Direction-aware topological descriptors for Young's modulus prediction in porous materials

TL;DR

This paper introduces a direction-aware topological data analysis framework that explicitly incorporates loading direction into descriptors, significantly improving the prediction of Young's modulus in porous materials with anisotropic structures.

Contribution

The study develops a novel direction-aware TDA method that enhances predictive accuracy for anisotropic porous materials and remains effective even for nominally isotropic structures.

Findings

Direction-aware descriptors outperform direction-agnostic ones in predictive accuracy.

Performance gains increase with material anisotropy.

Descriptors are competitive with CNNs while being more compact and transferable.

Abstract

Classical topological descriptors used in topological data analysis (TDA) are invariant under permutations of spatial axes and therefore cannot represent the loading direction, which is essential for modeling anisotropic mechanical response. Here, this limitation is addressed by introducing a \emph{direction-aware TDA framework} in which the compression axis is explicitly embedded into filtration functions used to compute both persistent homology and Euler characteristic profile descriptors. Across multiple porous-material datasets spanning a broad range of structural anisotropy, direction-aware descriptors yield higher predictive accuracy than their direction-agnostic counterparts, with performance gains that increase systematically with anisotropy. Notably, direction-aware descriptors remain competitive and often improve $R^2$ even for nominally isotropic ensembles, indicating sensitivity to mechanically relevant directional organization beyond bulk anisotropy measures. When used as inputs to gradient-boosted tree models, the proposed descriptors approach the accuracy of convolutional neural networks trained directly on voxelized structures while retaining a compact, transferable representation. The study considers multiple datasets spanning weak to strong anisotropy, enabling systematic validation of direction-aware topology across regimes. Overall, the results establish direction-aware TDA as a general route for linking porous structure to direction-dependent elastic properties and motivate its use in anisotropic materials modeling problems where a preferred direction naturally arises.