On the generalization of hydraulic-inspired graph neural networks for spatio-temporal flood simulations

The high computational cost of detailed numerical models for flood simulation hinders their use in real-time and limits uncertainty quantification. Deep-learning surrogates have thus emerged as an alternative to speed up simulations. However, most surrogate models currently work only for a single topography, meaning that they need to be retrained for different case studies, ultimately defeating their purpose. In this work, we propose a graph neural network (GNN) inspired by the shallow water equations used in flood modeling, that can generalize the spatio-temporal prediction of floods over unseen topographies. The proposed model works similarly to finite volume methods by propagating the flooding in space and time, given initial and boundary conditions. Following the Courant-Friedrichs-Lewy condition, we link the time step between consecutive predictions to the number of GNN layers employed in the model. We analyze the model's performance on a dataset of numerical simulations of river dike breach floods, with varying topographies and breach locations. The results suggest that the GNN-based surrogate can produce high-fidelity spatio-temporal predictions, for unseen topographies, unseen breach locations, and larger domain areas with respect to the training ones, while reducing computational times.