Surrogate modelling of dike wave overtopping hydrodynamics using an adapted deep learning Vision Transformer

Sea level rise can compromise the safety of coastal flood defences, as wave overtopping events are becoming more frequent and severe. This increasing threat emphasizes the need for accurate assessment of wave overtopping hydrodynamics over dikes, which is essential for evaluating flood safety. The currently available methods do not combine computational efficiency, detailed results and general applicability, which limits their use in modelling wave overtopping and the resulting dike erosion. To address these limitations, this study introduces the Wave Overtopping Surrogate Model (WOSM), a novel method for rapidly generating high-quality two-dimensional simulations of wave overtopping over the dike crest and landward slope. The foundation of the WOSM is the Vision Transformer Image to Image (ViTI2I), a new deep learning model that combines an adapted Vision Transformer with a convolutional decoder for next-frame prediction. Trained on CFD wave overtopping simulations, the WOSM accurately reproduces the overtopping hydrodynamics such as flow velocities, water depths, overtopping duration and vertical velocity profiles, including both spatial and temporal variations. The scope of the training data limits the applicability of the WOSM and its ability to consistently capture complex phenomena such as flow separation and reattachment, both of which could be improved by enriching the dataset. Its low computational demand makes it suitable for exploring additional applications, such as probabilistic design or simulating wave overtopping with evolving dike profiles for erosion assessment. Additionally, this study serves as a proof of concept that the WOSM framework could benefit other fields encountering comparable modelling constraints.