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 outof-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.

Decimation map in 2D for accelerating HMC

“…The state of the art algorithm for the gauge field generation in QCD is the Hybrid Monte Carlo (HMC) [1], and there are two major directions to cope with the critical slowing down in this algorithmic framework (see [2,3] for reviews). One is to align the velocity in the molecular dynamics (MD) among all the Fourier modes [4][5][6][7][8], and the other is to construct a field transformation such that the resulting effective action has advantageous sampling properties [10,11] (see also [12][13][14][15][16][17][18]).…”