Physics-Informed Graph Neural Networks for Stress Prediction in Welded Structures

The reliable prediction of stresses in welded structures is crucial for fatigue assessment and safety design. Conventional numerical methods such as the Finite Element Method (FEM) provide accurate results but are computationally expensive, which limits their use in large-scale optimization. Graph Neural Networks (GNNs) offer a promising alternative as they can exploit the inherent graph structure of finite element meshes and enable much faster evaluation once trained. In this work, we present a GNN model for stress prediction in welded components, with particular focus on the notch stress in weld seams, which are critical for fatigue life. A standard encoder-process-decoder GNN commonly used for stress prediction is compared to a physics-informed variant. The GNN is trained using FEM simulations that incorporate variations in the weld seam geometry, leading to substantial differences in the maximum notch stress. The proposed approach is applied to a butt joint and a fillet joint, representative of typical configurations found in welded structures. The physics-informed model demonstrates improved performance in predicting the critical maximum stresses in weld seams, although its overall accuracy across the full stress distribution is slightly lower. Furthermore, an evaluation metric is introduced that specifically quantifies fatigue-relevant stresses, as these aspects are often not adequately captured by conventional evaluation metrics for artificial intelligence models. The proposed metric provides a more meaningful assessment of model performance in terms of structural integrity and fatigue safety.

Keywords: Graph Neural Networks, Stress prediction, Welded structures, Deep learning, Physics-informed machine learning.