Classification strategies in machine learning techniques predicting regime changes and durations in the Lorenz system

In this paper, we use machine learning strategies aiming to predict chaotic time series obtained from the Lorenz system. Such strategies prove to be successful in predicting the evolution of dynamical variables over a short period of time. Transitions between the regimes and their duration can be predicted with great accuracy by means of counting and classification strategies, for which we train multi-layer perceptron ensembles. Even for the longest regimes the occurrences and duration can be predicted. We also show the use of an echo state network to generate data of the time series with an accuracy of up to a few hundreds time steps. The ability of the classification technique to predict the regime duration of more than 11 oscillations corresponds to around 10 Lyapunov times.