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