Beyond IID State Estimation: Physical Consistency and Topology-Shift Generalization in Graph Neural Networks for Power Systems

Graph neural networks are increasingly used to estimate the state of physical systems, but low prediction error under IID evaluation does not establish that a learned estimator remains reliable when the underlying physical structure changes. We study this problem in power-system state estimation, where topology changes alter the physical relationships governing measurements and system states. Using a published 55-bus distribution-system benchmark, we construct a controlled topology-shift evaluation in which models are trained on one network configuration and tested on strictly unseen N-1, N-2, and larger branch-modified topologies. We compare weighted least squares with MLP, GCN, GraphSAGE, GAT, and a lightweight physics-regularized GAT. Beyond state-estimation error, we evaluate physical measurement residuals, topology-distance degradation, measurement sparsity, noise robustness, and observability-controlled behavior. The experiments show that IID accuracy can substantially overstate reliability under structural distribution shift, while graph-based models degrade more gracefully than topology-agnostic models. Physics regularization further improves physical consistency and reduces degradation under severe topology shifts. These results suggest that evaluating learned physical-system models requires explicit structural distribution shifts and physical-consistency metrics rather than IID prediction accuracy alone.