Unsupervised learning of phase transitions: From principal component analysis to variational autoencoders

2017/03/12 by Sebastian J. Wetzel, Sebastian Johann Wetzel · 502 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #A priori and a posteriori #Algorithm #Artificial intelligence #Artificial neural network #Cluster analysis #Computer science #Hamiltonian (control theory) #Ising model #Latent variable #Machine learning #Mathematical optimization #Mathematics #Monte Carlo method #Pattern recognition (psychology) #Physics #Principal component analysis #Protein Structure and Dynamics #Statistical Mechanics and Entropy #Statistical physics #Theoretical and Computational Physics #Unsupervised learning #cond-mat.stat-mech #cs.LG #stat.ML

paper · pdf · doi:10.1103/physreve.96.022140

published in Physical review. E 96(2), 022140 (American Physical Society) · corrected typos

arxiv created 2017/03/12 · openalex publication_date 2017/08/18 · arxiv updated 2017/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We examine unsupervised machine learning techniques to learn features that best describe configurations of the two-dimensional Ising model and the three-dimensional XY model. The methods range from principal component analysis over manifold and clustering methods to artificial neural-network-based variational autoencoders. They are applied to Monte Carlo-sampled configurations and have, a priori, no knowledge about the Hamiltonian or the order parameter. We find that the most promising algorithms are principal component analysis and variational autoencoders. Their predicted latent parameters correspond to the known order parameters. The latent representations of the models in question are clustered, which makes it possible to identify phases without prior knowledge of their existence. Furthermore, we find that the reconstruction loss function can be used as a universal identifier for phase transitions.

Citations

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