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SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics
Accurately modelling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data. Although extensions have been developed to identify implic...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society Publishing
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7655768/ https://www.ncbi.nlm.nih.gov/pubmed/33214760 http://dx.doi.org/10.1098/rspa.2020.0279 |
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author | Kaheman, Kadierdan Kutz, J. Nathan Brunton, Steven L. |
author_facet | Kaheman, Kadierdan Kutz, J. Nathan Brunton, Steven L. |
author_sort | Kaheman, Kadierdan |
collection | PubMed |
description | Accurately modelling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data. Although extensions have been developed to identify implicit dynamics, or dynamics described by rational functions, these extensions are extremely sensitive to noise. In this work, we develop SINDy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities. The SINDy-PI framework includes multiple optimization algorithms and a principled approach to model selection. We demonstrate the ability of this algorithm to learn implicit ordinary and partial differential equations and conservation laws from limited and noisy data. In particular, we show that the proposed approach is several orders of magnitude more noise robust than previous approaches, and may be used to identify a class of ODE and PDE dynamics that were previously unattainable with SINDy, including for the double pendulum dynamics and simplified model for the Belousov–Zhabotinsky (BZ) reaction. |
format | Online Article Text |
id | pubmed-7655768 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | The Royal Society Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-76557682020-11-18 SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics Kaheman, Kadierdan Kutz, J. Nathan Brunton, Steven L. Proc Math Phys Eng Sci Research Article Accurately modelling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data. Although extensions have been developed to identify implicit dynamics, or dynamics described by rational functions, these extensions are extremely sensitive to noise. In this work, we develop SINDy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities. The SINDy-PI framework includes multiple optimization algorithms and a principled approach to model selection. We demonstrate the ability of this algorithm to learn implicit ordinary and partial differential equations and conservation laws from limited and noisy data. In particular, we show that the proposed approach is several orders of magnitude more noise robust than previous approaches, and may be used to identify a class of ODE and PDE dynamics that were previously unattainable with SINDy, including for the double pendulum dynamics and simplified model for the Belousov–Zhabotinsky (BZ) reaction. The Royal Society Publishing 2020-10 2020-10-07 /pmc/articles/PMC7655768/ /pubmed/33214760 http://dx.doi.org/10.1098/rspa.2020.0279 Text en © 2020 The Authors. http://creativecommons.org/licenses/by/4.0/ http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Research Article Kaheman, Kadierdan Kutz, J. Nathan Brunton, Steven L. SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics |
title | SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics |
title_full | SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics |
title_fullStr | SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics |
title_full_unstemmed | SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics |
title_short | SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics |
title_sort | sindy-pi: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7655768/ https://www.ncbi.nlm.nih.gov/pubmed/33214760 http://dx.doi.org/10.1098/rspa.2020.0279 |
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