Data-driven modeling from biased small training data using periodic orbits
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909247217860608 |
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| author | Nakai, Kengo Saiki, Yoshitaka |
| author_facet | Nakai, Kengo Saiki, Yoshitaka |
| contents | In this study, we investigate the effect of reservoir computing training data on the reconstruction of chaotic dynamics. Our findings indicate that a training time series comprising a few periodic orbits of low periods can successfully reconstruct the Lorenz attractor. We also demonstrate that biased training data does not negatively impact reconstruction success. Our method's ability to reconstruct a physical measure is much better than the so-called cycle expansion approach, which relies on weighted averaging. Additionally, we demonstrate that fixed point attractors and chaotic transients can be accurately reconstructed by a model trained from a few periodic orbits, even when using different parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06229 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Data-driven modeling from biased small training data using periodic orbits Nakai, Kengo Saiki, Yoshitaka Data Analysis, Statistics and Probability Chaotic Dynamics 37M10, 37Nxx, 68T05 In this study, we investigate the effect of reservoir computing training data on the reconstruction of chaotic dynamics. Our findings indicate that a training time series comprising a few periodic orbits of low periods can successfully reconstruct the Lorenz attractor. We also demonstrate that biased training data does not negatively impact reconstruction success. Our method's ability to reconstruct a physical measure is much better than the so-called cycle expansion approach, which relies on weighted averaging. Additionally, we demonstrate that fixed point attractors and chaotic transients can be accurately reconstructed by a model trained from a few periodic orbits, even when using different parameters. |
| title | Data-driven modeling from biased small training data using periodic orbits |
| topic | Data Analysis, Statistics and Probability Chaotic Dynamics 37M10, 37Nxx, 68T05 |
| url | https://arxiv.org/abs/2407.06229 |