Learning Lattice Quantum Field Theories with Equivariant Continuous Flows

Abstract

We propose a novel machine learning method for sampling from the high-dimensional probability distributions of Lattice Field Theories, which is based on a single neural ODE layer and incorporates the full symmetries of the problem. We test our model on the ${\varphi }^4$ theory, showing that it systematically outperforms previously proposed flow-based methods in sampling efficiency, and the improvement is especially pronounced for larger lattices. Furthermore, we demonstrate that our model can learn a continuous family of theories at once, and the results of learning can be transferred to larger lattices. Such generalizations further accentuate the advantages of machine learning methods.

arXiv comment17 pages, 9 figures, 1 table; slightly expanded published version, added 2 figures and 2 sections to appendix

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Cited by in corpus (19)

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• Diffusion Models as Stochastic Quantization in Lattice Field Theory
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• Numerical determination of the width and shape of the effective string using Stochastic Normalizing Flows
• Efficient mapping of phase diagrams with conditional Boltzmann Generators
• Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural network
• On learning higher-order cumulants in diffusion models
• Parallel Tempered Metadynamics: Overcoming potential barriers without surfing or tunneling
• Gauge covariant neural network for quarks and gluons
• Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
• Machine-learned RG-improved gauge actions and classically perfect gradient flows
• Non-Perturbative Trivializing Flows for Lattice Gauge Theories
• Bayesian RG Flow in Neural Network Field Theories
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• Efficient identification of critical regions via Flow Matching-based Monte Carlo initialization
• Group-Equivariant Diffusion Models for Lattice Field Theory
• NeuMC -- a package for neural sampling for lattice field theories