SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics

Proceedings. Mathematical, Physical, and Engineering Sciences
Kadierdan KahemanSteven L Brunton

Abstract

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.

References

Jun 8, 2007·Proceedings of the National Academy of Sciences of the United States of America·Josh Bongard, Hod Lipson
Dec 27, 2008·IEEE Transactions on Pattern Analysis and Machine Intelligence·John WrightYi Ma
Apr 4, 2009·Science·Michael Schmidt, Hod Lipson
Aug 13, 2011·Physical Biology·Michael D SchmidtHod Lipson
Sep 6, 2011·Biochemistry·Leonor MichaelisRoger S Goody
Feb 7, 2012·Proceedings of the National Academy of Sciences of the United States of America·Dimitrios Giannakis, Andrew J Majda
Jan 3, 2013·Chaos·Marko BudisićIgor Mezić
Aug 22, 2015·Nature Communications·Bryan C Daniels, Ilya Nemenman
Apr 2, 2016·Proceedings of the National Academy of Sciences of the United States of America·Steven L BruntonJ Nathan Kutz
Jan 7, 2017·Optics Express·Mariia SorokinaSergei Turitsyn
May 17, 2017·Science Advances·Samuel H RudyJ Nathan Kutz
Aug 24, 2017·Proceedings of the National Academy of Sciences of the United States of America·Or YairIoannis G Kevrekidis
Sep 8, 2017·Proceedings. Mathematical, Physical, and Engineering Sciences·N M ManganJ L Proctor
Sep 28, 2017·Physical Review. E·Hayden Schaeffer, Scott G McCalla
Jan 4, 2018·Nature Communications·Andreas MardtFrank Noé
Jun 12, 2018·Proceedings. Mathematical, Physical, and Engineering Sciences·Pantelis R VlachasPetros Koumoutsakos
Jul 2, 2018·The Journal of Chemical Physics·Lorenzo BoninsegnaCecilia Clementi
Jul 2, 2018·The Journal of Chemical Physics·Christoph Wehmeyer, Frank Noé
Jul 2, 2018·Chaos·Markus QuadeSteven L Brunton
Oct 20, 2018·Proceedings. Mathematical, Physical, and Engineering Sciences·Sheng Zhang, Guang Lin
Jan 17, 2019·The Journal of Chemical Physics·Moritz HoffmannFrank Noé
Mar 7, 2019·Proceedings. Mathematical, Physical, and Engineering Sciences·E KaiserS L Brunton
Apr 23, 2019·Proceedings. Mathematical, Physical, and Engineering Sciences·N M ManganJ L Proctor
Oct 23, 2019·Proceedings of the National Academy of Sciences of the United States of America·Kathleen ChampionSteven L Brunton
Feb 20, 2020·Physical Review. E·Patrick A K ReinboldRoman O Grigoriev
Mar 19, 2021·Frontiers in Artificial Intelligence·Brian M de SilvaJ Nathan Kutz

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Citations

Feb 16, 2021·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Ryan PyleAnkit B Patel

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Software Mentioned

implicit
PDE
SR3
LASSO
FIND
PI
CVX
SINDy

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