# Interpretable Embeddings From Molecular Simulations Using Gaussian Mixture Variational Autoencoders

arXiv: https://arxiv.org/abs/1912.12175 · HTML: https://mlsanity.com/paper/1912.12175/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2019.

## Built on by (most cited first, 13 of 13)

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- [Foundation Inference Models for Markov Jump Processes](https://mlsanity.com/paper/2406.06419/) (2024)
- [Neural Markov Jump Processes](https://mlsanity.com/paper/2305.19744/) (2023)
- [Revisiting Bayesian Autoencoders with MCMC](https://mlsanity.com/paper/2104.05915/) (2021)
- [Generative methods for sampling transition paths in molecular dynamics](https://mlsanity.com/paper/2205.02818/) (2022)
- [EXoN: EXplainable encoder Network](https://mlsanity.com/paper/2105.10867/) (2021)
- [Variational embedding of protein folding simulations using gaussian mixture variational autoencoders](https://mlsanity.com/paper/2108.12493/) (2021)
- [Understanding recent deep-learning techniques for identifying collective variables of molecular dynamics](https://mlsanity.com/paper/2307.00365/) (2023)
- [Learning Geometrically Disentangled Representations of Protein Folding Simulations](https://mlsanity.com/paper/2205.10423/) (2022)
- [A generative recommender system with GMM prior for cancer drug generation and sensitivity prediction](https://mlsanity.com/paper/2206.03555/) (2022)
- [Fast conformational clustering of extensive molecular dynamics simulation data](https://mlsanity.com/paper/2301.04492/) (2023)
- [Sampling - Variational Auto Encoder - Ensemble: In the Quest of Explainable Artificial Intelligence](https://mlsanity.com/paper/2309.14385/) (2023)
- [A Matrix Variational Auto-Encoder for Variant Effect Prediction in Pharmacogenes](https://mlsanity.com/paper/2507.02624/) (2025)

## Abstract (arXiv)

Extracting insight from the enormous quantity of data generated from molecular simulations requires the identification of a small number of collective variables whose corresponding low-dimensional free-energy landscape retains the essential features of the underlying system. Data-driven techniques provide a systematic route to constructing this landscape, without the need for extensive a priori intuition into the relevant driving forces. In particular, autoencoders are powerful tools for dimensionality reduction, as they naturally force an information bottleneck and, thereby, a low-dimensional embedding of the essential features. While variational autoencoders ensure continuity of the embedding by assuming a unimodal Gaussian prior, this is at odds with the multi-basin free-energy landscapes that typically arise from the identification of meaningful collective variables. In this work, we incorporate this physical intuition into the prior by employing a Gaussian mixture variational autoencoder (GMVAE), which encourages the separation of metastable states within the embedding. The GMVAE performs dimensionality reduction and clustering within a single unified framework, and is capable of identifying the inherent dimensionality of the input data, in terms of the number of Gaussians required to categorize the data. We illustrate our approach on two toy models, alanine dipeptide, and a challenging disordered peptide ensemble, demonstrating the enhanced clustering effect of the GMVAE prior compared to standard VAEs. The resulting embeddings appear to be promising representations for constructing Markov state models, highlighting the transferability of the dimensionality reduction from static equilibrium properties to dynamics.