Modelling continuous-time fault contagion in power grids with a graph neural Hawkes process.

Cascading failures in power transmission networks unfold in continuous time, each outage transiently raising the probability of further outages along electrically coupled pathways. Most data-driven approaches model this in discrete time and cannot represent the precise timing or the triggering relationships between events. We introduce the Neural-Hawkes graph (NHG) framework, which couples a graph-attention encoder with a spatiotemporal Hawkes decoder, conditioning the intensities of a marked point process on the learned electrical and structural state of every bus. Trained end-to-end by maximising the continuous-time sequence likelihood and evaluated on a digital twin of the IEEE 118-bus system, the NHG substantially outperforms tuned memoryless and classical statistical baselines on held-out likelihood (a negative log-likelihood of 1.54 versus 2.67 per event) and predicts the next affected bus well above chance. A controlled ablation across multiple electrical couplings, two networks, and a distribution shift shows that this advantage comes from the continuous-time self-exciting formulation rather than from any electrical prior, which instead serves as an interpretable, physically readable inductive bias. We further define an electrical branching ratio as a spectral-radius criticality diagnostic and characterise its behaviour through a ROC analysis. The framework offers an interpretable, parameter-efficient route to continuous-time reliability assessment.