Graph-theoretic active learning for the closed-loop discovery of stochastic heterogeneous composites

The inverse design of resilient infrastructure materials is hindered by the combinatorial complexity inherent in optimizing stochastic, heterogeneous microstructures. Traditional Euclidean deep learning architectures, such as Convolutional Neural Networks (CNNs), fail to efficiently encode the sparse, non-local topology of disordered porous media, resulting in prohibitive computational redundancy. This work articulates a comprehensive graph-theoretic framework for the predictive modeling and optimization of self-healing cementitious composites. We propose a robust methodology for discretizing volumetric tomography into permutation-invariant heterogeneous graphs, where nodes encode discrete physical entities (aggregates, pores, and microcapsules) and edges represent mechanical and hydraulic connectivity. To capture global fracture dynamics and local transport phenomena, we employ specialized architectures, specifically Pore-GNNs and Long-Short-Edge MeshGraphNets, which function as high-speed surrogate models for multiphysics simulations. Computational validation against high-fidelity numerical solvers confirms the system's efficacy: the proposed architecture achieves approximately 1.1×105-fold acceleration (inference plus preprocessing) in permeability prediction relative to Lattice Boltzmann Method simulations, while maintaining a prediction accuracy of R2 > 0.94 (mean±std over five random splits); the inference-only speedup, which excludes one-time graph-construction preprocessing, is approximately 1.8×106-fold. We note that the end-to-end figure (1.1×105) supersedes the inference-only figure quoted in the original submission metadata. Furthermore, the framework autonomously navigated the high-dimensional design space to isolate a non-intuitive geometric optimum within just 30 high-fidelity oracle evaluations: anisotropic microcapsules (ρc≈2.5) oriented at 45∘ relative to the shear plane. This configuration is predicted to resolve the conflicting physical constraints of the system, maximizing the probability of crack interception for effective healing. These results demonstrate that physics-informed graph learning can effectively decouple prediction accuracy from computational intensity, offering a scalable paradigm for the discovery of advanced functional materials.