A data-driven framework for learning hybrid dynamical systems

The existing data-driven identification methods for hybrid dynamical systems such as sparse optimization are usually limited to parameter identification for coefficients of pre-defined candidate functions or composition of prescribed function forms, which depend on the prior knowledge of the dynamical models. In this work, we propose a novel data-driven framework to discover the hybrid dynamical systems from time series data, without any prior knowledge required of the systems. More specifically, we devise a dual-loop algorithm to peel off the data subject to each subsystem of the hybrid dynamical system. Then, we approximate the subsystems by iteratively training several residual networks and estimate the transition rules by training a fully connected neural network. Several prototypical examples are presented to demonstrate the effectiveness and accuracy of our method for hybrid models with various dimensions and structures. This method appears to be an effective tool for learning the evolutionary governing laws of hybrid dynamical systems from available data sets with wide applications.