# Reweighted Manifold Learning of Collective Variables from Enhanced Sampling Simulations

arXiv: https://arxiv.org/abs/2207.14554 · HTML: https://mlsanity.com/paper/2207.14554/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 101 references that are in the map.
- First posted on arXiv 29 Jul 2022.

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

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Unfolding Hidden Barriers by Active Enhanced Sampling](https://mlsanity.com/paper/1705.07414/) (2017)
- [Introducing user-prescribed constraints in Markov chains for nonlinear dimensionality reduction](https://mlsanity.com/paper/1806.05096/) (2018)

## Built on by (most cited first, 4 of 4)

- [From Biased to Unbiased Dynamics: An Infinitesimal Generator Approach](https://mlsanity.com/paper/2406.09028/) (2024)
- [Spectral Map for Slow Collective Variables, Markovian Dynamics, and Transition State Ensembles](https://mlsanity.com/paper/2409.06428/) (2024)
- [Data-driven path collective variables](https://mlsanity.com/paper/2312.13868/) (2023)
- [Machine Learning of Slow Collective Variables and Enhanced Sampling via Spatial Techniques](https://mlsanity.com/paper/2412.20868/) (2024)

## Abstract (arXiv)

Enhanced sampling methods are indispensable in computational physics and chemistry, where atomistic simulations cannot exhaustively sample the high-dimensional configuration space of dynamical systems due to the sampling problem. A class of such enhanced sampling methods works by identifying a few slow degrees of freedom, termed collective variables (CVs), and enhancing the sampling along these CVs. Selecting CVs to analyze and drive the sampling is not trivial and often relies on physical and chemical intuition. Despite routinely circumventing this issue using manifold learning to estimate CVs directly from standard simulations, such methods cannot provide mappings to a low-dimensional manifold from enhanced sampling simulations as the geometry and density of the learned manifold are biased. Here, we address this crucial issue and provide a general reweighting framework based on anisotropic diffusion maps for manifold learning that takes into account that the learning data set is sampled from a biased probability distribution. We consider manifold learning methods based on constructing a Markov chain describing transition probabilities between high-dimensional samples. We show that our framework reverts the biasing effect yielding CVs that correctly describe the equilibrium density. This advancement enables the construction of low-dimensional CVs using manifold learning directly from data generated by enhanced sampling simulations. We call our framework reweighted manifold learning. We show that it can be used in many manifold learning techniques on data from both standard and enhanced sampling simulations.