Variational encoding of complex dynamics.

Area of Science:

• Computational Biophysics
• Machine Learning
• Data Analysis

Background:

• Analyzing time-series data from chemical and biophysical systems is challenging due to high dimensionality.
• Existing time-lagged covariate models struggle with nonlinear dynamics, limiting data compression.
• Deep learning's variational autoencoder (VAE) offers powerful dataset compression into simpler manifolds.

Purpose of the Study:

• To introduce the time-lagged variational autoencoder (VDE) for modeling complex, nonlinear biophysical dynamics.
• To demonstrate the VDE's capability in reducing high-dimensional time-series data into a low-dimensional embedding.
• To develop methods for interpreting VDE models and identifying salient features driving system dynamics.

Main Methods:

• Implementation of a time-lagged variational autoencoder (VDE) for nonlinear dynamical systems.
• Application of the VDE to Brownian dynamics and atomistic protein folding simulations.
• Development of a saliency mapping-inspired technique for VDE model analysis.

Main Results:

• The VDE successfully compressed complex nonlinear dynamics into a single embedding with high fidelity.
• The model accurately captured nontrivial dynamics in diverse biophysical examples.
• A novel analysis method was established to identify features crucial for VDE dynamics description.

Conclusions:

• The VDE is a powerful deep learning tool for modeling and interpreting complex nonlinear biophysical processes.
• This approach enhances the ability to extract meaningful insights from high-dimensional time-series data.
• The VDE represents a significant advancement in applying machine learning to biophysics.