Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling

Kookjin Lee, Nathaniel Trask, Panos Stinis
Proceedings of Mathematical and Scientific Machine Learning, PMLR 190:65-80, 2022.

Abstract

Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability guarantees. We present here a unification of the Sparse Identification of Nonlinear Dynamics (SINDy) formalism with neural ordinary differential equations. The resulting framework allows learning of both “black-box” dynamics and learning of structure preserving bracket formalisms for both reversible and irreversible dynamics. We present a suite of benchmarks demonstrating effectiveness and structure preservation, including for chaotic systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v190-lee22a, title = {Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling}, author = {Lee, Kookjin and Trask, Nathaniel and Stinis, Panos}, booktitle = {Proceedings of Mathematical and Scientific Machine Learning}, pages = {65--80}, year = {2022}, editor = {Dong, Bin and Li, Qianxiao and Wang, Lei and Xu, Zhi-Qin John}, volume = {190}, series = {Proceedings of Machine Learning Research}, month = {15--17 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v190/lee22a/lee22a.pdf}, url = {https://proceedings.mlr.press/v190/lee22a.html}, abstract = {Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability guarantees. We present here a unification of the Sparse Identification of Nonlinear Dynamics (SINDy) formalism with neural ordinary differential equations. The resulting framework allows learning of both “black-box” dynamics and learning of structure preserving bracket formalisms for both reversible and irreversible dynamics. We present a suite of benchmarks demonstrating effectiveness and structure preservation, including for chaotic systems.} }
Endnote
%0 Conference Paper %T Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling %A Kookjin Lee %A Nathaniel Trask %A Panos Stinis %B Proceedings of Mathematical and Scientific Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Bin Dong %E Qianxiao Li %E Lei Wang %E Zhi-Qin John Xu %F pmlr-v190-lee22a %I PMLR %P 65--80 %U https://proceedings.mlr.press/v190/lee22a.html %V 190 %X Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability guarantees. We present here a unification of the Sparse Identification of Nonlinear Dynamics (SINDy) formalism with neural ordinary differential equations. The resulting framework allows learning of both “black-box” dynamics and learning of structure preserving bracket formalisms for both reversible and irreversible dynamics. We present a suite of benchmarks demonstrating effectiveness and structure preservation, including for chaotic systems.
APA
Lee, K., Trask, N. & Stinis, P.. (2022). Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling. Proceedings of Mathematical and Scientific Machine Learning, in Proceedings of Machine Learning Research 190:65-80 Available from https://proceedings.mlr.press/v190/lee22a.html.

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