Machine-Learning Prediction for Quasi-PDF Matrix Elements

TL;DR

This paper investigates the use of machine learning algorithms to predict lattice QCD correlators, aiming to reduce computational costs in LaMET-based hadron structure calculations, with promising results for kaon, eta_s, and nucleon PDFs.

Contribution

The study demonstrates that gradient-boosting decision trees and linear models can reliably predict lattice QCD matrix elements, potentially decreasing computational effort in high-precision LaMET calculations.

Findings

ML models accurately predict target observables.

Predictions are more reliable for correlators with smaller displacements.

Machine learning reduces the need for extensive lattice computations.

Abstract

There have been rapid developments in the direct calculation in lattice QCD (LQCD) of the Bjorken-$x$ dependence of hadron structure through large-momentum effective theory (LaMET). LaMET overcomes the previous limitation of LQCD to moments (that is, integrals over Bjorken-$x$) of hadron structure, allowing LQCD to directly provide the kinematic regions where the experimental values are least known. LaMET requires large-momentum hadron states to minimize its systematics and allow us to reach small-$x$ reliably. This means that very fine lattice spacing to minimize lattice artifacts at order $(P_z a)^n$ will become crucial for next-generation LaMET-like structure calculations. Furthermore, such calculations require operators with long Wilson-link displacements (in finer lattice units), increasing the communication costs relative to that of the propagator inversion. In this work, we explore whether machine-learning (ML) algorithms can make correlator predictions to reduce the computational cost of these LQCD calculations. We consider two algorithms, gradient-boosting decision tree and linear models, applied to LaMET data, the matrix elements needed to determine the kaon and $\eta_s$ unpolarized parton distribution functions (PDFs), meson distribution amplitude (DA), and the nucleon gluon PDF. We find that both algorithms can reliably predict the target observables with different fit quality and systematic errors. The predictions from smaller displacement $z$ to larger ones work better than those for momentum $p$ due to the higher correlation among the data.