
| title | Ergodic sensitivity analysis of one-dimensional chaotic maps |
| title_full | Ergodic sensitivity analysis of one-dimensional chaotic maps |
| title_fullStr | Ergodic sensitivity analysis of one-dimensional chaotic maps |
| title_full_unstemmed | Ergodic sensitivity analysis of one-dimensional chaotic maps |
| title_short | Ergodic sensitivity analysis of one-dimensional chaotic maps |
| title_sort | ergodic sensitivity analysis of one dimensional chaotic maps |
| url | https://hdl.handle.net/1721.1/134415 |
| work_keys_str_mv | AT sliwiakadama ergodicsensitivityanalysisofonedimensionalchaoticmaps AT chandramoorthynisha ergodicsensitivityanalysisofonedimensionalchaoticmaps AT wangqiqi ergodicsensitivityanalysisofonedimensionalchaoticmaps |