Interpretable Phase Detection and Classification with Persistent Homology

Abstract

We apply persistent homology to the task of discovering and characterizing phase transitions, using lattice spin models from statistical physics for working examples. Persistence images provide a useful representation of the homological data for conducting statistical tasks. To identify the phase transitions, a simple logistic regression on these images is sufficient for the models we consider, and interpretable order parameters are then read from the weights of the regression. Magnetization, frustration and vortex-antivortex structure are identified as relevant features for characterizing phase transitions.

arXiv comment5 pages, 3 figures; shortened version of arXiv:2009.14231; accepted to NeurIPS 2020 Workshop on Topological Data Analysis and Beyond

References in corpus (9)

• Machine learning phases of matter
• Learning phase transitions by confusion
• Discovering Phase Transitions with Unsupervised Learning
• Detection of phase transition via convolutional neural network
• Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory
• Identifying Quantum Phase Transitions with Adversarial Neural Networks
• Persistent Homology analysis of Phase Transitions
• Machine Learning as a universal tool for quantitative investigations of phase transition
• Topological Persistence Machine of Phase Transitions