Data-driven ODE modeling of the high-frequency complex dynamics via a low-frequency dynamics model
This work addresses the challenge of accurately modeling intermittent fluid flow dynamics for researchers in chaos theory and fluid dynamics, representing an incremental improvement over their previous method.
The authors tackled the problem of modeling high-frequency complex dynamics from time series data by proposing a joint model that uses a simpler base variable to influence the target variable, successfully inferring short trajectories and reconstructing chaotic sets and statistical properties like density distributions.
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.