Control variates with neural networks

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.