Interpretable Machine Learning for the Thermodynamic Phases in 2D XY Model

Abstract

We study the interpretable machine learning of thermodynamic phases in the two-dimensional classical XY model. We find that the neural network can accurately classify the different phases. We utilize the anchor algorithm to explain the mechanism of classification during the machine learning. The prediction based on the anchor is very close to that according to the raw spin configurations. With the help of linearity measurement, we find that the neural network shows strong nonlinearity when classifies the low temperature phase and strong linearity when classifies the high temperature thermal equilibrium phase, which means that the machine has strong adaptability to the thermodynamic fluctuation. The interpretable machine learning can be applied to other classical or quantum many-body systems.