Real-time flood forecasting using physics-informed deep operator network for solving the shallow water equations

Accurate and efficient prediction of free-surface flows remains a major challenge in flood forecasting and hydraulic modelling. Here we develop a physics-informed deep operator network (PI-DeepONet) for the efficient solution of the Shallow Water Equations (SWEs), in which the governing equations are directly embedded into the learning framework. To address instabilities associated with wet–dry interfaces under frictional effects, we introduce a training strategy that adaptively selects physically admissible collocation points. The approach is validated on five representative problems, including idealised benchmarks and a real flood event. For scenarios involving multiple forcings, such as inflow and rainfall, parallel branch networks are used to encode input functions. Once trained, the model enables fast prediction of flow fields with good agreement with conventional solvers. These results indicate the potential of PI-DeepONet for scalable hydrodynamic prediction, while highlighting remaining challenges in resolving discontinuities, large-scale domains, and rapidly evolving flow regimes.