  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.

Machine Learning