用机器学习降低格点量子色动力学计算中的方差，提升精度。
Learning the generating functional for variance reduction in lattice QCD
- 用可逆神经网络建模生成泛函，编码场论信息。
- 对胶球关联函数和威尔逊环实现最高达千倍的方差降低。
- 适合高精度格点场论与粒子物理模拟的研究者。
量子场论中的生成泛函为构造关联函数提供了自然框架，可通过源算符的导数表示。本文提出一种方法，利用机器学习的归一化流（normalizing flows）来编码生成泛函，从而系统性地减少任意N点玻色子算符关联函数在格点规范场理论计算中的方差。该方法可逼近无噪声的关联函数估计。我们在量子色动力学（QCD）与杨-米尔斯理论中验证了该方法，应用于胶球关联函数和威尔逊环的计算，结果表明方差最高可降低三个数量级。
原文摘要 · Abstract (English)
The generating functional in quantum field theory provides the natural framework for constructing correlation functions as derivatives with respect to source operators. We present a methodology that leverages machine-learned normalizing flows to reduce the variance of arbitrary $N$-point correlation functions of bosonic operators in lattice gauge field theory calculations by encoding a representation of the generating functional. We show that it is possible to systematically approach noiseless estimators of correlation functions in this framework. We demonstrate this methodology with applications to calculations of glueball correlation functions and Wilson loops in Quantum Chromodynamics and Yang-Mills theory. The results show up to three orders of magnitude variance reduction.
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