PhysBridge: Response-supervised grid pretraining with physics-constrained local correction for transferable power-system intelligence

Operating modern power grids requires coordinated solutions for optimal dispatch, state estimation, price prediction, and contingency analysis, yet these tasks are usually modeled separately. We present PhysBridge, a response-oriented pretraining framework in which historical windows provide context while solver-generated perturbation responses, active constraints, and local sensitivities define the pretraining targets. PhysBridge combines a temporal-graph encoder with a Primal-Dual Response Bridge (PDR-Bridge) that performs safeguarded local refinement and outputs transferable primal, projection-dual, sensitivity, and health tokens. Across IEEE 14-, 30-, 57-, 118-, and 300-bus systems, the benchmark contains 26.3 million solver-generated perturbation-response pairs; in the 300-bus transfer setting, pretraining uses only the 21.04 million nominal pairs from the 14-, 30-, 57-, and 118-bus source topologies. Across three runs on unseen IEEE 300-bus transfer with 10% labels, PhysBridge obtains a 2.21±0.05% OPF cost gap, 96.3±0.2% feasibility, 1.84±0.05 $/MWh LMP MAE, and 91.6±0.3% contingency/fault event macro F1. Relative to a matched rollout-only model trained on the same source corpus without response targets or bridge refinement, these values correspond to a 50.8% lower OPF gap and a 7.4 percentage-point higher event F1. The bridge requires 12.4 ms per 300-bus forward pass and activates fallback on 4.6% of stressed windows. Comparisons with supervised-only OPF specialists that do not receive matched solver-generated pretraining are interpreted as task-relevant performance under the proposed pretraining regime, not as architecture-only superiority.