Data-driven model discovery with Kolmogorov-Arnold networks
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909323142103040 |
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| author | Moradi, Mohammadamin Panahi, Shirin Bollt, Erik M. Lai, Ying-Cheng |
| author_facet | Moradi, Mohammadamin Panahi, Shirin Bollt, Erik M. Lai, Ying-Cheng |
| contents | Data-driven model discovery of complex dynamical systems is typically done using sparse optimization, but it has a fundamental limitation: sparsity in that the underlying governing equations of the system contain only a small number of elementary mathematical terms. Examples where sparse optimization fails abound, such as the classic Ikeda or optical-cavity map in nonlinear dynamics and a large variety of ecosystems. Exploiting the recently articulated Kolmogorov-Arnold networks, we develop a general model-discovery framework for any dynamical systems including those that do not satisfy the sparsity condition. In particular, we demonstrate non-uniqueness in that a large number of approximate models of the system can be found which generate the same invariant set with the correct statistics such as the Lyapunov exponents and Kullback-Leibler divergence. An analogy to shadowing of numerical trajectories in chaotic systems is pointed out. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_15167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Data-driven model discovery with Kolmogorov-Arnold networks Moradi, Mohammadamin Panahi, Shirin Bollt, Erik M. Lai, Ying-Cheng Machine Learning Dynamical Systems Chaotic Dynamics Data Analysis, Statistics and Probability Data-driven model discovery of complex dynamical systems is typically done using sparse optimization, but it has a fundamental limitation: sparsity in that the underlying governing equations of the system contain only a small number of elementary mathematical terms. Examples where sparse optimization fails abound, such as the classic Ikeda or optical-cavity map in nonlinear dynamics and a large variety of ecosystems. Exploiting the recently articulated Kolmogorov-Arnold networks, we develop a general model-discovery framework for any dynamical systems including those that do not satisfy the sparsity condition. In particular, we demonstrate non-uniqueness in that a large number of approximate models of the system can be found which generate the same invariant set with the correct statistics such as the Lyapunov exponents and Kullback-Leibler divergence. An analogy to shadowing of numerical trajectories in chaotic systems is pointed out. |
| title | Data-driven model discovery with Kolmogorov-Arnold networks |
| topic | Machine Learning Dynamical Systems Chaotic Dynamics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2409.15167 |