Data-driven ODE modeling of the high-frequency complex dynamics of a fluid flow
<|reference_start|>Data-driven ODE modeling of the high-frequency complex dynamics of a fluid flow: 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.<|reference_end|>
@article{tsutsumi2024data-driven,
    title={Data-driven ODE modeling of the high-frequency complex dynamics via a
  low-frequency dynamics model},
    author={Natsuki Tsutsumi, Kengo Nakai, Yoshitaka Saiki},
    journal={arXiv preprint arXiv:2409.00668},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.00668},
    primaryClass={nlin.CD cs.LG physics.data-an stat.ML}
}