Fully convolutional diffusion models trained on small lattices transfer to unseen larger volumes for 2D/3D phi^4 sampling across phases, matching or beating same-size training on most observables.
Conditional Normalizing flow for Monte Carlo sampling in lattice scalar field theory
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abstract
The cost of Monte Carlo sampling of lattice configurations is very high in the critical region of lattice field theory due to the high correlation between the samples. This paper suggests a Conditional Normalizing Flow (C-NF) model for sampling lattice configurations in the critical region to solve the problem of critical slowing down. We train the C-NF model using samples generated by Hybrid Monte Carlo (HMC) in non-critical regions with low simulation costs. The trained C-NF model is employed in the critical region to build a Markov chain of lattice samples with negligible autocorrelation. The C-NF model is used for both interpolation and extrapolation to the critical region of lattice theory. Our proposed method is assessed using the 1+1-dimensional scalar $\phi^4$ theory. This approach enables the construction of lattice ensembles for many parameter values in the critical region, which reduces simulation costs by avoiding the critical slowing down.
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Out-of-equilibrium simulations with open-to-periodic boundary switching plus a tailored stochastic normalizing flow enable efficient topology sampling in the continuum limit of four-dimensional SU(3) Yang-Mills theory.
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Diffusion Models for Sampling Near Criticality in Lattice Field Theories
Fully convolutional diffusion models trained on small lattices transfer to unseen larger volumes for 2D/3D phi^4 sampling across phases, matching or beating same-size training on most observables.
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Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
Out-of-equilibrium simulations with open-to-periodic boundary switching plus a tailored stochastic normalizing flow enable efficient topology sampling in the continuum limit of four-dimensional SU(3) Yang-Mills theory.