Variational Encoding of Complex Dynamics

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.

Fixed typos and added references

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• A unified framework for machine learning collective variables for enhanced sampling simulations: $\text{mlcolvar}$
• Special Topic: Markov Models of Molecular Kinetics
• Ensemble Learning of Coarse-Grained Molecular Dynamics Force Fields with a Kernel Approach
• GraphVAMPNet, using graph neural networks and variational approach to markov processes for dynamical modeling of biomolecules
• Simulations meet Machine Learning in Structural Biology
• Enhanced Sampling in the Age of Machine Learning: Algorithms and Applications
• Multiscale reweighted stochastic embedding (MRSE): Deep learning of collective variables for enhanced sampling
• Targeted free energy perturbation revisited: Accurate free energies from mapped reference potentials
• Capabilities and Limitations of Time-lagged Autoencoders for Slow Mode Discovery in Dynamical Systems
• Extracting Interpretable Physical Parameters from Spatiotemporal Systems using Unsupervised Learning
• Differentiable Molecular Simulations for Control and Learning
• A Deep Autoencoder Framework for Discovery of Metastable Ensembles in Biomacromolecules
• Neural Canonical Transformation with Symplectic Flows
• Application of Adaptive Multilevel Splitting to High-Dimensional Dynamical Systems
• Fast conformational clustering of extensive molecular dynamics simulation data
• Multidimensional minimum-work control of a 2D Ising model
• Deeptime: a Python library for machine learning dynamical models from time series data
• Understanding the role of predictive time delay and biased propagator in RAVE
• Deep learning the slow modes for rare events sampling
• Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems
• Note: Variational Encoding of Protein Dynamics Benefits from Maximizing Latent Autocorrelation
• Thermodynamically Optimized Machine-learned Reaction Coordinates for Hydrophobic Ligand Dissociation
• Machine Learning of coarse-grained Molecular Dynamics Force Fields
• Spacetime Autoencoders Using Local Causal States
• Internal-Coordinate Density Modelling of Protein Structure: Covariance Matters
• Unsupervised Videographic Analysis of Rodent Behaviour
• Machine learning approaches for analyzing and enhancing molecular dynamics simulations
• DeVLearn: A Deep Visual Learning Framework for Localizing Temporary Faults in Power Systems
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• Accelerated Simulations of Molecular Systems through Learning of their Effective Dynamics