mlsanityData to 7 Oct 2026

Gauge-equivariant neural networks as preconditioners in lattice QCD

arXiv 2302.05419 ↗First posted 10 Feb 2023hep-lat cs.LG cs.NAcited by 8

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Abstract (arXiv)

We demonstrate that a state-of-the art multi-grid preconditioner can be learned efficiently by gauge-equivariant neural networks. We show that the models require minimal re-training on different gauge configurations of the same gauge ensemble and to a large extent remain efficient under modest modifications of ensemble parameters. We also demonstrate that important paradigms such as communication avoidance are straightforward to implement in this framework.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 12 of its 39 references that are in the map. First posted on arXiv 10 Feb 2023.

Builds on

12 of 39 references.

References · 12

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2016Group Equivariant Convolutional Networkscited by 1,154
  3. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
  4. 2020Equivariant flow-based sampling for lattice gauge theorycited by 102
  5. 2020Sampling using SU(N) gauge equivariant flowscited by 83
  6. 2019Learning to Optimize Multigrid PDE Solverscited by 79
  7. 2020Learning Algebraic Multigrid Using Graph Neural Networkscited by 54
  8. 2020Lattice gauge equivariant convolutional neural networkscited by 45
  9. 2022Gauge-equivariant flow models for sampling in lattice field theories with pseudofermionscited by 30
  10. 2021Learning optimal multigrid smoothers via neural networkscited by 17
  11. 2020MGIC: Multigrid-in-Channels Neural Network Architecturescited by 8
  12. 2022MGiaD: Multigrid in all dimensions. Efficiency and robustness by coarsening in resolution and channel dimensionscited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 1; 2025: 2; 2026: 2.

8 papers.

  1. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23
  2. 2023Geometrical aspects of lattice gauge equivariant convolutional neural networkscited by 6
  3. 2023Gauge-equivariant pooling layers for preconditioners in lattice QCDcited by 5
  4. 2024Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural networkcited by 2
  5. 2026Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theoriescited by 2
  6. 2026Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theoriescited by 1
  7. 2025Graph Lineages and Skeletal Graph Productscited by 0
  8. 2025Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theorycited by 0