# Chasing Collective Variables using Autoencoders and biased trajectories

arXiv: https://arxiv.org/abs/2104.11061 · HTML: https://mlsanity.com/paper/2104.11061/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 67 references that are in the map.
- First posted on arXiv 22 Apr 2021.

## Builds on (most cited first, 8 of 8)

- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics](https://mlsanity.com/paper/1710.11239/) (2017)
- [Molecular enhanced sampling with autoencoders: On-the-fly collective variable discovery and accelerated free energy landscape exploration](https://mlsanity.com/paper/1801.00203/) (2017)
- [Variational Koopman models: slow collective variables and molecular kinetics from short off-equilibrium simulations](https://mlsanity.com/paper/1610.06773/) (2016)
- [Nonlinear Discovery of Slow Molecular Modes using State-Free Reversible VAMPnets](https://mlsanity.com/paper/1902.03336/) (2019)
- [Interpretable Embeddings From Molecular Simulations Using Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1912.12175/) (2019)
- [Automated design of collective variables using supervised machine learning](https://mlsanity.com/paper/1802.10510/) (2018)
- [Predictive Collective Variable Discovery with Deep Bayesian Models](https://mlsanity.com/paper/1809.06913/) (2018)

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

- [Differentiable Simulations for Enhanced Sampling of Rare Events](https://mlsanity.com/paper/2301.03480/) (2023)
- [From Biased to Unbiased Dynamics: An Infinitesimal Generator Approach](https://mlsanity.com/paper/2406.09028/) (2024)
- [Learning noise-induced transitions by multi-scaling reservoir computing](https://mlsanity.com/paper/2309.05413/) (2023)
- [GANs and Closures: Micro-Macro Consistency in Multiscale Modeling](https://mlsanity.com/paper/2208.10715/) (2022)
- [Micro-Macro Consistency in Multiscale Modeling: Score-Based Model Assisted Sampling of Fast/Slow Dynamical Systems](https://mlsanity.com/paper/2312.05715/) (2023)
- [Computing non-equilibrium trajectories by a deep learning approach](https://mlsanity.com/paper/2210.04042/) (2022)
- [Understanding recent deep-learning techniques for identifying collective variables of molecular dynamics](https://mlsanity.com/paper/2307.00365/) (2023)
- [Machine Learning of Slow Collective Variables and Enhanced Sampling via Spatial Techniques](https://mlsanity.com/paper/2412.20868/) (2024)
- [PETIMOT: A Novel Framework for Inferring Protein Motions from Sparse Data Using SE(3)-Equivariant Graph Neural Networks](https://mlsanity.com/paper/2504.02839/) (2025)
- [Learning Structure, Energy, and Dynamics: A Survey of Artificial Intelligence for Protein Dynamics](https://mlsanity.com/paper/2604.25244/) (2026)
- [Transferring Chemical and Energetic Knowledge Between Molecular Systems with Machine Learning](https://mlsanity.com/paper/2205.03339/) (2022)
- [Neumann eigenmaps for landmark embedding](https://mlsanity.com/paper/2502.06689/) (2025)
- [Random functions as data compressors for machine learning of molecular processes](https://mlsanity.com/paper/2509.17937/) (2025)

## Abstract (arXiv)

Free energy biasing methods have proven to be powerful tools to accelerate the simulation of important conformational changes of molecules by modifying the sampling measure. However, most of these methods rely on the prior knowledge of low-dimensional slow degrees of freedom, i.e. Collective Variables (CV). Alternatively, such CVs can be identified using machine learning (ML) and dimensionality reduction algorithms. In this context, approaches where the CVs are learned in an iterative way using adaptive biasing have been proposed: at each iteration, the learned CV is used to perform free energy adaptive biasing to generate new data and learn a new CV. In this paper, we introduce a new iterative method involving CV learning with autoencoders: Free Energy Biasing and Iterative Learning with AutoEncoders (FEBILAE). Our method includes a reweighting scheme to ensure that the learning model optimizes the same loss at each iteration, and achieves CV convergence. Using the alanine dipeptide system and the solvated chignolin mini-protein system as examples, we present results of our algorithm using the extended adaptive biasing force as the free energy adaptive biasing method.