Learning dynamical systems from data: Gradient-based dictionary optimization
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909682048696320 |
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| author | Tabish, Mohammad Chada, Neil K. Klus, Stefan |
| author_facet | Tabish, Mohammad Chada, Neil K. Klus, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04775 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning dynamical systems from data: Gradient-based dictionary optimization Tabish, Mohammad Chada, Neil K. Klus, Stefan Dynamical Systems Machine Learning 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. |
| title | Learning dynamical systems from data: Gradient-based dictionary optimization |
| topic | Dynamical Systems Machine Learning |
| url | https://arxiv.org/abs/2411.04775 |