Physics informed distributionally robust learning for urban distribution network resilience under extreme events

Extreme events expose urban distribution networks to correlated branch outages, uncertain hazard evolution, and rapidly changing operating conditions. Static indices and repeated Monte Carlo studies remain useful, but they either compress recovery behavior into a fixed score or impose substantial computational cost when many hazard realizations must be screened. This study develops a physics-informed, distributionally robust graph-learning framework for estimating node- and system-level resilience from scenario-dependent topology, measured post-event operating states, and hazard information. The contribution lies in the joint implementation of masked graph propagation, auxiliary electrical-state reconstruction, Wasserstein-robust training, and a common recovery-prioritization interface; none of these ingredients is claimed as new in isolation.The network encoder uses branch-availability masks and physical edge attributes to update graph messages. An auxiliary decoder reconstructs voltage, active and reactive injection, and branch-flow quantities, allowing AC-balance, voltage, and thermal residuals to regularize the latent representation. These penalties promote physical consistency but do not constitute hard feasibility guarantees. Distributional uncertainty is represented by a Wasserstein ball over normalized continuous operating and hazard features, while discrete topology masks remain fixed during each inner maximization. The learned resilience score is supervised by a transparent trajectory-based target constructed from restored service, unmet demand, time to 50% recovery, and voltage-violation exposure. The principal quantitative evaluation uses 20,000 operating states generated from 500 hazard scenarios on a modified IEEE 123-bus feeder. Across five random seeds, the full model attains an MAE of \(0.031\pm 0.002\) , an RMSE of \(0.042\pm 0.003\) , and an \(R^2\) of \(0.935\pm 0.008\) . Removing Wasserstein training increases RMSE to \(0.058\pm 0.004\) , while removing the operator block increases it to \(0.052\pm 0.004\) . When every assessment method is coupled to the same restoration simulator, the proposed ranking signal is associated with \(25.1\%\pm 1.5\%\) load shedding at hazard intensity \(\xi =0.8\) and a \(2.48\pm 0.16\) h time to 50% restoration. These recovery quantities measure the effect of assessment-informed prioritization under fixed restoration assumptions; the learning model does not directly issue switching, dispatch, or repair actions.