# Machine Learning of Slow Collective Variables and Enhanced Sampling via Spatial Techniques

arXiv: https://arxiv.org/abs/2412.20868 · HTML: https://mlsanity.com/paper/2412.20868/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 212 references that are in the map.
- First posted on arXiv 30 Dec 2024.

## Builds on (most cited first, 21 of 21)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Manifold learning: what, how, and why](https://mlsanity.com/paper/2311.03757/) (2023)
- [Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics](https://mlsanity.com/paper/1710.11239/) (2017)
- [Variational approach for learning Markov processes from time series data](https://mlsanity.com/paper/1707.04659/) (2017)
- [Computing Committor Functions for the Study of Rare Events Using Deep Learning](https://mlsanity.com/paper/1906.06285/) (2019)
- [Molecular enhanced sampling with autoencoders: On-the-fly collective variable discovery and accelerated free energy landscape exploration](https://mlsanity.com/paper/1801.00203/) (2017)
- [Double Diffusion Maps and their Latent Harmonics for Scientific Computations in Latent Space](https://mlsanity.com/paper/2204.12536/) (2022)
- [Nonlinear Discovery of Slow Molecular Modes using State-Free Reversible VAMPnets](https://mlsanity.com/paper/1902.03336/) (2019)
- [Chasing Collective Variables using Autoencoders and biased trajectories](https://mlsanity.com/paper/2104.11061/) (2021)
- [High-resolution Markov state models for the dynamics of Trp-cage miniprotein constructed over slow folding modes identified by state-free reversible VAMPnets](https://mlsanity.com/paper/1906.04890/) (2019)
- [Landmark Diffusion Maps (L-dMaps): Accelerated manifold learning out-of-sample extension](https://mlsanity.com/paper/1706.09396/) (2017)
- [Multitask machine learning of collective variables for enhanced sampling of rare events](https://mlsanity.com/paper/2012.03909/) (2020)
- [Representation Learning: A Statistical Perspective](https://mlsanity.com/paper/1911.11374/) (2019)
- [Unfolding Hidden Barriers by Active Enhanced Sampling](https://mlsanity.com/paper/1705.07414/) (2017)
- [Capabilities and Limitations of Time-lagged Autoencoders for Slow Mode Discovery in Dynamical Systems](https://mlsanity.com/paper/1906.00325/) (2019)
- [Characterizing metastable states with the help of machine learning](https://mlsanity.com/paper/2204.07391/) (2022)
- [Reweighted Manifold Learning of Collective Variables from Enhanced Sampling Simulations](https://mlsanity.com/paper/2207.14554/) (2022)
- [Spectral Map for Slow Collective Variables, Markovian Dynamics, and Transition State Ensembles](https://mlsanity.com/paper/2409.06428/) (2024)
- [Unbiasing Enhanced Sampling on a High-dimensional Free Energy Surface with Deep Generative Model](https://mlsanity.com/paper/2312.09404/) (2023)

## Built on by (most cited first, 2 of 2)

- [AI-based Methods for Simulating, Sampling, and Predicting Protein Ensembles](https://mlsanity.com/paper/2509.17224/) (2025)
- [Unraveling the Mechanism of Drug Binding to SARS-CoV-2 RNA Pseudoknot with Thermodynamics-Driven Machine Learning](https://mlsanity.com/paper/2604.14906/) (2026)

## Abstract (arXiv)

Understanding the long-time dynamics of complex physical processes depends on our ability to recognize patterns. To simplify the description of these processes, we often introduce a set of reaction coordinates, customarily referred to as collective variables (CVs). The quality of these CVs heavily impacts our comprehension of the dynamics, often influencing the estimates of thermodynamics and kinetics from atomistic simulations. Consequently, identifying CVs poses a fundamental challenge in chemical physics. Recently, significant progress was made by leveraging the predictive ability of unsupervised machine learning techniques to determine CVs. Many of these techniques require temporal information to learn slow CVs that correspond to the long timescale behavior of the studied process. Here, however, we specifically focus on techniques that can identify CVs corresponding to the slowest transitions between states without needing temporal trajectories as input, instead using the spatial characteristics of the data. We discuss the latest developments in this category of techniques and briefly discuss potential directions for thermodynamics-informed spatial learning of slow CVs.