A Machine Learning Approach for Lattice Gauge Fixing

TL;DR

This paper introduces a machine learning framework using neural networks and Wilson lines to improve the efficiency and scalability of lattice gauge fixing in quantum chromodynamics, addressing computational bottlenecks.

Contribution

It presents a novel hybrid machine learning approach that enhances gauge fixing efficiency and demonstrates transferability across lattice sizes in SU(3) gauge theory.

Findings

Improved gauge fixing efficiency on SU(3) ensembles.

Model transferability across different lattice sizes.

Potential to mitigate critical slowing down.

Abstract

Gauge fixing is an essential step in lattice QCD calculations, particularly for studying gauge-dependent observables. Traditional iterative algorithms are computationally expensive and often suffer from critical slowing down and scaling bottlenecks on large lattices. We present a novel machine learning framework for lattice gauge fixing, where Wilson lines are utilized to construct gauge transformation matrices within a convolutional neural network. The model parameters are optimized via backpropagation, and we introduce a hybrid strategy that combines a neural-network-based transformation with subsequent iterative methods. Preliminary tests on SU(3) gauge theory ensembles for Coulomb gauge demonstrate the potential of this approach to improve the efficiency of lattice gauge fixing. Furthermore, we show that the model exhibits lattice size transferability, where parameters optimized on smaller lattices remain effective for larger volumes without additional training. This framework provides a scalable path toward mitigating critical slowing down in high-precision gauge fixing.