Attractor reconstruction by machine learning

A machine-learning approach called "reservoir computing" has been used successfully for short-term prediction and attractor reconstruction of chaotic dynamical systems from time series data. We present a theoretical framework that describes conditions under which reservoir computing can create an empirical model capable of skillful short-term forecasts and accurate long-term ergodic behavior. We illustrate this theory through numerical experiments. We also argue that the theory applies to certain other machine learning methods for time series prediction.