Urban-CSTPNet: Time-Conditioned Multi-Relational Spatio-Temporal Probabilistic Forecasting for Smart Urban Electric Vehicle Charging Networks

Accurate regional demand forecasting supports reliable operation of urban electric vehicle (EV) charging networks. However, public charging demand exhibits spatial heterogeneity, multi-scale periodicity, and uncertainty. This paper proposes Urban-CSTPNet, a multi-relational spatio-temporal probabilistic forecasting framework. Five semantically explicit graphs represent geographical adjacency, spatial distance, historical demand correlation, pricing-pattern similarity, and static regional attributes. Sample-level time-conditioned graph gating fuses these relations using historical demand states and calendar context. Independent recent, daily, and weekly branches capture short-term variation, daily repetition, and weekly regularity, and are combined through temporal gating. The model produces multiple conditional quantiles and applies horizon-specific conformalized quantile regression using an independent calibration set. Experiments on the Shenzhen UrbanEV dataset at 1, 3, 6, 12, and 24 h horizons achieve a mean absolute error (MAE) of 60.44, root mean squared error (RMSE) of 192.44, and Pinball Loss of 16.96. These values are 11.51%, 6.04%, and 9.50% lower than those of ST-MGF-Q. For calibrated 90% intervals, the prediction interval coverage probability (PICP), prediction interval normalized average width (PINAW), and Interval Score are 0.9024, 0.0175, and 349.60. Results confirm improved forecasting accuracy, probabilistic quality, and empirical interval reliability.