Generalization-aware structured mesh smoothing via graph neural networks

Abstract

Structured meshes provide computationally efficient discretization for scientific simulations through geometrically ordered mesh units. Because of their strict orthogonality constraints, it is still challenging to generate high-quality structured meshes. Although traditional optimization techniques employ iterative node relocation to enhance element quality, they suffer from accuracy-efficiency trade-offs. Existing intelligent methods based on supervised learning attempt to circumvent these limitations through data-driven optimization. However, these methods are inherently limited by their dependence on domain-specific training data and their inability to generalize across diverse complex geometries. To overcome these problems, we propose Structured-Mesh Graph Neural Network-based smoothing(SMGNN-Smoothing), a generalization-aware unsupervised method for structured mesh optimization. Our method integrates three key innovations: (1) a graph neural network that aggregates neighborhood features to predict optimized node configurations, (2) an adaptive normalization technique enabling consistent processing of multi-resolution meshes, (3) a well-designed loss function controls the whole training process, StructureLoss. SMGNN-Smoothing realizes excellent optimization performance across multiple quality metrics. It outperforms existing supervised learning methods and shows strong generalization capability. Compared with optimization-based smoothing, it achieves an order-of-magnitude improvement in computational efficiency.