# Data-driven path collective variables

arXiv: https://arxiv.org/abs/2312.13868 · HTML: https://mlsanity.com/paper/2312.13868/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 73 references that are in the map.
- First posted on arXiv 21 Dec 2023.

## Builds on (most cited first, 4 of 4)

- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Computing Committor Functions for the Study of Rare Events Using Deep Learning](https://mlsanity.com/paper/1906.06285/) (2019)
- [Automated design of collective variables using supervised machine learning](https://mlsanity.com/paper/1802.10510/) (2018)
- [Reweighted Manifold Learning of Collective Variables from Enhanced Sampling Simulations](https://mlsanity.com/paper/2207.14554/) (2022)

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

- [Learning Collective Variables with Synthetic Data Augmentation through Physics-Inspired Geodesic Interpolation](https://mlsanity.com/paper/2402.01542/) (2024)
- [From Biased to Unbiased Dynamics: An Infinitesimal Generator Approach](https://mlsanity.com/paper/2406.09028/) (2024)

## Abstract (arXiv)

Identifying optimal collective variables to model transformations, using atomic-scale simulations, is a long-standing challenge. We propose a new method for the generation, optimization, and comparison of collective variables, which can be thought of as a data-driven generalization of the path collective variable concept. It consists in a kernel ridge regression of the committor probability, which encodes a transformation's progress. The resulting collective variable is one-dimensional, interpretable, and differentiable, making it appropriate for enhanced sampling simulations requiring biasing. We demonstrate the validity of the method on two different applications: a precipitation model, and the association of Li^+ and F^- in water. For the former, we show that global descriptors such as the permutation invariant vector allow to reach an accuracy far from the one achieved textitvia simpler, more intuitive variables. For the latter, we show that information correlated with the transformation mechanism is contained in the first solvation shell only, and that inertial effects prevent the derivation of optimal collective variables from the atomic positions only.