Gauge-equivariant pooling layers for preconditioners in lattice QCD
This work addresses computational bottlenecks in lattice quantum chromodynamics, offering a domain-specific improvement for physics simulations.
The paper tackled the problem of critical slowing down in lattice QCD simulations by developing gauge-equivariant pooling layers for multigrid preconditioners, showing that these layers perform as well as traditional methods and can eliminate critical slowing down.
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.