  Often the analysis of time-dependent chemical and biophysical systems
produces high-dimensional time-series data for which it can be difficult to
interpret which individual features are most salient. While recent work from
our group and others has demonstrated the utility of time-lagged co-variate
models to study such systems, linearity assumptions can limit the compression
of inherently nonlinear dynamics into just a few characteristic components.
Recent work in the field of deep learning has led to the development of
variational autoencoders (VAE), which are able to compress complex datasets
into simpler manifolds. We present the use of a time-lagged VAE, or variational
dynamics encoder (VDE), to reduce complex, nonlinear processes to a single
embedding with high fidelity to the underlying dynamics. We demonstrate how the
VDE is able to capture nontrivial dynamics in a variety of examples, including
Brownian dynamics and atomistic protein folding. Additionally, we demonstrate a
method for analyzing the VDE model, inspired by saliency mapping, to determine
what features are selected by the VDE model to describe dynamics. The VDE
presents an important step in applying techniques from deep learning to more
accurately model and interpret complex biophysics.
