Learning dynamical systems from data: Gradient-based dictionary optimization

• URL: http://arxiv.org/abs/2411.04775v1
• Date: Thu, 07 Nov 2024 15:15:27 GMT
• Title: Learning dynamical systems from data: Gradient-based dictionary optimization
• Authors: Mohammad Tabish, Neil K. Chada, Stefan Klus,
• Abstract summary: We present a novel gradient descent-based optimization framework for learning suitable basis functions from data. We show how it can be used in combination with EDMD, SINDy, and PDE-FIND.
• Score: 0.8643517734716606
• License:
• 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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