  We propose a deep generative Markov State Model (DeepGenMSM) learning
framework for inference of metastable dynamical systems and prediction of
trajectories. After unsupervised training on time series data, the model
contains (i) a probabilistic encoder that maps from high-dimensional
configuration space to a small-sized vector indicating the membership to
metastable (long-lived) states, (ii) a Markov chain that governs the
transitions between metastable states and facilitates analysis of the long-time
dynamics, and (iii) a generative part that samples the conditional distribution
of configurations in the next time step. The model can be operated in a
recursive fashion to generate trajectories to predict the system evolution from
a defined starting state and propose new configurations. The DeepGenMSM is
demonstrated to provide accurate estimates of the long-time kinetics and
generate valid distributions for molecular dynamics (MD) benchmark systems.
Remarkably, we show that DeepGenMSMs are able to make long time-steps in
molecular configuration space and generate physically realistic structures in
regions that were not seen in training data.
