Using Echo-State Networks to Reproduce Rare Events in Chaotic Systems

Machine learning has emerged as an alternative approach for solving partial differential equations, reproducing trajectories of dynamical systems, emulating statistical properties of chaotic systems, etc. Neural networks and deep learning play a particularly important role in developing new techniques for understanding and solving various dynamical systems. Reservoir computing [15, 30] is a particular class of machine learning models; it utilizes a large recurrent network (reservoir), and only a linear output layer is trained to match the trajectory. Echo-State Networks refer to reservoirs that have the Echo-State Property (see e.g.