Classifying Topological Charge in SU(3) Yang-Mills Theory with Machine Learning

TL;DR

This paper demonstrates that neural networks can accurately predict the topological charge in SU(3) Yang-Mills theory from early-stage gauge configurations, showing robustness and high accuracy.

Contribution

It introduces a machine learning approach that predicts topological charge from initial gauge data, outperforming traditional methods and revealing insights into relevant features.

Findings

Neural networks achieve over 99% accuracy in predicting topological charge.

Prediction accuracy remains high across different simulation parameters.

Convolutional neural networks do not rely on spatial structures for charge determination.

Abstract

We apply a machine learning technique for identifying the topological charge of quantum gauge configurations in four-dimensional SU(3) Yang-Mills theory. The topological charge density measured on the original and smoothed gauge configurations with and without dimensional reduction is used as inputs for the neural networks (NN) with and without convolutional layers. The gradient flow is used for the smoothing of the gauge field. We find that the topological charge determined at a large flow time can be predicted with high accuracy from the data at small flow times by the trained NN; for example, the accuracy exceeds $99\%$ with the data at $t/a^2\le0.3$. High robustness against the change of simulation parameters is also confirmed with a fixed physical volume. We find that the best performance is obtained when the spatial coordinates of the topological charge density are fully integrated out in preprocessing, which implies that our convolutional NN does not find characteristic structures in multi-dimensional space relevant for the determination of the topological charge.