# Variational Encoding of Complex Dynamics

arXiv: https://arxiv.org/abs/1711.08576 · HTML: https://mlsanity.com/paper/1711.08576/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2017.

## Built on by (most cited first, 21 of 21)

- [Deeptime: a Python library for machine learning dynamical models from time series data](https://mlsanity.com/paper/2110.15013/) (2021)
- [Reconstructing Nonlinear Dynamical Systems from Multi-Modal Time Series](https://mlsanity.com/paper/2111.02922/) (2021)
- [Coupling streaming AI and HPC ensembles to achieve 100-1000x faster biomolecular simulations](https://mlsanity.com/paper/2104.04797/) (2021)
- [GraphVAMPNet, using graph neural networks and variational approach to markov processes for dynamical modeling of biomolecules](https://mlsanity.com/paper/2201.04609/) (2022)
- [GD-VAEs: Geometric Dynamic Variational Autoencoders for Learning Nonlinear Dynamics and Dimension Reductions](https://mlsanity.com/paper/2206.05183/) (2022)
- [Latent Representation and Simulation of Markov Processes via Time-Lagged Information Bottleneck](https://mlsanity.com/paper/2309.07200/) (2023)
- [Phi-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilation](https://mlsanity.com/paper/2209.15609/) (2022)
- [Multi-Scale Simulation of Complex Systems: A Perspective of Integrating Knowledge and Data](https://mlsanity.com/paper/2306.10275/) (2023)
- [Using pretrained graph neural networks with token mixers as geometric featurizers for conformational dynamics](https://mlsanity.com/paper/2409.19838/) (2024)
- [Learning Intuitive Physics with Multimodal Generative Models](https://mlsanity.com/paper/2101.04454/) (2021)
- [Beyond Ensembles: Simulating All-Atom Protein Dynamics in a Learned Latent Space](https://mlsanity.com/paper/2509.02196/) (2025)
- [Accelerated Simulations of Molecular Systems through Learning of their Effective Dynamics](https://mlsanity.com/paper/2102.08810/) (2021)
- [Collective variable discovery in the age of machine learning: reality, hype and everything in between](https://mlsanity.com/paper/2112.03202/) (2021)
- [Understanding recent deep-learning techniques for identifying collective variables of molecular dynamics](https://mlsanity.com/paper/2307.00365/) (2023)
- [Internal-Coordinate Density Modelling of Protein Structure: Covariance Matters](https://mlsanity.com/paper/2302.13711/) (2023)
- [Enhanced Sampling with Machine Learning: A Review](https://mlsanity.com/paper/2306.09111/) (2023)
- [Learning collective variables that preserve transition rates](https://mlsanity.com/paper/2506.01222/) (2025)
- [Learning Collective Variables from BioEmu with Time-Lagged Generation](https://mlsanity.com/paper/2507.07390/) (2025)
- [Fast conformational clustering of extensive molecular dynamics simulation data](https://mlsanity.com/paper/2301.04492/) (2023)
- [Latent Thermodynamic Flows: Unified Representation Learning and Generative Modeling of Temperature-Dependent Behaviors from Limited Data](https://mlsanity.com/paper/2507.03174/) (2025)
- [Random functions as data compressors for machine learning of molecular processes](https://mlsanity.com/paper/2509.17937/) (2025)

## Abstract (arXiv)

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.