Gauge-equivariant neural networks as preconditioners in lattice QCD

2023/01/01 by Christoph Lehner, Lehner, Christoph, Tilo Wettig +1 · 6 citations
Mathematics · Medicine · Physics and Astronomy · #Advanced Neuroimaging Techniques and Applications #Algebra over a field #Algorithm #Artificial intelligence #Artificial neural network #Atomic and Subatomic Physics Research #Combinatorics #Computer science #Equivariant map #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Gauge (firearms) #Gauge theory #Geometry #Grid #High Energy Physics - Lattice (hep-lat) #Iterative method #Lattice (music) #Lattice QCD #Lattice gauge theory #Machine Learning (cs.LG) #Materials science #Mathematics #Numerical Analysis (math.NA) #Particle physics #Physics #Preconditioner #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Theoretical physics #Topology (electrical circuits)

paper · pdf · doi:10.48550/arxiv.2302.05419

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2023/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We demonstrate that a state-of-the-art multigrid preconditioner can be learned efficiently by gauge-equivariant neural networks. We show that the models require minimal retraining 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.

Cited by

• Reinforcement Learning techniques for the flavor problem in particle physics
• Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory
• Graph Lineages and Skeletal Graph Products
• Accelerating multigrid with streaming chiral SVD for Wilson fermions in lattice QCD
• Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories
• A first look at Structured-Multiscale Algebraic Multigrid for Lattice Field Theory

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