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Data-driven sparse identification of nonlinear dynamical systems using linear multistep methods

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Abstract

Linear multistep methods (LMMs) are popular time discretization schemes for solving the forward problem on differential equations. Recently, LMMs together with deep neural networks have been shown to successfully discover dynamical systems from data. In this work, we propose a class of LMM-based sparse regression approaches for the discovery of nonlinear dynamical systems. The work builds on the sparse identification of nonlinear dynamics (SINDy) framework presented in Brunton et al. (Proc Natl Acad Sci USA 113: 3932–3937, 2016), allowing closed form expression for the governing equations and therefore the resulting data-driven model can give insights into the underlying physics. Compared to the standard SINDy algorithm, the proposed LMM-based SINDy approach allows for more accurate and robust model recovery from data with a wide range of noise levels, without requiring pointwise derivative approximations and conventional noise filtering. Numerical results are presented to demonstrate the effectiveness of the proposed method.

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Acknowledgements

The authors are very grateful to the referees for their constructive comments and valuable suggestions, which greatly improved the original manuscript of the paper. This work was supported by the Scientific and Technological Research Program of Chongqing Municipal Education Commission (No. KJQN202000543), the Natural Science Foundation Project of CQ CSTC (No. cstc2021jcyj-msxmX0034), and the Program of Chongqing Innovation Research Group Project in University (No. CXQT19018).

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  1. College of Mathematics Science, Chongqing Normal University, Chongqing, China

    Hao Chen

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Chen, H. Data-driven sparse identification of nonlinear dynamical systems using linear multistep methods. Calcolo 60, 11 (2023). https://doi.org/10.1007/s10092-023-00507-7

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