A Monte Carlo estimator of flow fields for sampling and noise problems

TL;DR

This paper introduces a Monte Carlo method for estimating flow fields in lattice field theory, reducing noise and enabling improved sampling and training data generation for machine learning applications.

Contribution

A novel Monte Carlo estimator for flow fields that mitigates statistical noise, applicable to lattice field theory and machine learning data generation.

Findings

Effective in U(1) transport problems

Reduces noise in SU(N) glueball correlator calculations

Enhances sampling efficiency in complex field theories

Abstract

Learned field transformations may help address ubiquitous critical slowing down and signal-to-noise problems in lattice field theory. In the context of an annealed sequence of distributions, field transformations are defined by integrating flow fields that exactly solve a local transport problem. These proceedings discuss a new Monte Carlo approach to evaluating these flow fields, which can then be used directly in such contexts or as a means of generating unbiased training data for machine learning approaches. By defining the Monte Carlo estimator using coupled Langevin noise, the statistical noise in the required integrals is significantly mitigated. Demonstrations of the method include a U(1) transport problem and an SU(N) glueball correlator.