  In this article we study if a Deep Learning technique can be used to obtain
an approximated value of the Lyapunov exponents of a dynamical system.
Moreover, we want to know if Machine Learning techniques are able, once
trained, to provide the complete Lyapunov exponents spectrum with just
single-variable time series. We train a Convolutional Neural Network and we use
the resulting network to approximate the complete spectrum using the time
series of just one variable from the studied systems (Lorenz system and coupled
Lorenz system). The results are quite stunning as all the values are well
approximated with only partial data. This strategy permits to speed up the
complete analysis of the systems and also to study the hyperchaotic dynamics in
the coupled Lorenz system.
