AI-Driven Control of Chaos: A Transformer-Based Approach for Dynamical Systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912433105272832 |
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| author | Valle, David Capeáns, Rubén Wagemakers, Alexandre Sanjuán, Miguel A. F. |
| author_facet | Valle, David Capeáns, Rubén Wagemakers, Alexandre Sanjuán, Miguel A. F. |
| contents | Chaotic behavior in dynamical systems poses a significant challenge in trajectory control, traditionally relying on computationally intensive physical models. We present a machine learning-based algorithm to compute the minimum control bounds required to confine particles within a region indefinitely, using only samples of orbits that iterate within the region before diverging. This model-free approach achieves high accuracy, with a mean squared error of $2.88 \times 10^{-4}$ and computation times in the range of seconds. The results highlight its efficiency and potential for real-time control of chaotic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17357 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | AI-Driven Control of Chaos: A Transformer-Based Approach for Dynamical Systems Valle, David Capeáns, Rubén Wagemakers, Alexandre Sanjuán, Miguel A. F. Chaotic Dynamics Chaotic behavior in dynamical systems poses a significant challenge in trajectory control, traditionally relying on computationally intensive physical models. We present a machine learning-based algorithm to compute the minimum control bounds required to confine particles within a region indefinitely, using only samples of orbits that iterate within the region before diverging. This model-free approach achieves high accuracy, with a mean squared error of $2.88 \times 10^{-4}$ and computation times in the range of seconds. The results highlight its efficiency and potential for real-time control of chaotic systems. |
| title | AI-Driven Control of Chaos: A Transformer-Based Approach for Dynamical Systems |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2412.17357 |