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Equivariant flow-based sampling for lattice gauge theory

arXiv 2003.06413 ↗First posted 13 Mar 2020hep-lat cond-mat.stat-mech cs.LGcited by 103

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Abstract (arXiv)

We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge-invariant by construction. We demonstrate the application of this framework to U(1) gauge theory in two spacetime dimensions, and find that near critical points in parameter space the approach is orders of magnitude more efficient at sampling topological quantities than more traditional sampling procedures such as Hybrid Monte Carlo and Heat Bath.

Key facts. Cited by 103 papers in the map (data through 14 Oct 2026). First posted on arXiv 13 Mar 2020.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 26; 2022: 18; 2023: 22; 2024: 8; 2025: 17; 2026: 12.

103 papers.

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  1. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 150
  2. 2023Equivariant flow matchingcited by 135
  3. 2022Predicting Physics in Mesh-reduced Space with Temporal Attentioncited by 84
  4. 2023Spontaneous Symmetry Breaking in Generative Diffusion Modelscited by 80
  5. 2021A Living Review of Machine Learning for Particle Physicscited by 78
  6. 2023Swallowing the Bitter Pill: Simplified Scalable Conformer Generationcited by 56
  7. 2022Learning Lattice Quantum Field Theories with Equivariant Continuous Flowscited by 37
  8. 2023EDGI: Equivariant Diffusion for Planning with Embodied Agentscited by 36
  9. 2021Machine-learning hidden symmetriescited by 31
  10. 2021Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlatorscited by 29
  11. 2025Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physicscited by 29
  12. 2022Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inferencecited by 28
38 more
  1. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited by 26
  2. 2023Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspectivecited by 26
  3. 2022Stochastic normalizing flows as non-equilibrium transformationscited by 25
  4. 2021Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flowscited by 24
  5. 2023Diffusion Models as Stochastic Quantization in Lattice Field Theorycited by 24
  6. 2022Symmetry Group Equivariant Architectures for Physicscited by 23
  7. 2022Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flowscited by 23
  8. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23
  9. 2023Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principlescited by 22
  10. 2025Tilt Matching for Scalable Sampling and Fine-Tuningcited by 22
  11. 2021Topological Obstructions to Autoencodingcited by 20
  12. 2024Dynamical Measure Transport and Neural PDE Solvers for Samplingcited by 20
  13. 2021Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Modelscited by 18
  14. 2021Generalization capabilities of translationally equivariant neural networkscited by 18
  15. 2021Quantum field-theoretic machine learningcited by 16
  16. 2021Ab-initio study of interacting fermions at finite temperature with neural canonical transformationcited by 16
  17. 2023Renormalizing Diffusion Modelscited by 16
  18. 2022Applications of Machine Learning to Lattice Quantum Field Theorycited by 14
  19. 2023Generative Diffusion Models for Lattice Field Theorycited by 13
  20. 2021Differentiable Physics: A Position Piececited by 12
  21. 2022Hierarchical autoregressive neural networks for statistical systemscited by 12
  22. 2023Sampling the lattice Nambu-Goto string using Continuous Normalizing Flowscited by 12
  23. 2025Generalised Flow Maps for Few-Step Generative Modelling on Riemannian Manifoldscited by 12
  24. 2021Equivariant Finite Normalizing Flowscited by 11
  25. 2022Path-Gradient Estimators for Continuous Normalizing Flowscited by 11
  26. 2022Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulationcited by 11
  27. 2021Continuous normalizing flows on manifoldscited by 10
  28. 2021Latent Space Refinement for Deep Generative Modelscited by 10
  29. 2021Implicit Riemannian Concave Potential Mapscited by 10
  30. 2021Machine Learning of Thermodynamic Observables in the Presence of Mode Collapsecited by 10
  31. 2022Simulating 2+1D Lattice Quantum Electrodynamics at Finite Density with Neural Flow Wavefunctionscited by 10
  32. 2024On learning higher-order cumulants in diffusion modelscited by 10
  33. 2023Gauge-equivariant neural networks as preconditioners in lattice QCDcited by 9
  34. 2025Physics-Conditioned Diffusion Models for Lattice Gauge Theorycited by 9
  35. 2021Deep Learning Hamiltonian Monte Carlocited by 7
  36. 2022Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fieldscited by 7
  37. 2022Deep Variational Free Energy Approach to Dense Hydrogencited by 7
  38. 2023Learning Distributions on Manifolds with Free-Form Flowscited by 7

50 most cited of 103 All 103 (JSON)