发表机构
Center for Computational Sciences, University of Tsukuba; Department of Information and Mathematical Sciences, Tokyo Woman’s Christian University; RIKEN Center for Computational Science; Department of Physics, Kyoto University（筑波大学计算科学中心; 东京女子基督教大学信息与数学科学学院; 理化学研究所计算科学中心; 京都大学物理学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过格点QCD数据集，以两种监督学习方法估计逆狄拉克算子迹量，校正偏差后可用于评估手征凝聚累积量，还能降低狄拉克逆运算成本。
AI 中文摘要
我们开展了一项回顾性案例研究，基于固定格点量子色动力学（lattice QCD）数据集，对逆狄拉克算子迹量 $\ ext{Tr}\,M^{-n}$（$n=1,2,3,4$）的偏差校正机器学习（ML）估计进行分析，考察结果如何依赖于标记集与训练集的相对比例。研究检验了两种监督学习方法：一种以 $\ ext{Tr}\,M^{-1}$ 作为输入特征，另一种采用如 plaquette（面元）和 rectangle（矩形）等规范可观测量。除直接估计 $\ ext{Tr}\,M^{-n}$ 外，我们进一步探究了 ML 估计的两个衍生应用：单系综内手征凝聚累积量的评估，以及通过不同夸克质量系综间的多系综重加权得到的手征凝聚累积量评估。在该固定数据集内，偏差校正估计在采用的评估准则下与全数据参考值吻合度较高，而未校正的估计在经过非线性累积量和重加权步骤后会出现放大的偏差。对于以 $\ ext{Tr}\,M^{-1}$ 作为输入特征的方法，名义求解计数核算表明，在当前设置下，狄拉克逆运算成本可降至传统计算的约 $25.75\%$；该值为成本预测而非端到端基准，其假设连续逆运算成本相当，且未包含模型训练与分析开销。
英文摘要
We present a retrospective case study of bias-corrected machine learning (ML) estimates of traces of the inverse Dirac operator, $\text{Tr}\,M^{-n}$ ($n=1,2,3,4$), using a fixed lattice QCD dataset and examining how the results depend on the relative proportions of the labeled and training sets. Two supervised learning approaches are examined: one using $\text{Tr}\,M^{-1}$ as the input feature, and the other employing gauge observables such as the plaquette and rectangle. Beyond the direct estimation of $\text{Tr}\,M^{-n}$, we further investigate two derived applications of the ML estimations: the evaluation of the cumulants of the chiral condensate within a single ensemble and that obtained through multi-ensemble reweighting across ensembles with different quark masses. Within this fixed dataset, the bias-corrected estimates show close agreement with the full-data reference under the adopted evaluation criteria, while the uncorrected estimates can exhibit amplified deviations after the nonlinear cumulant and reweighting steps. For the approach using $\text{Tr}\,M^{-1}$ as the input feature, nominal solve-count accounting suggests that the Dirac-inversion cost could be reduced to approximately $25.75\%$ of that of the conventional calculation in the present setup. This value is a cost projection rather than an end-to-end benchmark: it assumes comparable costs for successive inversions and excludes model-training and analysis overhead.
Comments27 pages, 16 figures, 3 tables
