Machine-learning techniques as noise reduction strategies in lattice calculations of the muon $g-2$

TL;DR

This paper explores the use of machine learning as a cost-effective noise reduction method in lattice calculations of the muon g-2, aiming to improve accuracy and efficiency in complex quantum field computations.

Contribution

It introduces machine learning techniques to estimate lattice QCD contributions, offering a novel approach to reduce computational costs while maintaining precision.

Findings

ML models provide approximate estimates of mixed contributions

Bias correction ensures exact results from ML estimates

Potential for significant cost reduction in lattice calculations

Abstract

Lattice calculations of the hadronic contributions to the muon anomalous magnetic moment are numerically highly demanding due to the necessity of reaching total errors at the sub-percent level. Noise-reduction techniques such as low-mode averaging have been applied successfully to determine the vector-vector correlator with high statistical precision in the long-distance regime, but display an unfavourable scaling in terms of numerical cost. This is particularly true for the mixed contribution in which one of the two quark propagators is described in terms of low modes. Here we report on an ongoing project aimed at investigating the potential of machine learning as a cost-effective tool to produce approximate estimates of the mixed contribution, which are then bias-corrected to produce an exact result. A second example concerns the determination of electromagnetic isospin-breaking corrections by combining the predictions from a trained model with a bias correction.