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arXiv · 2109.05364

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

Kookjin Lee·Nathaniel Trask·Panos Stinis
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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.

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Kookjin Lee, Nathaniel Trask, Panos Stinis. 2021-09-11. Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling. https://arxiv.org/abs/2109.05364

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