Gauge-equivariant neural networks as preconditioners in lattice QCD

TL;DR

This paper introduces gauge-equivariant neural networks as efficient, adaptable preconditioners for lattice QCD simulations, capable of minimal retraining and easy integration of communication strategies.

Contribution

It presents a novel approach using gauge-equivariant neural networks to learn multi-grid preconditioners that are adaptable and efficient across different gauge configurations.

Findings

Neural networks can effectively learn multi-grid preconditioners for lattice QCD.

Models require minimal retraining across similar gauge configurations.

Communication avoidance techniques are easily incorporated into the framework.

Abstract

We demonstrate that a state-of-the art multi-grid preconditioner can be learned efficiently by gauge-equivariant neural networks. We show that the models require minimal re-training on different gauge configurations of the same gauge ensemble and to a large extent remain efficient under modest modifications of ensemble parameters. We also demonstrate that important paradigms such as communication avoidance are straightforward to implement in this framework.