Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these correlations can be exploited for variance reduction in the computation of observables. Three different proof-of-concept applications are demonstrated using a novel residual flow architecture: continuum limits of gauge theories, the mass dependence of QCD observables, and hadronic matrix elements based on the Feynman-Hellmann approach. In all three cases, it is shown that statistical uncertainties are significantly reduced when machine-learned flows are incorporated as compared with the same calculations performed with uncorrelated ensembles or direct reweighting.

翻译：机器学习正则化流可用于格点量子场论中，生成不同作用量参数下统计关联的格点规范场系综。本文展示了如何利用这些关联降低观测量的计算方差。通过新型残差流架构，论证了三种概念验证性应用：规范理论的连续极限、QCD观测量的质量依赖性，以及基于费曼-海尔曼方法的强子矩阵元计算。在所有三种情况下，与使用非关联系综或直接重加权进行的相同计算相比，引入机器学习流的统计不确定性均显著降低。