Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics

Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that our time-lagged autoencoder reliably finds low-dimensional embeddings for highdimensional feature spaces which capture the slow dynamics of the underlying stochastic processes-beyond the capabilities of linear dimension reduction techniques. Molecular dynamics (MD) simulation allows us to probe the full spatiotemporal detail of molecular processes, but its usefulness has long been limited by the sampling problem. If we do not want to choose the library of feature functions by hand, but instead want to optimize the nonlinear mapping E by employing a neural network, we have again two options: (1) employ the variational approach. In this paper we investigate option (2), which naturally leads to using a time-lagged autoencoder (TAE).