Stochastic normalizing flows for lattice field theory

TL;DR

This paper introduces stochastic normalizing flows, a hybrid deep generative model combining normalizing flows and Monte Carlo methods, applied to lattice field theory, with theoretical links to Jarzynski's equality and practical examples in 2D phi^4 theory.

Contribution

It presents a novel hybrid algorithm for sampling in lattice field theory, connecting deep generative models with non-equilibrium statistical mechanics.

Findings

Theoretical connection to Jarzynski's equality established.

Application demonstrated on 2D phi^4 field theory.

Potential for improved sampling efficiency in lattice simulations.

Abstract

Stochastic normalizing flows are a class of deep generative models that combine normalizing flows with Monte Carlo updates and can be used in lattice field theory to sample from Boltzmann distributions. In this proceeding, we outline the construction of these hybrid algorithms, pointing out that the theoretical background can be related to Jarzynski's equality, a non-equilibrium statistical mechanics theorem that has been successfully used to compute free energy in lattice field theory. We conclude with examples of applications to the two-dimensional $\phi^4$ field theory.