Variance reduction in lattice QCD observables via normalizing flows

2026-03-03

AI Summary

This work addresses the severe variance problem in computing gluonic observables in lattice quantum chromodynamics (QCD), which critically limits both efficiency and precision. For the first time, normalizing flows are introduced into four-dimensional SU(3) Yang–Mills theory and two-flavor QCD to construct unbiased, low-variance estimators for gluonic operator insertions that depend on derivatives of the action with respect to its parameters. The method achieves a 10- to 60-fold reduction in variance for glueball correlation functions and gluonic matrix elements relevant to hadron structure. Notably, the variance suppression exhibits approximate independence from lattice volume, enabling transferability across volumes and substantially reducing training costs.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Normalizing flows can be used to construct unbiased, reduced-variance estimators for lattice field theory observables that are defined by a derivative with respect to action parameters. This work implements the approach for observables involving gluonic operator insertions in the SU(3) Yang-Mills theory and two-flavor Quantum Chromodynamics (QCD) in four space-time dimensions. Variance reduction by factors of $10$-$60$ is achieved in glueball correlation functions and in gluonic matrix elements related to hadron structure, with demonstrated computational advantages. The observed variance reduction is found to be approximately independent of the lattice volume, so that volume transfer can be utilized to minimize training costs.

Problem

• variance reduction
• lattice QCD
• gluonic observables
• normalizing flows
• statistical noise

Innovation

• normalizing flows
• variance reduction
• lattice QCD
• gluonic observables
• volume transfer