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.

翻译：我们证明，规范等变池化和反池化层在格点QCD的多网格预处理器模型中，能够达到与传统限制和延拓层相当的性能。这些层在粗网格上引入规范自由度，从而允许在粗网格上使用显式规范等变的层。我们研究了粗网格规范场的构建方式，并分析了其在预处理器模型中的效率。结果表明，采用伽辽金构造粗网格规范场的组合多网格神经网络，能够消除临界 slowdown（关键减速）现象。