Geometry-Aware Error Diagnosis for Data Acquisition and Training Strategy Selection in Graph Neural Network

High-fidelity finite element (FE) analysis is widely used for simulating complex physical phenomena, but its computational cost limits repeated evaluations over large parametric design spaces. Graph neural network (GNN)-based surrogate models offer a promising alternative by directly representing irregular FE meshes and enabling rapid structural-response prediction. However, their accuracy can deteriorate in localized high-stress regimes. When large prediction errors occur, it is often unclear whether the relevant geometric information is present in the model input but sparsely represented in the training data, or whether the stress-driving geometry is insufficiently exposed by the input representation. Because additional FE data require substantial simulation effort, distinguishing these failure mechanisms is important for deciding whether to acquire more data, modify the representation, or use both. We investigate this problem using three-dimensional FE data from 2,315 parametric perforated-plate specimens for nodal von Mises stress prediction in a fixed region of interest. We evaluate two interventions—targeted FE data enrichment and explicit geometric conditioning—in a controlled 2 by 2 design consisting of a baseline model, enrichment alone, conditioning alone, and their combination. Geometric conditioning augments the baseline input with node-wise relational geometry and structure-level descriptors derived from CAD and mesh information. Across two seeds, adding 315 targeted training specimens changes node-level RMSE from 0.0889 to 0.0862 MPa, whereas geometric conditioning applied to the same 1,605-specimen base training set reduces RMSE to 0.0425 MPa. Using both interventions gives 0.0363 MPa. The value of conditioning is strongly geometry-dependent. In the narrow-ligament regime, conditioning reduces median peak relative error by 1.158–1.858 percentage points across the two seeds, and the conditioned model trained on 1,605 specimens outperforms the unconditioned model trained on 1,920 specimens in both runs. Thus, the investigated 315-specimen enrichment is insufficient to substitute for conditioning in this regime. Sample-level analysis further illustrates distinct failure mechanisms. In one specimen, a non-intersecting hole drives the stress concentration but is not explicitly described at the prediction nodes; all 242 severely underpredicted nodes persist after enrichment but disappear under geometric conditioning, consistent with representation insufficiency. In another specimen from the Intersecting regime, the stress-driving geometry is locally reflected in the prediction-region input; targeted enrichment reduces severe underpredictions from 40 nodes to 15, and the combined condition removes them. Feature ablation further shows that most of the observed improvement is associated with node-wise relational geometry rather than structure-level scalars alone. These results show that additional simulation data and geometric conditioning are not uniformly interchangeable across the design space. Their effects depend on the geometric response regime and are not simply additive. The results therefore support assessing whether stress-driving geometry is sufficiently observable before committing additional FE simulation budget.