Pressure and flow estimation in Water Distribution Networks (WDN) allows water management companies to optimize their control operations. For many years, mathematical simulation tools have been the most common approach to reconstructing an estimate of the WDN hydraulics. However, pure physics-based simulations involve several challenges, e.g. partially observable data, high uncertainty, and extensive manual configuration. Thus, data-driven approaches have gained traction to overcome such limitations. In this work, we combine physics-based modeling and Graph Neural Networks (GNN), a data-driven approach, to address the pressure estimation problem. First, we propose a new data generation method using a mathematical simulation but not considering temporal patterns and including some control parameters that remain untouched in previous works; this contributes to a more diverse training data. Second, our training strategy relies on random sensor placement making our GNN-based estimation model robust to unexpected sensor location changes. Third, a realistic evaluation protocol considers real temporal patterns and additionally injects the uncertainties intrinsic to real-world scenarios. Finally, a multi-graph pre-training strategy allows the model to be reused for pressure estimation in unseen target WDNs. Our GNN-based model estimates the pressure of a large-scale WDN in The Netherlands with a MAE of 1.94mH$_2$O and a MAPE of 7%, surpassing the performance of previous studies. Likewise, it outperformed previous approaches on other WDN benchmarks, showing a reduction of absolute error up to approximately 52% in the best cases.
