Variational Encoding of Complex Dynamics

TL;DR

This paper introduces a time-lagged variational autoencoder, called VDE, that effectively compresses and interprets complex nonlinear dynamics in high-dimensional time-series data from chemical and biophysical systems.

Contribution

The paper presents the VDE model, a novel deep learning approach that captures nonlinear dynamics in a single, high-fidelity embedding and includes a method for interpreting the features it uses.

Findings

VDE accurately captures complex dynamics in simulated systems.

VDE provides interpretable insights into the features driving the dynamics.

Demonstrated effectiveness on protein folding and Brownian motion data.

Abstract

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.