A novel gauge-equivariant neural-network architecture for preconditioners in lattice QCD

TL;DR

This paper introduces a gauge-equivariant neural network preconditioner for lattice QCD that reduces computational costs and generalizes well across configurations, addressing critical slowing down.

Contribution

A novel gauge-equivariant neural network architecture for preconditioning the Dirac equation, improving efficiency and transferability in lattice QCD simulations.

Findings

Mitigates critical slowing down in lattice QCD

Transfers effectively to unseen gauge configurations

Reduces computational expense of Dirac equation solutions

Abstract

Lattice QCD simulations are computationally expensive, with the solution of the Dirac equation being the major computational bottleneck of many calculations. We introduce a novel gauge-equivariant neural-network architecture for preconditioning the Dirac equation in the regime where critical slowing down occurs. We study the behavior of this preconditioner as a function of topological charge and lattice volume and show that it mitigates critical slowing down. We also show that this preconditioner transfers to unseen gauge configurations without any retraining, therefore enabling applications not possible with competing methods.