Learning Trivializing Flows

TL;DR

This paper introduces a modified Hybrid Monte Carlo algorithm utilizing Normalizing Flows to reduce autocorrelations in lattice gauge theory sampling, demonstrating improved efficiency and scalability in a 2D φ^4 theory.

Contribution

It presents a novel HMC variant that employs trivializing flows with Normalizing Flows, enabling more efficient sampling by reducing autocorrelations and demonstrating scalability towards the continuum limit.

Findings

Reduced autocorrelation times compared to standard HMC

Effective training at small volumes for use in physical conditions

Scalable performance towards the continuum limit

Abstract

The recent introduction of Machine Learning techniques, especially Normalizing Flows, for the sampling of lattice gauge theories has shed some hope on improving the sampling efficiency of the traditional Hybrid Monte Carlo (HMC) algorithm. In this work we study a modified HMC algorithm that draws on the seminal work on trivializing flows by L\"uscher. Autocorrelations are reduced by sampling from a simpler action that is related to the original action by an invertible mapping realised through Normalizing Flows models with a minimal set of training parameters. We test the algorithm in a $\phi^{4}$ theory in 2D where we observe reduced autocorrelation times compared with HMC, and demonstrate that the training can be done at small unphysical volumes and used in physical conditions. We also study the scaling of the algorithm towards the continuum limit under various assumptions on the network architecture.