Physics-Informed Neural Networks for Flood Modelling: Review and Canonical Test-Cases

Flood hazard is intensifying globally due to climate change, pervasive land-use alterations, and ageing infrastructure, demanding modelling frameworks that are both physically consistent and computationally tractable. Flood modelling has traditionally relied on one of the two: Numerical solvers (model-driven) and data-driven approaches acting as surrogates for prediction and emulation. Each paradigm presents structural strengths and limitations. Numerical solvers ensure mechanistic consistency but can be computationally intensive and sensitive to parameter uncertainty, whereas purely data-driven models enable rapid prediction but often struggle with extrapolation and physical interpretability. Physics-informed neural networks (PINNs) aim to take the best of the two worlds, as they have been proposed as a hybrid approach that embeds governing equations directly within neural network training. This paper provides a structured review of the theoretical foundations, methodological developments, and emerging applications of PINNs in flood modelling, positioning them relative to established model-driven and data-driven approaches. To reinforce the synthesis, three canonical process-oriented test cases are examined under controlled conditions, illustrating PINN behaviour in rainfall-driven flow, flow–topography interaction, and boundary-driven wetting dynamics. The analysis identifies key methodological challenges including training stability for hyperbolic systems, boundary condition enforcement, scalability to high-resolution domains, and uncertainty quantification. PINNs represent a potentially valuable intermediate modelling strategy, but remain limited in large-scale forward flood simulation. PINNs have shown to be particularly useful for inverse problems and data-scarce or partially observed systems. Their large-scale operational deployment remains limited by unresolved issues in training stability, scalability, and boundary condition enforcement.