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.

利用机器学习的归一化流，在格点量子场论上可以生成具有统计相关性的不同作用参数下的格子规范场集合，本研究展示如何利用这些相关性来减少计算可观测量时的方差。通过一种新颖的残差流架构展示了三种概念验证应用：规范理论的连续极限、量子色动力学可观测量的质量依赖和基于费曼 - 赫尔曼方法的强子矩阵元素。在这三种情况下，相比于使用不相关的集合或直接改重赋权重进行的相同计算，显示出机器学习流的加入可以显著减小统计误差。