Data-driven ODE modeling of the high-frequency complex dynamics via a low-frequency dynamics model
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929585218650112 |
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| author | Tsutsumi, Natsuki Nakai, Kengo Saiki, Yoshitaka |
| author_facet | Tsutsumi, Natsuki Nakai, Kengo Saiki, Yoshitaka |
| contents | In our previous paper [N. Tsutsumi, K. Nakai and Y. Saiki, Chaos 32, 091101 (2022)], we proposed a method for constructing a system of differential equations of chaotic behavior from only observable deterministic time series, which we call the radial function-based regression (RfR) method. However, when the targeted variable's behavior is rather complex, the direct application of the RfR method does not function well. In this study, we propose a novel method of modeling such dynamics, including the high-frequency intermittent behavior of a fluid flow, by considering another variable (base variable) showing relatively simple, less intermittent behavior. We construct an autonomous joint model composed of two parts: the first is an autonomous system of a base variable, and the other concerns the targeted variable being affected by a term involving the base variable to demonstrate complex dynamics. The constructed joint model succeeded in not only inferring a short trajectory but also reconstructing chaotic sets and statistical properties obtained from a long trajectory such as the density distributions of the actual dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Data-driven ODE modeling of the high-frequency complex dynamics via a low-frequency dynamics model Tsutsumi, Natsuki Nakai, Kengo Saiki, Yoshitaka Chaotic Dynamics Machine Learning Data Analysis, Statistics and Probability 37Mxx, 37Nxx, 65Txx, 76-10 In our previous paper [N. Tsutsumi, K. Nakai and Y. Saiki, Chaos 32, 091101 (2022)], we proposed a method for constructing a system of differential equations of chaotic behavior from only observable deterministic time series, which we call the radial function-based regression (RfR) method. However, when the targeted variable's behavior is rather complex, the direct application of the RfR method does not function well. In this study, we propose a novel method of modeling such dynamics, including the high-frequency intermittent behavior of a fluid flow, by considering another variable (base variable) showing relatively simple, less intermittent behavior. We construct an autonomous joint model composed of two parts: the first is an autonomous system of a base variable, and the other concerns the targeted variable being affected by a term involving the base variable to demonstrate complex dynamics. The constructed joint model succeeded in not only inferring a short trajectory but also reconstructing chaotic sets and statistical properties obtained from a long trajectory such as the density distributions of the actual dynamics. |
| title | Data-driven ODE modeling of the high-frequency complex dynamics via a low-frequency dynamics model |
| topic | Chaotic Dynamics Machine Learning Data Analysis, Statistics and Probability 37Mxx, 37Nxx, 65Txx, 76-10 |
| url | https://arxiv.org/abs/2409.00668 |