Deep Learning for chaos detection
Roberto Barrio, Álvaro Lozano Rojo, Ana Mayora-Cebollero, Carmen Mayora-Cebollero, Antonio Miguel, Alfonso Ortega, Sergio Serrano, Rubén Vigara
Abstract
In this article, we study how a chaos detection problem can be solved using Deep Learning techniques. We consider two classical test examples: the Logistic map as a discrete dynamical system and the Lorenz system as a continuous dynamical system. We train three types of artificial neural networks (multi-layer perceptron, convolutional neural network, and long short-term memory cell) to classify time series from the mentioned systems into regular or chaotic. This approach allows us to study biparametric and triparametric regions in the Lorenz system due to their low computational cost compared to traditional techniques.