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Machine learning for four-dimensional SU(3) lattice gauge theories

arXiv 2604.12416 ↗First posted 14 Apr 2026hep-lat cs.LGcited by 0

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Abstract (arXiv)

In this review I summarize how machine learning can be used in lattice gauge theory simulations and what ap-proaches are currently available to improve the sampling of gauge field configurations, with a focus on applications in four-dimensional SU(3) gauge theories. These include approaches based on generative machine-learning models such as (stochastic) normalizing flows and diffusion processes, and an approach based on renormalization group (RG) transformations, more specifically the machine learning of RG-improved gauge actions using gauge-equivariant convolutional neural networks. In particular, I present scaling results for a machine-learned fixed-point action in four-dimensional SU(3) gauge theory towards the continuum limit. The results include observables based on the classically perfect gradient-flow scales, which are free of tree-level lattice artefacts to all orders, and quantities related to the static potential and the deconfinement transition.

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References · 20

  1. 2020Equivariant flow-based sampling for lattice gauge theorycited by 102
  2. 2020Lattice gauge equivariant convolutional neural networkscited by 45
  3. 2022Gauge-equivariant flow models for sampling in lattice field theories with pseudofermionscited by 30
  4. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited by 26
  5. 2022Stochastic normalizing flows as non-equilibrium transformationscited by 25
  6. 2023Diffusion Models as Stochastic Quantization in Lattice Field Theorycited by 24
  7. 2023Normalizing flows for lattice gauge theory in arbitrary space-time dimensioncited by 23
  8. 2024Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defectscited by 13
  9. 2024Applications of flow models to the generation of correlated lattice QCD ensemblescited by 10
  10. 2024Scaling of Stochastic Normalizing Flows in SU(3) lattice gauge theorycited by 10
  11. 2025Physics-Conditioned Diffusion Models for Lattice Gauge Theorycited by 9
  12. 2024Practical applications of machine-learned flows on gauge fieldscited by 6
8 more
  1. 2025Scaling flow-based approaches for topology sampling in SU(3) gauge theorycited by 6
  2. 2025Combining complex Langevin dynamics with score-based and energy-based diffusion modelscited by 5
  3. 2023Fixed point actions from convolutional neural networkscited by 3
  4. 2026Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theorycited by 3
  5. 2024Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural networkcited by 2
  6. 2026Variance reduction in lattice QCD observables via normalizing flowscited by 2
  7. 2024Exploring gauge-fixing conditions with gradient-based optimizationcited by 1
  8. 2026A scalable flow-based approach to mitigate topological freezingcited by 1

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