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arXiv · 2411.04775

Learning dynamical systems from data: Gradient-based dictionary optimization

Mohammad Tabish·Neil K. Chada·Stefan Klus
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Abstract

The Koopman operator plays a crucial role in analyzing the global behavior of dynamical systems. Existing data-driven methods for approximating the Koopman operator or discovering the governing equations of the underlying system typically require a fixed set of basis functions, also called dictionary. The optimal choice of basis functions is highly problem-dependent and often requires domain knowledge. We present a novel gradient descent-based optimization framework for learning suitable and interpretable basis functions from data and show how it can be used in combination with EDMD, SINDy, and PDE-FIND. We illustrate the efficacy of the proposed approach with the aid of various benchmark problems such as the Ornstein-Uhlenbeck process, Chua's circuit, a nonlinear heat equation, as well as protein-folding data.

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BibTeXRIS

Mohammad Tabish, Neil K. Chada, Stefan Klus. 2024-11-07. Learning dynamical systems from data: Gradient-based dictionary optimization. https://doi.org/10.1016/j.physd.2025.134822

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