A General-purpose Solver of Fourier Neural Swarm Operator Towards Accurate and Efficient Mechanical Modeling of Ultra Large Composite Materials

Abstract

Composite media with complex microstructures exhibit highly tailorable mechanical properties but remain challenging to model efficiently and accurately. Conventional homogenization often oversimplifies microstructural effects, whereas multiscale approaches typically require costly coupling across spatial and temporal scales. To address these limitations, we propose a two-scale neural-swarm framework for large-scale mechanical modeling of heterogeneous composites. At the local scale, the mechanical characteristics of representative microstructural features are encoded into building-block Fourier neural operators (FNOs) using level-set representations. At the global scale, these pretrained FNOs are assembled into an FNO swarm according to the spatial distribution of microstructural constituents. A coarse-mesh finite element model is employed to provide global physical guidance, while Schwarz iteration is used to synchronize neighboring FNOs and enforce consistency across shared interfaces. The proposed framework is validated through nonlinear simulations of SiC-Al composites with diverse microstructural configurations. Compared with nonlinear finite element analysis, the FNO-swarm method achieves comparable accuracy while reducing computational cost by orders of magnitude. For an extreme dual-property SiC-Al composite containing more than a billion nodal points, the proposed approach predicts the mechanical response within approximately one hour, demonstrating exceptional scalability. Furthermore, the framework naturally accommodates arbitrary Dirichlet boundary conditions and complex domain geometries. The proposed neural-swarm strategy provides a robust and scalable paradigm for large-scale mechanics simulations, reconciling the longstanding trade-off between computational efficiency and physical fidelity in heterogeneous materials modeling.