Cargando…

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...

Descripción completa

Detalles Bibliográficos
Autores principales: Kaheman, Kadierdan, Kutz, J. Nathan, Brunton, Steven L.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society Publishing 2020
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
_version_ 1783608237158825984
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
work_keys_str_mv AT kahemankadierdan sindypiarobustalgorithmforparallelimplicitsparseidentificationofnonlineardynamics
AT kutzjnathan sindypiarobustalgorithmforparallelimplicitsparseidentificationofnonlineardynamics
AT bruntonstevenl sindypiarobustalgorithmforparallelimplicitsparseidentificationofnonlineardynamics