Data-driven dynamics reconstruction using RBF network

Abstract

Constructing the governing dynamical equations of complex systems from observational data is of great interest for both theory and applications. However, it is a difficult inverse problem to explicitly construct the dynamical equations for many real complex systems based on observational data. Here, we propose to implicitly represent the dynamical equations of a complex system using a radial basis function (RBF) network trained on the observed data of the system. We show that the RBF network trained on trajectory data of the classical Lorenz and Chen system can faithfully reproduce the orbits, fixed points, and local bifurcations of the original dynamical equations. We also apply this method to electrocardiogram (ECG) data and show that the fixed points of the RBF network trained using ECG can discriminate healthy people from patients with heart disease, indicating that the method can be applied to real complex systems.

Keywords

• RBF network
• dynamics reconstruction
• fixed point
• governing equations