# Automated design of collective variables using supervised machine learning

arXiv: https://arxiv.org/abs/1802.10510 · HTML: https://mlsanity.com/paper/1802.10510/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2018.

## Built on by (most cited first, 10 of 10)

- [Action-Minimization Meets Generative Modeling: Efficient Transition Path Sampling with the Onsager-Machlup Functional](https://mlsanity.com/paper/2504.18506/) (2025)
- [Chasing Collective Variables using Autoencoders and biased trajectories](https://mlsanity.com/paper/2104.11061/) (2021)
- [Differentiable Simulations for Enhanced Sampling of Rare Events](https://mlsanity.com/paper/2301.03480/) (2023)
- [Pandemic Drugs at Pandemic Speed: Infrastructure for Accelerating COVID-19 Drug Discovery with Hybrid Machine Learning- and Physics-based Simulations on High Performance Computers](https://mlsanity.com/paper/2103.02843/) (2021)
- [Learning Collective Variables with Synthetic Data Augmentation through Physics-Inspired Geodesic Interpolation](https://mlsanity.com/paper/2402.01542/) (2024)
- [Collective variable discovery in the age of machine learning: reality, hype and everything in between](https://mlsanity.com/paper/2112.03202/) (2021)
- [Data-driven path collective variables](https://mlsanity.com/paper/2312.13868/) (2023)
- [Entangled Schr"odinger Bridge Matching](https://mlsanity.com/paper/2511.07406/) (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)

## Abstract (arXiv)

Selection of appropriate collective variables for enhancing sampling of molecular simulations remains an unsolved problem in computational biophysics. In particular, picking initial collective variables (CVs) is particularly challenging in higher dimensions. Which atomic coordinates or transforms there of from a list of thousands should one pick for enhanced sampling runs? How does a modeler even begin to pick starting coordinates for investigation? This remains true even in the case of simple two state systems and only increases in difficulty for multi-state systems. In this work, we solve the initial CV problem using a data-driven approach inspired by the filed of supervised machine learning. In particular, we show how the decision functions in supervised machine learning (SML) algorithms can be used as initial CVs (SML_cv) for accelerated sampling. Using solvated alanine dipeptide and Chignolin mini-protein as our test cases, we illustrate how the distance to the Support Vector Machines' decision hyperplane, the output probability estimates from Logistic Regression, the outputs from deep neural network classifiers, and other classifiers may be used to reversibly sample slow structural transitions. We discuss the utility of other SML algorithms that might be useful for identifying CVs for accelerating molecular simulations.