mlsanityData to 7 Oct 2026

Flow-based sampling for fermionic lattice field theories

arXiv 2106.05934 ↗First posted 10 Jun 2021hep-lat cond-mat.stat-mech cs.LGcited by 27

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Abstract (arXiv)

Algorithms based on normalizing flows are emerging as promising machine learning approaches to sampling complicated probability distributions in a way that can be made asymptotically exact. In the context of lattice field theory, proof-of-principle studies have demonstrated the effectiveness of this approach for scalar theories, gauge theories, and statistical systems. This work develops approaches that enable flow-based sampling of theories with dynamical fermions, which is necessary for the technique to be applied to lattice field theory studies of the Standard Model of particle physics and many condensed matter systems. As a practical demonstration, these methods are applied to the sampling of field configurations for a two-dimensional theory of massless staggered fermions coupled to a scalar field via a Yukawa interaction.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). Builds on 1 of its 55 references that are in the map. First posted on arXiv 10 Jun 2021.

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1 of 55 references.

References · 1

  1. 2018A high-bias, low-variance introduction to Machine Learning for physicistscited by 108

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 6; 2023: 7; 2024: 5; 2025: 4; 2026: 2.

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  1. 2023Learning Interpolations between Boltzmann Densitiescited by 42
  2. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited 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. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23
  7. 2022Applications of Machine Learning to Lattice Quantum Field Theorycited by 14
  8. 2023Sampling the lattice Nambu-Goto string using Continuous Normalizing Flowscited by 12
  9. 2024Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flowscited by 9
  10. 2023Geometrical aspects of lattice gauge equivariant convolutional neural networkscited by 6
  11. 2024AdvNF: Reducing Mode Collapse in Conditional Normalising Flows using Adversarial Learningcited by 6
  12. 2024Practical applications of machine-learned flows on gauge fieldscited by 6
15 more
  1. 2025Scaling flow-based approaches for topology sampling in SU(3) gauge theorycited by 6
  2. 2021Machine Learning Trivializing Maps: A First Step Towards Understanding How Flow-Based Samplers Scale Upcited by 5
  3. 2022Simulating first-order phase transition with hierarchical autoregressive networkscited by 5
  4. 2021Machine Learning in Nuclear Physicscited by 4
  5. 2022Estimating the Euclidean quantum propagator with deep generative modeling of Feynman pathscited by 3
  6. 2023Understanding Deep Generative Models with Generalized Empirical Likelihoodscited by 3
  7. 2023Training normalizing flows with computationally intensive target probability distributionscited by 2
  8. 2025Neural Triangular Transport Maps: A New Approach Towards Sampling in Lattice QCDcited by 2
  9. 2022Deformations of Boltzmann Distributionscited by 1
  10. 2024Multi-Lattice Sampling of Quantum Field Theories via Neural Operator-based Flowscited by 1
  11. 2025NeuMC -- a package for neural sampling for lattice field theoriescited by 1
  12. 2026A scalable flow-based approach to mitigate topological freezingcited by 1
  13. 2024Flow Perturbation to Accelerate Unbiased Sampling of Boltzmann distributioncited by 0
  14. 2025A Critical Review of Monte Carlo Algorithms Balancing Performance and Probabilistic Accuracy with AI Augmented Frameworkcited by 0
  15. 2026Sampling the Schwinger Model with Gauge-Equivariant Diffusioncited by 0