Deep Learning of Chaos Classification
This provides a faster, more robust chaos indicator for physicists and engineers studying dynamical systems, though it is incremental as it applies existing neural network methods to a new domain.
The researchers tackled the problem of classifying chaotic versus regular dynamics in discrete maps using a convolutional neural network, achieving superior performance over traditional Lyapunov exponent methods for short trajectories down to 10 Lyapunov times.
We train an artificial neural network which distinguishes chaotic and regular dynamics of the two-dimensional Chirikov standard map. We use finite length trajectories and compare the performance with traditional numerical methods which need to evaluate the Lyapunov exponent. The neural network has superior performance for short periods with length down to 10 Lyapunov times on which the traditional Lyapunov exponent computation is far from converging. We show the robustness of the neural network to varying control parameters, in particular we train with one set of control parameters, and successfully test in a complementary set. Furthermore, we use the neural network to successfully test the dynamics of discrete maps in different dimensions, e.g. the one-dimensional logistic map and a three-dimensional discrete version of the Lorenz system. Our results demonstrate that a convolutional neural network can be used as an excellent chaos indicator.