Data-driven ODE modeling of the high-frequency complex dynamics via a low-frequency dynamics model

• URL: http://arxiv.org/abs/2409.00668v2
• Date: Sun, 10 Nov 2024 04:58:40 GMT
• Title: Data-driven ODE modeling of the high-frequency complex dynamics via a low-frequency dynamics model
• Authors: Natsuki Tsutsumi, Kengo Nakai, Yoshitaka Saiki,
• Abstract summary: We propose a novel method of modeling such dynamics, including the high-frequency intermittent behavior of a fluid flow. 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. 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.
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• Abstract: 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.

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