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Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows

arXiv 2110.02673 ↗First posted 6 Oct 2021cs.LG cond-mat.stat-mech hep-latcited by 24

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Abstract (arXiv)

We propose a continuous normalizing flow for sampling from the high-dimensional probability distributions of Quantum Field Theories in Physics. In contrast to the deep architectures used so far for this task, our proposal is based on a shallow design and incorporates the symmetries of the problem. We test our model on the φ4 theory, showing that it systematically outperforms a realNVP baseline in sampling efficiency, with the difference between the two increasing for larger lattices. On the largest lattice we consider, of size 32× 32, we improve a key metric, the effective sample size, from 1% to 66% w.r.t. the realNVP baseline.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 13 of its 24 references that are in the map. First posted on arXiv 6 Oct 2021.

Builds on

13 of 24 references.

References · 13

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  4. 2016Density estimation using Real NVPcited by 2,029
  5. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  6. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  7. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 147
  8. 2019Machine learning for molecular simulationcited by 109
  9. 2020Equivariant flow-based sampling for lattice gauge theorycited by 102
  10. 2021Provably efficient machine learning for quantum many-body problemscited by 91
  11. 2021Introduction to Normalizing Flows for Lattice Field Theorycited by 35
  12. 2021Flow-based sampling for fermionic lattice field theoriescited by 27
1 more
  1. 2021Flow-based sampling for multimodal and extended-mode distributions in lattice field theorycited by 25

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 8; 2023: 5; 2024: 5; 2025: 2; 2026: 2.

24 papers.

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  1. 2022Continual Repeated Annealed Flow Transport Monte Carlocited by 66
  2. 2023Learning Interpolations between Boltzmann Densitiescited by 42
  3. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited by 26
  4. 2022Stochastic normalizing flows as non-equilibrium transformationscited by 25
  5. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23
  6. 2022Applications of Machine Learning to Lattice Quantum Field Theorycited by 14
  7. 2023Generative Diffusion Models for Lattice Field Theorycited by 13
  8. 2023Sampling the lattice Nambu-Goto string using Continuous Normalizing Flowscited by 12
  9. 2021Machine Learning of Thermodynamic Observables in the Presence of Mode Collapsecited by 10
  10. 2022Path-Gradient Estimators for Continuous Normalizing Flowscited by 10
  11. 2024On learning higher-order cumulants in diffusion modelscited by 10
  12. 2024Bayesian RG Flow in Neural Network Field Theoriescited by 9
12 more
  1. 2025Physics-Conditioned Diffusion Models for Lattice Gauge Theorycited by 9
  2. 2023Geometrical aspects of lattice gauge equivariant convolutional neural networkscited by 6
  3. 2024Numerical determination of the width and shape of the effective string using Stochastic Normalizing Flowscited by 6
  4. 2024Non-Perturbative Trivializing Flows for Lattice Gauge Theoriescited by 3
  5. 2025Demonstrating Real Advantage of Machine-Learning-Enhanced Monte Carlo for Combinatorial Optimizationcited by 3
  6. 2022Neural Simulated Annealingcited by 2
  7. 2022Amortized Bayesian Inference of GISAXS Data with Normalizing Flowscited by 1
  8. 2022Deformations of Boltzmann Distributionscited by 1
  9. 2024Multi-Lattice Sampling of Quantum Field Theories via Neural Operator-based Flowscited by 1
  10. 2026The critical slowing down in training diffusion modelscited by 1
  11. 2021Lattice gauge symmetry in neural networkscited by 0
  12. 2026Accurate Sampling from Diffusion Modelscited by 0