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Learning dynamical systems from data: Gradient-based dictionary optimization
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DOI：10.1016/j.physd.2025.134822.png)
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Abstract
En 中文
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.
Keywords:
Koopman operator
System identification
Dictionary learning
Gradient descent
Journal
P
IF:
2.9
Papers:
389
Citations:
1.5W
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