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

Area of Science:

• Statistical Mechanics
• Machine Learning
• Computational Physics

Background:

• Understanding phase transitions in physical models is crucial.
• Unsupervised machine learning offers novel approaches to analyze complex systems.
• Traditional methods often require prior knowledge of model parameters.

Purpose of the Study:

• To explore unsupervised machine learning techniques for feature learning in physical models.
• To identify which methods best describe configurations of the 2D Ising and 3D XY models.
• To assess the ability of these methods to detect phase transitions without prior information.

Main Methods:

• Application of Principal Component Analysis (PCA).
• Utilization of manifold and clustering methods.
• Implementation of Variational Autoencoders (VAEs) based on artificial neural networks.
• Analysis of Monte Carlo-sampled configurations.

Main Results:

• Principal Component Analysis and Variational Autoencoders emerged as the most promising techniques.
• Learned latent parameters from these methods directly correspond to known order parameters.
• Clustered latent representations enabled phase identification without prior knowledge.
• Reconstruction loss function served as a universal phase transition identifier.

Conclusions:

• Unsupervised machine learning, particularly PCA and VAEs, can effectively learn relevant features for physical models.
• These methods facilitate the discovery of model phases and phase transitions.
• The reconstruction loss offers a generalizable approach for detecting phase transitions.