  Physics-based models are computationally time-consuming and infeasible for
real-time scenarios of urban drainage networks, and a surrogate model is needed
to accelerate the online predictive modelling. Fully-connected neural networks
(NNs) are potential surrogate models, but may suffer from low interpretability
and efficiency in fitting complex targets. Owing to the state-of-the-art
modelling power of graph neural networks (GNNs) and their match with urban
drainage networks in the graph structure, this work proposes a GNN-based
surrogate of the flow routing model for the hydraulic prediction problem of
drainage networks, which regards recent hydraulic states as initial conditions,
and future runoff and control policy as boundary conditions. To incorporate
hydraulic constraints and physical relationships into drainage modelling,
physics-guided mechanisms are designed on top of the surrogate model to
restrict the prediction variables with flow balance and flooding occurrence
constraints. According to case results in a stormwater network, the GNN-based
model is more cost-effective with better hydraulic prediction accuracy than the
NN-based model after equal training epochs, and the designed mechanisms further
limit prediction errors with interpretable domain knowledge. As the model
structure adheres to the flow routing mechanisms and hydraulic constraints in
urban drainage networks, it provides an interpretable and effective solution
for data-driven surrogate modelling. Simultaneously, the surrogate model
accelerates the predictive modelling of urban drainage networks for real-time
use compared with the physics-based model.
