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

• URL: http://arxiv.org/abs/2109.05364v1
• Date: Sat, 11 Sep 2021 20:32:10 GMT
• Title: Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling
• Authors: Kookjin Lee, Nathaniel Trask, Panos Stinis
• Abstract summary: We present a unification of the Sparse Identification of 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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