Interpretable and unsupervised phase classification

TL;DR

This paper introduces an interpretable, unsupervised machine learning approach for phase classification in physical systems, providing direct insights into phase diagrams and an automated way to construct order parameters, demonstrated on the Falicov-Kimball model.

Contribution

It presents a novel, interpretable unsupervised learning method for phase classification and an alternative physically-motivated scheme based on mean input features.

Findings

Method yields direct physical insights into phase diagrams.

Mean-based scheme is computationally efficient and interpretable.

Successfully applied to the Falicov-Kimball model.

Abstract

Fully automated classification methods that yield direct physical insights into phase diagrams are of current interest. Here, we demonstrate an unsupervised machine learning method for phase classification which is rendered interpretable via an analytical derivation of its optimal predictions and allows for an automated construction scheme for order parameters. Based on these findings, we propose and apply an alternative, physically-motivated, data-driven scheme which relies on the difference between mean input features. This mean-based method is computationally cheap and directly interpretable. As an example, we consider the physically rich ground-state phase diagram of the spinless Falicov-Kimball model.