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<p>Modal analysis requires solving eigenvalue problems to obtain natural frequencies and mode shapes. While a single finite-element (FE) eigen-solve can be efficient, practical workflows often demand thousands of repeated solves for multi-dimensional design-space exploration and tolerance/uncertainty screening, and the cost further increases when local geometric or topological perturbations trigger re-meshing. We propose a graph-based deep learning surrogate for structural eigenvalue problems that predicts multi-order natural frequencies and mode shapes directly from mesh representations. FE meshes are encoded as graphs with continuous and categorical node features, and a Graphormer-based processor captures global vibration coupling. A dual-head decoder jointly outputs eigenfrequencies and displacement fields, trained with an uncertainty-weighted objective combining frequency regression and mode-shape consistency. To address supervision ambiguity under clustered eigenvalues (e.g., mode interaction and degeneracy), we adopt a modal matching training (MMT) strategy that aligns predictions and ground truth by modal similarity, enabling stable mode tracking across samples. Experiments demonstrate high accuracy and strong mode-shape consistency across multi-parameter datasets; we further evaluate generalization from central-range samples to tail samples under a unified sampling pool, and report the corresponding performances. In addition, surrogate inference yields up to 196× speedup over the FE eigen-solver. Overall, the proposed surrogate supports rapid screening and large-scale design exploration, complementing high-fidelity FE modal analysis.</p>

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

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Chengqi Lin,
  • Junzhe Ding,
  • Jianlin Chen,
  • Yuan Wang,
  • Jianhao Jiao,
  • Pui-In Mak,
  • Nan Wang

摘要

Modal analysis requires solving eigenvalue problems to obtain natural frequencies and mode shapes. While a single finite-element (FE) eigen-solve can be efficient, practical workflows often demand thousands of repeated solves for multi-dimensional design-space exploration and tolerance/uncertainty screening, and the cost further increases when local geometric or topological perturbations trigger re-meshing. We propose a graph-based deep learning surrogate for structural eigenvalue problems that predicts multi-order natural frequencies and mode shapes directly from mesh representations. FE meshes are encoded as graphs with continuous and categorical node features, and a Graphormer-based processor captures global vibration coupling. A dual-head decoder jointly outputs eigenfrequencies and displacement fields, trained with an uncertainty-weighted objective combining frequency regression and mode-shape consistency. To address supervision ambiguity under clustered eigenvalues (e.g., mode interaction and degeneracy), we adopt a modal matching training (MMT) strategy that aligns predictions and ground truth by modal similarity, enabling stable mode tracking across samples. Experiments demonstrate high accuracy and strong mode-shape consistency across multi-parameter datasets; we further evaluate generalization from central-range samples to tail samples under a unified sampling pool, and report the corresponding performances. In addition, surrogate inference yields up to 196× speedup over the FE eigen-solver. Overall, the proposed surrogate supports rapid screening and large-scale design exploration, complementing high-fidelity FE modal analysis.