Monotone Physics-Constrained Graph Neural Networks for Image-Based Structural Damage Assessment: Theory and Leakage-Free Evaluation

Image-based structural damage assessment requires automated methods that respect physical constraints. We formulate graph-neural-network message passing as a pseudo-time iteration of a monotone operator on a spatial-region graph. Under non-negative projected weights, order-preserving activations, and a self-loop maximum, the operator preserves boundedness and converges to a fixed point. A leakage audit of Aircraft Damage Detection 2 identified 41.7% of images crossing original split boundaries; we constructed a frozen group-level split avoiding this contamination. On the corrected split, hard physical constraints improve accuracy from 92.42% to 94.87% (McNemar significant across all seeds). A component-wise ablation indicates that no single constraint carries the gain: non-negative weights alone fall below the backbone, and the benefit emerges only from the complete monotone operator. Soft penalties and unconstrained networks underperform the baseline, indicating that constraint enforcement method matters. The approach provides a leakage-free protocol and demonstrates that monotone structure—not specific topology—drives the benefit.