  Complex high dimensional stochastic dynamic systems arise in many
applications in the natural sciences and especially biology. However, while
these systems are difficult to describe analytically, "snapshot" measurements
that sample the output of the system are often available. In order to model the
dynamics of such systems given snapshot data, or local transitions, we present
a deep neural network framework we call Dynamics Modeling Network or DyMoN.
DyMoN is a neural network framework trained as a deep generative Markov model
whose next state is a probability distribution based on the current state.
DyMoN is trained using samples of current and next-state pairs, and thus does
not require longitudinal measurements. We show the advantage of DyMoN over
shallow models such as Kalman filters and hidden Markov models, and other deep
models such as recurrent neural networks in its ability to embody the dynamics
(which can be studied via perturbation of the neural network) and generate
longitudinal hypothetical trajectories. We perform three case studies in which
we apply DyMoN to different types of biological systems and extract features of
the dynamics in each case by examining the learned model.
