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

TL;DR

This paper introduces a data-driven modeling approach for complex high-frequency dynamics by combining a simple base variable model with a targeted variable influenced by it, effectively capturing chaotic and statistical behaviors.

Contribution

It proposes a novel joint modeling method that integrates a simple base variable with a complex targeted variable, improving the modeling of chaotic high-frequency dynamics.

Findings

Successfully reconstructed chaotic sets and statistical properties.

Demonstrated effectiveness on fluid flow high-frequency intermittent behavior.

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.