Identifying differential equation governing dynamical system is an important problem with wide applications. Copula Entropy (CE) is a mathematical concept for measuring statistical independence in information theory. In this paper we propose a method for identifying differential equation of dynamical systems with CE. The problem is considered as a variable selection problem and solved with the previously proposed CE-based method for variable selection. The proposed method composed of two components: the difference operator and the CE estimator. Since both components can be done non-parametrically, the proposed method is therefore model-free and hyperparameter-free. The simulation experiment with the 3D Lorenz system verified the effectiveness of the proposed method.

翻译：辨识控制动力系统的微分方程是一个重要且具有广泛应用的问题。Copula熵（CE）是信息论中用于度量统计独立性的数学概念。本文提出了一种基于CE辨识动力系统微分方程的方法。该问题被转化为变量选择问题，并通过先前提出的基于CE的变量选择方法加以解决。所提方法由两个部分组成：差分算子和CE估计器。由于这两个部分均可通过非参数方式实现，因此该方法无需模型假设和超参数。基于三维洛伦兹系统的仿真实验验证了所提方法的有效性。