Topological Signatures of Diffusive Release in Porous Media

2026-07-08

AI Summary

This study addresses the influence of microstructure—particularly multiscale topological features that are difficult to quantify—on diffusion-driven release behavior in porous media. For the first time in this domain, persistent homology is employed to characterize the multiscale geometry and topology of the solid phase through topological data analysis, which is then integrated with statistical modeling to establish a quantitative link to release dynamics. The results demonstrate that release characteristics are governed not only by porosity but also critically by the topological organization of the solid phase. The proposed topological descriptors effectively and accurately discriminate between distinct release curve types, offering substantially faster feature extraction than conventional finite element simulations while maintaining computational efficiency and interpretability.

Abstract

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.

Problem

• porous media
• diffusive release
• topological features
• multiscale organization
• persistent homology

Innovation

• persistent homology
• porous media
• diffusive release
• topological features
• multiscale geometry