Unsupervised machine learning for detection of phase transitions in off-lattice systems I. Foundations

TL;DR

This paper shows how unsupervised machine learning, specifically PCA, can automatically detect phase transitions in off-lattice systems without prior knowledge of order parameters, simplifying phase behavior analysis.

Contribution

It introduces PCA as an unsupervised tool to identify phase transitions and discover order-parameter-like quantities in off-lattice systems.

Findings

PCA detects freezing transitions in hard-disk and hard-sphere systems.

PCA identifies liquid-gas phase separation in patchy colloids.

The method reduces the need for predefined order parameters.

Abstract

We demonstrate the utility of an unsupervised machine learning tool for the detection of phase transitions in off-lattice systems. We focus on the application of principal component analysis (PCA) to detect the freezing transitions of two-dimensional hard-disk and three-dimensional hard-sphere systems as well as liquid-gas phase separation in a patchy colloid model. As we demonstrate, PCA autonomously discovers order-parameter-like quantities that report on phase transitions, mitigating the need for a priori construction or identification of a suitable order parameter--thus streamlining the routine analysis of phase behavior. In a companion paper, we further develop the method established here to explore the detection of phase transitions in various model systems controlled by compositional demixing, liquid crystalline ordering, and non-equilibrium active forces.