发表机构
Institute of Mathematics of the Polish Academy of Sciences; University of Silesia in Katowice（波兰科学院数学研究所; 卡托维兹西里西亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出可扩展的持久配对图计算方法，应用于多孔介质渗透率预测，证明图结构信息超越持久区间，但存在领域依赖性和代表性敏感性。
AI 中文摘要
我们提出了一种可扩展的方法，用于从大型立方体过滤中计算持久配对图，并利用该方法检验持久类之间的图组织是否包含超出单纯持久区间的信息。该方法在全局约简之前取消等值对，以流式形式构建压缩复形，并通过投影关系和三角事件求解从一次持久约简中恢复图转换。我们将该方法应用于DRP-372多孔介质数据集中的119个带符号距离体，以进行渗透率预测。每个256立方体在收缩前诱导超过1.35亿个立方体单元，而中位压缩复形包含37,471个生成元。在按材料族分组的验证中，在岭回归和偏最小二乘回归下，添加持久配对图描述符比仅使用持久汇总能改善预测。在更严格的实验中，即每次留出一个源项目，岭回归相对于仅使用持久性仍保持适度改善，尽管除几何和持久性之外的额外收益在不同项目间并不一致。两个零模型表明，观察到的持久性与图耦合以及边目标组织具有强烈的非随机性，但两者都不能唯一解释预测改进；有用的信号似乎主要存在于较粗的图和事件组织中。空间分析同样区分了持久幅度与图显著性，并揭示了代数相关的持久事件之间的非局部组织。这些结果表明，持久配对图提供了超越条形码的结构性信息汇总，同时暴露了领域依赖性和代表性敏感性，这促使我们开发更不变的关联描述符。
英文摘要
We present a scalable method for computing persistence pairing graphs from large cubical filtrations and use it to test whether graph organization among persistent classes contains information beyond persistence intervals alone. The method cancels equal-value pairs before global reduction, constructs the compressed complex in streaming form, and recovers graph transitions from one persistence reduction through projected relations and triangular event solves. We apply the method to 119 signed distance volumes from the DRP-372 porous media collection for permeability prediction. Each 256-cubed volume induces more than 135 million cubical cells before contraction, whereas the median compressed complex contains 37,471 generators. In validation grouped by material family, adding persistence pairing graph descriptors improves prediction over persistence summaries under both Ridge regression and partial least squares regression. In the stricter experiment that holds out one source project at a time, Ridge retains a modest improvement over persistence alone, although additional benefit beyond geometry and persistence is not consistent across projects. Two null models show that the observed persistence and graph coupling and edge target organization are strongly nonrandom, but neither uniquely explains the predictive improvement; the useful signal appears to reside mainly in coarser graph and event organization. Spatial analyses likewise distinguish persistence magnitude from graph prominence and reveal nonlocal organization among algebraically related persistence events. These results show that persistence pairing graphs provide structurally informative summaries beyond the barcode while exposing domain dependence and representative sensitivity that motivate more invariant relational descriptors.
