Uncovering Magnetic Phases with Synthetic Data and Physics-Informed Training

TL;DR

This paper demonstrates how physics-informed neural networks trained on synthetic data can effectively identify magnetic phases and phase transitions in complex systems like the diluted Ising model.

Contribution

It introduces a combined supervised and unsupervised neural network approach with physics-informed guidance to detect phases without explicit labels.

Findings

Neural networks accurately identify phase boundaries in the diluted Ising model.

Physics-informed training improves sensitivity to symmetry breaking.

Synthetic data training offers a low-cost alternative to traditional methods.

Abstract

We investigate the efficient learning of magnetic phases using artificial neural networks trained on synthetic data, combining computational simplicity with physics-informed strategies. Focusing on the diluted Ising model, which lacks an exact analytical solution, we explore two complementary approaches: a supervised classification using simple dense neural networks, and an unsupervised detection of phase transitions using convolutional autoencoders trained solely on idealized spin configurations. To enhance model performance, we incorporate two key forms of physics-informed guidance. First, we exploit architectural biases which preferentially amplify features related to symmetry breaking. Second, we include training configurations that explicitly break $\mathbb{Z}_2$ symmetry, reinforcing the network's ability to detect ordered phases. These mechanisms, acting in tandem, increase the network's sensitivity to phase structure even in the absence of explicit labels. We validate the machine learning predictions through comparison with direct numerical estimates of critical temperatures and percolation thresholds. Our results show that synthetic, structured, and computationally efficient training schemes can reveal physically meaningful phase boundaries, even in complex systems. This framework offers a low-cost and robust alternative to conventional methods, with potential applications in broader condensed matter and statistical physics contexts.