用机器学习提升四维SU(3)规范理论采样效率，加速物理结果逼近连续极限。
Machine learning for four-dimensional SU(3) lattice gauge theories
- 用生成模型和重整化群神经网络学习改进的规范作用量
- 在4D SU(3)理论中实现接近连续极限的精确观测量计算
- 适合高能物理与量子场论研究者关注机器学习新方法
本文综述了机器学习在格点规范理论模拟中的应用，重点介绍用于提升四维SU(3)规范场构型采样效率的方法。包括基于生成式模型（如随机归一化流和扩散过程）以及基于重整化群（RG）变换的方法，特别是利用规范等变卷积神经网络学习改进的RG作用量。特别展示了机器学习得到的固定点作用量在四维SU(3)规范理论中向连续极限收敛的尺度行为。结果涵盖基于经典完美梯度流尺度的可观测量（对所有阶次无树级格点误差），以及与静态势和去禁闭相变相关的物理量。
原文摘要 · Abstract (English)
In this review I summarize how machine learning can be used in lattice gauge theory simulations and what ap\-proaches are currently available to improve the sampling of gauge field configurations, with a focus on applications in four-dimensional SU(3) gauge theories. These include approaches based on generative machine-learning models such as (stochastic) normalizing flows and diffusion processes, and an approach based on renormalization group (RG) transformations, more specifically the machine learning of RG-improved gauge actions using gauge-equivariant convolutional neural networks. In particular, I present scaling results for a machine-learned fixed-point action in four-dimensional SU(3) gauge theory towards the continuum limit. The results include observables based on the classically perfect gradient-flow scales, which are free of tree-level lattice artefacts to all orders, and quantities related to the static potential and the deconfinement transition.
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