Modeling Dynamics with Deep Transition-Learning Networks

We present an approach to learning Markovian dynamics, specifically the transition (next-state) vector field of a stochastic dynamic system, using a neural network model that we call the transcoder. Focusing on the stochastic transition has several advantages in biology including next-state prediction from current measurements (when history is not available), generation of stochastic trajectories, and a model of transitions that allows us to predict interactions. In addition, here we propose to utilize the neural network itself as a white-box model to examine features of the dynamic process such as identifying features that most control transitions in parts of the data space. We validate our method on systems such as a single and a double pendulum, Frey faces trajectories, and MCMC sampling of a Gaussian Mixture Model. We then apply it to single-cell data of T-cell development and neuronal calcium imaging data of mice presented with a visual stimulus.