CNN-FCNN2: A hybrid surrogate model for spatial correlations in random composite materials

Statistical homogenization provides a powerful framework for estimating the effective mechanical behavior of heterogeneous materials under external loading. A central challenge in its application is the identification of statistical descriptors that accurately represent spatial correlations within complex microstructures. In practice, limitations in experimental characterization and theoretical modeling hinder the accurate estimation of these descriptors, while the high computational cost associated with modeling on a microstructural level further complicates the task. To address these difficulties, we propose a machine learning-based approach for identifying accurate two-point spatial descriptors. Our method leverages a combination of neural networks to extract the underlying probability functions directly from microstructure images, focusing solely on the geometric configuration of the microstructure itself. The approach is fully independent of boundary conditions and imposes no requirement for periodicity. By coupling a convolutional neural network (CNN) with fully connected neural networks (FCNNs) and training them simultaneously, the proposed architecture is capable of learning efficient and generalizable representations. This hybrid design enables effective training using small datasets, significantly reducing data requirements while providing excellent accuracy and applicability to a wide range of materials. • Novel neural network for fast extraction of spatial correlations from microstructures. • Highly adaptable, purely geometry-based approach. • Statistically explainable across different material systems.