Gauge-equivariant pooling layers for preconditioners in lattice QCD

TL;DR

This paper introduces gauge-equivariant pooling layers for multigrid preconditioners in lattice QCD, enabling gauge-equivariance on coarse grids and effectively eliminating critical slowing down in simulations.

Contribution

It presents a novel gauge-equivariant pooling approach for multigrid preconditioners, improving efficiency in lattice QCD computations.

Findings

Gauge-equivariant pooling performs as well as traditional methods

Coarse-grid gauge fields constructed via Galerkin approach improve preconditioner efficiency

Elimination of critical slowing down in lattice QCD simulations

Abstract

We demonstrate that gauge-equivariant pooling and unpooling layers can perform as well as traditional restriction and prolongation layers in multigrid preconditioner models for lattice QCD. These layers introduce a gauge degree of freedom on the coarse grid, allowing for the use of explicitly gauge-equivariant layers on the coarse grid. We investigate the construction of coarse-grid gauge fields and study their efficiency in the preconditioner model. We show that a combined multigrid neural network using a Galerkin construction for the coarse-grid gauge field eliminates critical slowing down.