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This research applies neural generative samplers, specifically flow-matching techniques, to lattice field theory to address the high computational costs of training and evaluating models in physics simulations. By projecting trained velocities onto vector fields derived from lattice operators, the study successfully separates collective variables like magnetization from momentum fluctuations to improve distribution overlap. While the method shows promise for specific parameterizations, its effectiveness diminishes at larger volumes where proposal-target overlaps deteriorate significantly.
Operator-Guided Model Reduction for Generative Sampling in Lattice Field Theory
arXiv:2605.11199v2 Announce Type: replace-cross Abstract: Neural generative samplers for lattice field theory can be costly to train and evaluate. When they miss modes or assign them incorrect relative weights, biased observables do not reveal which collective variables are responsible. We project a trained flow-matching velocity onto vector fields built from lattice operators and Fourier modes. In two-dimensional lattice $\phi^4$ theory, the projection separates changes in the overall magnetization from the lowest nonzero-momentum fluctuations and guides an explicit invertible proposal that treats them separately. Allowing the amplitude of the lowest nonzero-momentum fluctuations to depend on the magnetization improves the overlap between the proposal and target distributions, while the same two-parameter modification at higher momenta gives smaller improvements. The Metropolis--Hastings correction defines a Markov chain with the target Boltzmann distribution as its stationary law, and the normalized proposal density yields finite-volume partition-function estimates consistent with an independent HMC calculation. At the larger tested volume, the overlap between the proposal and target distributions deteriorates substantially, limiting the range over which the same parameterization remains effective.
Abstract:Neural generative samplers for lattice field theory can be costly to train and evaluate. When they miss modes or assign them incorrect relative weights, biased observables do not reveal which collective variables are responsible. We project a trained flow-matching velocity onto vector fields built from lattice operators and Fourier modes. In two-dimensional lattice $\phi^4$ theory, the projection separates changes in the overall magnetization from the lowest nonzero-momentum fluctuations and guides an explicit invertible proposal that treats them separately. Allowing the amplitude of the lowest nonzero-momentum fluctuations to depend on the magnetization improves the overlap between the proposal and target distributions, while the same two-parameter modification at higher momenta gives smaller improvements. The Metropolis--Hastings correction defines a Markov chain with the target Boltzmann distribution as its stationary law, and the normalized proposal density yields finite-volume partition-function estimates consistent with an independent HMC calculation. At the larger tested volume, the overlap between the proposal and target distributions deteriorates substantially, limiting the range over which the same parameterization remains effective.
High Energy Physics - Lattice (hep-lat); Machine Learning (cs.LG)
arXiv:2605.11199 [hep-lat]
(or arXiv:2605.11199v2 [hep-lat] for this version)
https://doi.org/10.48550/arXiv.2605.11199 Focus to learn more arXiv-issued DOI via DataCite
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