Stochastic normalizing flows as non-equilibrium transformations

Abstract

Normalizing flows are a class of deep generative models that provide a promising route to sample lattice field theories more efficiently than conventional Monte Carlo simulations. In this work we show that the theoretical framework of stochastic normalizing flows, in which neural-network layers are combined with Monte Carlo updates, is the same that underlies out-of-equilibrium simulations based on Jarzynski's equality, which have been recently deployed to compute free-energy differences in lattice gauge theories. We lay out a strategy to optimize the efficiency of this extended class of generative models and present examples of applications.

arXiv comment1+28 pages, 8 figures; v2: 1+29 pages, 8 figures, added references, discussion in section 4 improved; v3: 1+31 pages, 9 figures, added references, discussion in section 4 expanded, matches published version

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• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions
• Learning Trivializing Gradient Flows for Lattice Gauge Theories
• Fourier-Flow model generating Feynman paths
• Flow-based density of states for complex actions
• Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths
• Free Energy Evaluation Using Marginalized Annealed Importance Sampling