论文标题
仅使用标量时间序列构建微分方程
Constructing differential equations using only a scalar time-series about continuous time chaotic dynamics
论文作者
论文摘要
我们提出了一种仅根据可观察到的时间序列数据回归的回归来构建混沌行为微分方程系统的简单方法。估计的系统使我们能够重建不变的集和统计属性，并推断出短时间序列。我们成功的建模依赖于引入一组高斯径向基础功能来捕获局部结构。所提出的方法用于构建一个普通微分方程的系统，该系统的轨道重建了众所周知的Lorenz系统变量的时间序列，作为一个简单但典型的示例。还构建了用于宏观流体变量的系统。
We propose a simple method of constructing a system of differential equations of chaotic behavior based on the regression only from a scalar observable time-series data. The estimated system enables us to reconstruct invariant sets and statistical properties as well as to infer short time-series. Our successful modeling relies on the introduction of a set of Gaussian radial basis functions to capture local structure. The proposed method is used to construct a system of ordinary differential equations whose orbit reconstructs a time-series of a variable of the well-known Lorenz system as a simple but typical example. A system for a macroscopic fluid variable is also constructed.
