Graph-based surrogate modeling for structural eigenvalue problems with modal matching training

Modal analysis of mechanical structures often requires repeated finite element (FE) simulations across varying geometric parameters and topological conditions, which is computationally prohibitive in high-dimensional design spaces. To address this challenge, we propose a graph-based deep learning surrogate model for structural eigenvalue problems, capable of predicting multi-order natural frequencies and mode shapes directly from mesh representations. The method encodes FE meshes into graph structures, integrates continuous and categorical node features, and employs a Graphormer-based processor to capture global vibration coupling. A dual-head decoder jointly outputs eigenfrequencies and displacement fields, optimized through a weighted loss combining frequency regression and mode-shape consistency. To resolve modal ambiguity arising from veering, crossover, and degenerate modes, we introduce a modal matching training (MMT) strategy, which aligns predictions with ground truth via consistency optimization and ensures consistent trajectory tracking. Comprehensive experiments demonstrate that the proposed model achieves over 99 % relative accuracy in frequency prediction and high mode-shape consistency across single- and multi-parameter datasets. Furthermore, the model generalizes to unseen topological perturbations, effectively capturing localized distortions and symmetry-breaking effects in degenerate modes. These results highlight the potential of graph-based surrogate modeling to provide efficient and physically consistent alternatives to traditional FE-based modal analysis, particularly in scenarios