mlsanityData to 14 Oct 2026

Gauge-equivariant pooling layers for preconditioners in lattice QCD

arXiv 2304.10438 ↗First posted 20 Apr 2023hep-lat cs.LG cs.NAcited by 6

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Abstract (arXiv)

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.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 15 of its 71 references that are in the map. First posted on arXiv 20 Apr 2023.

Builds on

15 of 71 references.

References · 15

  1. 2016Group Equivariant Convolutional Networkscited by 1,165
  2. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 267
  3. 2020Equivariant flow-based sampling for lattice gauge theorycited by 103
  4. 2020Sampling using SU(N) gauge equivariant flowscited by 84
  5. 2019Learning to Optimize Multigrid PDE Solverscited by 79
  6. 2020Learning Algebraic Multigrid Using Graph Neural Networkscited by 54
  7. 2020Lattice gauge equivariant convolutional neural networkscited by 45
  8. 2022Gauge-equivariant flow models for sampling in lattice field theories with pseudofermionscited by 31
  9. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited by 26
  10. 2021Learning optimal multigrid smoothers via neural networkscited by 17
  11. 2023Gauge-equivariant neural networks as preconditioners in lattice QCDcited by 9
  12. 2020MGIC: Multigrid-in-Channels Neural Network Architecturescited by 8
3 more
  1. 2022Neural-network preconditioners for solving the Dirac equation in lattice gauge theorycited by 6
  2. 2023Geometrical aspects of lattice gauge equivariant convolutional neural networkscited by 6
  3. 2022MGiaD: Multigrid in all dimensions. Efficiency and robustness by coarsening in resolution and channel dimensionscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 1; 2025: 2; 2026: 2.

6 papers.

  1. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23
  2. 2025Physics-Driven Learning for Inverse Problems in Quantum Chromodynamicscited by 7
  3. 2026Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theoriescited by 3
  4. 2024Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural networkcited by 2
  5. 2025Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theorycited by 0
  6. 2026Emergent Loop Geometry in Gauge-Equivariant Graph Neural Networkscited by 0