Control variates with neural networks

TL;DR

This paper introduces a neural network-based method for constructing control variates to reduce stochastic noise in lattice QCD calculations, demonstrating significant variance reduction in scalar and gauge theories.

Contribution

It presents a novel neural network framework for automatic control variate construction, improving noise reduction over heuristic methods in complex lattice QCD simulations.

Findings

Significant variance reduction achieved in 1+1D scalar field theory

Effective noise suppression in strong coupling regimes

Potential applicability to diverse gauge theories

Abstract

The precision of lattice QCD calculations is often hindered by the stochastic noise inherent in these methods. The control variates method can provide an effective noise reduction but are typically constructed using heuristic approaches, which may be inadequate for complex theories. In this work, we introduce a neural network-based framework for parametrizing control variates, eliminating the reliance on manual guesswork. Using $1+1$ dimensional scalar field theory as a test case, we demonstrate significant variance reduction, particularly in the strong coupling regime. Furthermore, we extend this approach to gauge theories, showcasing its potential to tackle signal-to-noise problems in diverse lattice QCD applications.