Statistical learning of structure-property relationships for transport in porous media, using hybrid AI modeling

TL;DR

This study addresses how 3D microstructure controls transport in porous media by deploying a hybrid AI framework that fuses symbolic regression with deep learning and graph attention networks to derive analytical structure–property relationships. Using a large dataset of $90{,}000$ virtual microstructures generated from nine stochastic models, the approach uncovers a precise relation between porosity and geodesic tortuosity and the $M$-factor via the equation $M = \dfrac{\varepsilon}{m(\tau_{\mathrm{geo}})^{8.483}}$, achieving near-perfect predictive performance ($R^2 \approx 0.992$–$0.993$). A dual GAT strategy enhances data augmentation and reveals feature interactions, while a synthetic validation scheme with controlled noise tests robustness. The work demonstrates high predictive accuracy and interpretability, with potential to guide design of porous materials, and it suggests future integration with transformer-based reasoning to further refine equation discovery and cross-domain applicability.

Abstract

The 3D microstructure of porous media, such as electrodes in lithium-ion batteries or fiber-based materials, significantly impacts the resulting macroscopic properties, including effective diffusivity or permeability. Consequently, quantitative structure-property relationships, which link structural descriptors of 3D microstructures such as porosity or geodesic tortuosity to effective transport properties, are crucial for further optimizing the performance of porous media. To overcome the limitations of 3D imaging, parametric stochastic 3D microstructure modeling is a powerful tool to generate many virtual but realistic structures at the cost of computer simulations. The present paper uses 90,000 virtually generated 3D microstructures of porous media derived from literature by systematically varying parameters of stochastic 3D microstructure models. Previously, this data set has been used to establish quantitative microstructure-property relationships. The present paper extends these findings by applying a hybrid AI framework to this data set. More precisely, symbolic regression, powered by deep neural networks, genetic algorithms, and graph attention networks, is used to derive precise and robust analytical equations. These equations model the relationships between structural descriptors and effective transport properties without requiring manual specification of the underlying functional relationship. By integrating AI with traditional computational methods, the hybrid AI framework not only generates predictive equations but also enhances conventional modeling approaches by capturing relationships influenced by specific microstructural features traditionally underrepresented. Thus, this paper significantly advances the predictive modeling capabilities in materials science, offering vital insights for designing and optimizing new materials with tailored transport properties.

Figures (8)

• Figure 1: 3D renderings of simulated structures, where transport takes place in the transparent pore space. The structures correspond to the nine different types of stochastic microstructure models, namely fiber system (I), channel system (II), spatial graph (III), level set of a Gaussian random field (IV), level set of a spinodal decomposition (V), as well as systems of hard ellipsoids (VI), smoothed hard ellipsoids, (VII), soft ellipsoids (VIII), and smoothed soft ellipsoids (IX). The figure is reproduced from prifling2021.
• Figure 2: Graph attention network (GAT) Workflow in the hybrid AI framework, showing the four sub-modules: Data pre-processing, Graph attention network, Dataset preparation, and Symbolic regression, which collectively enhance data analysis and model predictions.
• Figure 3: Correlation coefficients (left) and importance scores (right) of the features affecting $M$-factor, emphasizing the significant roles of porosity ($\varepsilon$) and geodesic tortuosity $(m(\tau_\mathrm{geo}))$.
• Figure 4: Actual $M$-factor vs. predicted $M$-factor (left) and a more detailed visualization (right) including the main samples (blue) and (right) validation samples (red). The corresponding performance metrics are given in Table \ref{['tab:metrics']}.
• Figure 5: Relative frequency (left) and coefficient error (right) of the true and alternative equations across noise levels for "GAT data" (blue) and "Featured data" (orange).