Multi-scale hydraulic graph neural networks for flood modelling

Abstract. Deep learning-based surrogate models represent a powerful alternative to numerical models for speeding up flood mapping while preserving accuracy. In particular, solutions based on hydraulic-based graph neural networks (SWE-GNN) enable transferability to domains not used for training and allow including physical constraints. However, these models are limited due to four main aspects. First, they cannot model rapid differences in flow propagation speeds; secondly, they can face instabilities during training when using a large number of layers, needed for effective modelling; third, they cannot accommodate time-varying boundary conditions; and fourth, they require initial conditions from a numerical solver. To address these issues, we propose a multi-scale hydraulic-based graph neural network (mSWE-GNN) that models the flood at different resolutions and propagation speeds. We include time-varying boundary conditions via ghost cells, which enforce the solution at the domain's boundary and drop the need of a numerical solver for the initial conditions. To improve generalization over unseen meshes and reduce the data demand, we use invariance principles and make the inputs independent from coordinates' rotations. Numerical results on dike-breach floods show that the model predicts the full spatio-temporal simulation of the flood over unseen irregular meshes, topographies, and time-varying boundary conditions, with mean absolute errors in time of 0.05 m for water depths and 0.003 m² s⁻¹ for unit discharges. We further corroborate the mSWE-GNN in a realistic case study in The Netherlands and show generalization capabilities with only one fine-tuning sample, with mean absolute errors of 0.12 m for water depth, critical success index for a water depth threshold of 0.05 m of 87.68 %, and speed-ups of over 700 times. Overall, the approach opens up several avenues for probabilistic analyses of realistic configurations and flood scenarios.