Neural-Embedded Graphical Model for Self-Consistent Hierarchical Upscaling of Complex Composites

Abstract

A persistent challenge in computational physical modeling is the substantial disparity between the characteristic length scales of microstructures and macroscopic structural components. Multiscale modeling has been widely adopted to bridge this gap by coupling methodologies tailored to different scales. However, conventional approaches, such as asymptotic homogenization (bottom-up) and submodeling (top-down), often entail rigorous mathematical prerequisites or intricate interfacing procedures. To address these limitations, we introduce a fully scalable neural-embedded graphical model (NEGM) that provides a unified framework for the progressive upscaling of highly heterogeneous composite materials. Specifically, NEGM encodes all microstructure- and material-related complexities into constituent neural network blocks, which are then organized into a hypergraph to simulate progressively larger domains. Extensive numerical benchmarks demonstrate that NEGM reliably predicts the physical responses of 2D and 3D composites exhibiting strong material nonlinearity, arbitrary boundary conditions, and irregular geometries. Crucially, because NEGM relies solely on neural network training and inference, it offers a scale-invariant formulation. This enables iterative application of NEGM to upscale from the microscale to arbitrarily large scales, circumventing the need for complex interfacing protocols between disparate modeling frameworks. We validate this progressive upscaling strategy on a large mosaic composite domain, showing that the accumulated error can be effectively contained provided the constituent blocks achieve sufficiently high prediction accuracy. Our findings suggest that artificial neural networks not only enhance the efficiency of direct single-scale simulations, as previously demonstrated, but also provide a clean and elegant pathway toward streamlined multiscale modeling.