Machine learning the Ising transition: A comparison between discriminative and generative approaches

TL;DR

This paper compares discriminative and generative machine learning methods for detecting phase transitions in the 2D Ising model, analyzing their effectiveness and suitability based on various factors.

Contribution

It provides a systematic numerical comparison of discriminative and generative approaches for phase classification in many-body physics.

Findings

Discriminative methods perform better with larger datasets.

Generative methods are more data-efficient with limited data.

The choice depends on available system knowledge and computational resources.

Abstract

The detection of phase transitions is a central task in many-body physics. To automate this process, the task can be phrased as a classification problem. Classification problems can be approached in two fundamentally distinct ways: through either a discriminative or a generative method. In general, it is unclear which of these two approaches is most suitable for a given problem. The choice is expected to depend on factors such as the availability of system knowledge, dataset size, desired accuracy, computational resources, and other considerations. In this work, we answer the question of how one should approach the solution of phase-classification problems by performing a numerical case study on the thermal phase transition in the classical two-dimensional square-lattice ferromagnetic Ising model.