AI 中文总结
研究多孔介质中扩散释放行为，利用持久同调量化其多尺度拓扑和几何结构，发现拓扑特征与释放行为密切相关，能分类释放曲线状态，且特征提取比有限元扩散模拟快，为筛选扩散释放行为提供新描述符。
AI 中文摘要
我们使用持久同调量化多孔介质的多尺度拓扑和几何结构，包括固体连通性以及跨空间尺度的环状和腔状结构的形成。通过统计分析表明，这些拓扑和几何特征与多孔介质中扩散驱动的释放行为密切相关。具体而言，即使在每个目标孔隙率水平内，具有更丰富拓扑特征的样本往往呈现长尾释放，这表明释放行为不仅取决于孔隙空间的量，还取决于固相的多尺度结构。我们进一步表明，基于持久同调的特征可以使用简单分类模型对释放曲线状态进行分类。值得注意的是，特征提取比有限元扩散模拟快得多。这些结果共同表明，持久同调为筛选多孔介质中的扩散释放行为提供了一种轻量级、可解释且基于几何的描述符。
英文摘要
We used persistent homology to quantify the multiscale topological and geometric organization of porous media, including solid connectivity and the formation of loop-like and cavity-like structures across spatial scales. Through statistical analysis, we show that these topological and geometric features are closely associated with diffusion-driven release behavior in porous media. In particular, even within each target-porosity level, samples with richer topological features tend to exhibit long-tailed release, indicating that release behavior depends not only on the amount of pore space but also on the multiscale organization of the solid phase. We further show that persistent homology-based features can classify release-curve regimes using a simple classification model. Notably, feature extraction is substantially faster than finite element diffusion simulations. Together, these results suggest that persistent homology provides a lightweight, interpretable, and geometry-based descriptor for screening diffusive release behavior in porous media.
Comments15 pages, 5 figures, 6 tables, Under review
