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。

流模型在相关格点 QCD 系列生成中的应用

Applications of flow models to the generation of correlated lattice QCD  ensembles

Sampling from known probability distributions is a ubiquitous task in
computational science, underlying calculations in domains from linguistics to
biology and physics. Generative machine-learning (ML) models have emerged as a
promising tool in this space, building on the success of this approach in
applications such as image, text, and audio generation. Often, however,
generative tasks in scientific domains have unique structures and features --
such as complex symmetries and the requirement of exactness guarantees -- that
present both challenges and opportunities for ML. This Perspective outlines the
advances in ML-based sampling motivated by lattice quantum field theory, in
particular for the theory of quantum chromodynamics. Enabling calculations of
the structure and interactions of matter from our most fundamental
understanding of particle physics, lattice quantum chromodynamics is one of the
main consumers of open-science supercomputing worldwide. The design of ML
algorithms for this application faces profound challenges, including the
necessity of scaling custom ML architectures to the largest supercomputers, but
also promises immense benefits, and is spurring a wave of development in
ML-based sampling more broadly. In lattice field theory, if this approach can
realize its early promise it will be a transformative step towards
first-principles physics calculations in particle, nuclear and condensed matter
physics that are intractable with traditional approaches.

从已知的概率分布中采样是计算科学中普遍存在的任务，为从语言学到生物学和物理学的各个领域的计算提供支持。然而，科学领域中的生成任务具有独特的结构和特征，如复杂对称性和精确性保证的要求，对机器学习提出了挑战和机会。本文介绍了以格点量子场论为动机的基于机器学习的采样方法的进展，尤其是在量子色动力学理论的应用中。这种方法使我们能够从粒子物理学的最基本理解中计算物质的结构和相互作用，在全球范围内是开放科学超级计算的主要消费者。本文还涵盖了该应用中的机器学习算法设计所面临的深层次挑战，包括将自定义机器学习架构扩展到最大的超级计算机，但也揭示了巨大的潜力和在机器学习采样领域中发展的浪潮。在格点场论中，如果这种方法能够实现早期的承诺，将是迈向无法用传统方法计算的粒子、核和凝聚态物理的第一性原理物理计算的转变性进展。