Gauge-equivariant pooling layers for preconditioners in lattice QCD

Understand

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.