Modeling Dynamics with Deep Transition-Learning Networks

Markov processes, both classical and higher order, are often used to model dynamic processes, such as stock prices, molecular dynamics, and Monte Carlo methods. Previous works have shown that an autoencoder can be formulated as a specific type of Markov chain. Here, we propose a generative neural network known as a transition encoder, or transcoder, which learns such continuous-state dynamic processes. We show that the transcoder is able to learn both deterministic and stochastic dynamic processes on several systems. We explore a number of applications of the transcoder including generating unseen trajectories and examining the propensity for chaos in a dynamic system. Further, we show that the transcoder can speed up Markov Chain Monte Carlo (MCMC) sampling to a convergent distribution by training it to make several steps at a time. Finally, we show that the hidden layers of a transcoder are useful for visualization and salient feature extraction of the transition process itself.