Predicting Critical Transitions in Multiscale Dynamical Systems Using Reservoir Computing

We study the problem of rare event prediction for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution. By taking advantage of recent advances in machine learning, we present a data-driven method to predict the future evolution of the state. We show that our method is capable of predicting a rare event at least several time steps in advance. We demonstrate our method using numerical experiments on three examples of systems, ranging from low dimensional to high dimensional. We discuss the mathematical and broader implications of our results.