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.
Highlights
Phase diagrams and phase transitions are of paramount importance to physics [1,2,3]
While many-body systems have a large number of degrees of freedom, their phases are usually characterized by a small set of physical quantities like response functions or order parameters
We find that principal component analysis (PCA) and k-means clustering assigns configuration samples related through transformations of p4m to different clusters when using the raw configuration samples as input in the noise-free case
Summary
Phase diagrams and phase transitions are of paramount importance to physics [1,2,3]. While many-body systems have a large number of degrees of freedom, their phases are usually characterized by a small set of physical quantities like response functions or order parameters. At each such point pi a set of samples {Si} is generated Based on these samples, a scalar indicator for phase transitions I (pi ) is calculated. We gain a full understanding of the resulting phase classification and the associated values of the indicator for phase transitions These insights pave the way for the key result of this paper: A physically motivated, general, data-driven, unsupervised phase classification approach. It relies on the difference between mean input features as an indicator for phase transitions (Fig. 1); it is conceptually simple. We derive the form of its optimal predictive model and discuss how this analytical expression makes the prediction-based method and its corresponding phase classification explainable.
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