AI 中文总结
本文针对重离子碰撞中临界涨落信号微弱难以提取的问题，提出结合TDA与深度学习的两阶段拓扑机器学习框架，成功恢复归一化阶乘矩的幂律标度，确立了拓扑机器学习探测QCD临界点的工具价值。
AI 中文摘要
重离子碰撞中的夸克胶子等离子体（QGP）到强子物质的相变及量子色动力学（QCD）临界点，可通过间歇度分析研究末态粒子间的空间涨落来识别。本文首次提出在二维角（赝快度η、方位角φ）相空间中，以EPOS作为背景模型的基于持续同调簇（CMC）的间歇度分析。临界涨落信号极弱，仅占总事例样本的百分之几，且被占绝对多数的非临界背景严重稀释，致使传统间歇度分析无法可靠提取信号。为提取微弱的临界信号，本文采用结合拓扑数据分析（TDA）与深度学习的两阶段拓扑机器学习框架：第一阶段将粒子事例表示为二维点云，构建基于德劳内（Delaunay）的子水平集过滤，提取贝蒂（Betti）曲线作为多尺度拓扑不变量，通过方位角随机化校正多重性偏差，并用拓扑点网络（TPN）与提升决策树（BDT）两种互补架构分类；由于仅事例级分类不足以恢复临界标度，第二阶段应用粒子级密度过滤器，明确剥离弥散的热背景并隔离密集堆积的临界团簇。该两阶段流程成功恢复了归一化阶乘矩的幂律标度，实现了（η, φ）空间中间歇度指数的准确恢复，确立了拓扑机器学习作为一种鲁棒的数据驱动工具，用于探测大型强子对撞机（LHC）能量下重离子碰撞中QCD临界点与强相互作用物质的相结构。
英文摘要
The QGP-to-hadronic matter phase transition and QCD critical point in heavy-ion collisions can be identified by studying spatial fluctuations among final-state particles using intermittency analysis. First CMC-based intermittency analysis in the two-dimensional angular ($η$, $φ$) phase space, using EPOS as the background model is presented. Critical fluctuation signals are extremely weak, constituting only a few percent of the total event sample and are severely diluted by the overwhelming non-critical background, rendering traditional intermittency analyses insufficient for reliable signal extraction. To extract the weak critical signal, we employ a two-stage topological machine learning framework combining Topological Data Analysis (TDA) with deep learning. In the first stage, particle events are represented as two-dimensional point clouds and a Delaunay-based sub-level set filtration is constructed to extract Betti curves as multiscale topological invariants, corrected for multiplicity bias via azimuthal randomisation and classified by two complementary architectures, a TopoPointNet (TPN) and Boosted Decision Trees (BDT). Since event-level classification alone is insufficient to restore the critical scaling, a second stage applies a particle-level density filter, explicitly stripping away the diffuse thermal background and isolating the densely packed critical clusters. The two stage pipeline successfully restores the power-law scaling of the normalized factorial moments, enabling accurate recovery of the intermittency index in ($η$, $φ$) space and establishing topological machine learning as a robust data driven tool for probing the QCD critical point and the phase structure of strongly interacting matter in heavy-ion collisions at LHC energies.
Comments16 pages, 12 figures
