Topology-modulated end-to-end graph learning for spatiotemporal state inference of urban drainage systems under sparse monitoring.

Reliable perception of urban drainage systems is essential for understanding the dynamic behaviour and managing water-environment risks. Yet structural and hydraulic complexity and sparse sensor deployment constrain the characterisation of evolving operational states. Here, we propose an end-to-end graph learning framework (STGAT) that extracts the spatiotemporal regularities across nodes from sparse and heterogeneous monitoring data. STGAT transforms multi-variable temporal sequences into aligned node-level latent representations within a shared feature space. It then introduces a topology-modulated graph attention mechanism that combines a fixed GIS-derived topology prior with input-dependent attention coefficients to learn state-dependent inter-node dependencies. This design integrates temporal alignment, spatial information routing, and physical prior embedding within a single differentiable architecture. Consequently, forecasting and anomaly-related errors can guide feature extraction and dependency learning during end-to-end optimisation. Results demonstrate that STGAT achieves high-fidelity capture of hydraulic and water-quality patterns (NSE ≥ 0.90). It also maintains stronger predictive skill than a range of baseline models across increasing forecast horizons, particularly for outlet flow and overflow-prone water levels. Its anomaly detection rate (Recall ≥ 82%) and restoration accuracy (NSE = 0.92), compared with NSE values of 0.45-0.77 for the baseline models. These results demonstrate that end-to-end graph learning provides a new pathway towards topology-aware and data-efficient state perception in urban drainage systems.