Manifold Learning in Atomistic Simulations: A Conceptual Review

TL;DR

This review discusses unsupervised manifold learning methods based on Markov transition probabilities for analyzing high-dimensional atomistic simulation data, aiding in understanding complex physical processes.

Contribution

It provides a conceptual overview of manifold learning techniques specifically using Markov transition probabilities, highlighting their theoretical foundations and limitations.

Findings

Focus on methods based on Markov transition probabilities

Applicable to standard and enhanced sampling datasets

Discusses theoretical frameworks and limitations

Abstract

Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex systems where even thousands of degrees of freedom are sampled. An abundance of such data makes gaining insight into a specific physical problem strenuous. Our primary aim in this review is to focus on unsupervised machine learning methods that can be used on simulation data to find a low-dimensional manifold providing a collective and informative characterization of the studied process. Such manifolds can be used for sampling long-timescale processes and free-energy estimation. We describe methods that can work on datasets from standard and enhanced sampling atomistic simulations. Unlike recent reviews on manifold learning for atomistic simulations, we consider only methods that construct low-dimensional manifolds based on Markov transition probabilities between high-dimensional samples. We discuss these techniques from a conceptual point of view, including their underlying theoretical frameworks and possible limitations.