Directional Topology for Young’s Modulus Prediction in Porous Solids
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Mechanical response in porous materials is governed not only by geometry across scales, but by how that geometry is organized relative to a loading direction. This talk considers direction-aware topological data analysis (TDA) as a general framework for characterizing microstructure in settings where elastic stiffness depends on orientation. Standard topological summaries, despite their success in many applications, are inherently symmetric with respect to spatial axes and therefore tend to obscure directional effects. By introducing filtrations that encode a preferred axis associated with loading or deformation, topological descriptors can be made sensitive to directional connectivity and alignment of solid pathways, while retaining the multiscale and noise-robust character of TDA. Such representations provide a compact and interpretable view of microstructure that complements learning-based approaches built directly on raw geometry. Comparisons with convolutional neural networks serve to clarify what information is captured implicitly by high-capacity models and what can be expressed explicitly through topology-informed descriptors, highlighting trade-offs between accuracy, interpretability, and physical insight.
