.png){kind=icon}
.png){kind=icon}
Return
Graph-based surrogate modeling for structural eigenvalue problems with modal matching training
.png){kind=icon}
PRE
AI
DOI：10.1007/s00366-026-02310-8.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
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.
Keywords:
Finite elements
Field prediction
Eigenvalue problems
Graph neural networks
Clustered Eigenvalues
Journal
IF:
4.9
Papers:
2.6K
Citations:
9.3K
View more organizations