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Gauge-equivariant pooling layers for preconditioners in lattice QCD

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arxiv 2304.10438 v1 pith:EUOUBSCA submitted 2023-04-20 hep-lat cs.LGcs.NAmath.NA

Christoph Lehner , Tilo Wettig This is my paper · ORCID
classification hep-latcs.LGcs.NAmath.NA
keywords layersgaugegauge-equivariantcoarsecoarse-gridconstructiongridlattice
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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.

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  1. Symmetry-preserving neural networks in lattice field theories

    hep-lat 2025-06 conditional novelty 4.0 of 10

    Translation- and gauge-equivariant neural networks (L-CNNs) predict Wilson loops, topological charge, and flux observables with orders-of-magnitude lower error than symmetry-breaking baselines, and neural gradient flo...

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