用低频变量建模高频复杂动态，实现混沌轨迹与统计特性重建
Data-driven ODE modeling of the high-frequency complex dynamics via a low-frequency dynamics model
- 构建双变量耦合的自治模型，以低频基变量驱动高频目标变量
- 成功复现长时程的混沌集与密度分布，精度接近真实数据
- 适合研究流体等复杂非线性系统动力学的科研人员
在先前工作中，我们提出了基于径向函数回归（RfR）的方法，仅通过可观测的确定性时间序列构建混沌系统的微分方程。然而，当目标变量行为高度复杂时，RfR方法表现不佳。本文提出新方法：利用一个行为相对简单、间歇性较弱的辅助变量（基变量），构建包含两部分的自治联合模型——第一部分为基变量的自治系统，第二部分描述目标变量受基变量影响所呈现的复杂动态。该联合模型不仅成功推断出短时轨迹，还能重建长期轨迹中的混沌集合及统计特性，如实际动力学的密度分布，表现出优异的泛化能力。
原文摘要 · Abstract (English)
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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