Reconstructing shared dynamics with a deep neural network

Determining hidden shared patterns behind dynamic phenomena can be a game-changer in multiple areas of research. Here we present the principles and show a method to identify hidden shared dynamics from time series by a two-module, feedforward neural network architecture: the Mapper-Coach network. We reconstruct unobserved, continuous latent variable input, the time series generated by a chaotic logistic map, from the observed values of two simultaneously forced chaotic logistic maps. The network has been trained to predict one of the observed time series based on its own past and conditioned on the other observed time series by error-back propagation. It was shown, that after this prediction have been learned successfully, the activity of the bottleneck neuron, connecting the mapper and the coach module, correlated strongly with the latent shared input variable. The method has the potential to reveal hidden components of dynamical systems, where experimental intervention is not possible.