Multimodal machine learning approaches for accurate wave overtopping discharge predictions

Accurate prediction of wave overtopping discharge is essential for designing resilient coastal defences against increasing climate threats. This study demonstrates the superior performance of advanced machine learning models over traditional methods. Using an extensive dataset from EurOtop manual, authors developed and benchmarked models including convolutional and long short-term memory neural networks (CNNs and LSTMs), enhanced with attention mechanisms. Bayesian hyperparameter optimisation ensured robust performance. Predictive uncertainty was quantified via bootstrap resampling (100 ensembles). Results show LSTMs with attention achieved the highest predictive accuracy (R2 = 0.8704, RMSE = 0.0620), effectively capturing complex non-linear dependencies in wave-structure interactions. Coverage analysis revealed systematic under-coverage: 66.7% for the lowest predicted quartile rising to 89.2% for the highest, indicating overconfidence. Partial dependence plots are used to visualise the marginal effect of top input features of the best model, confirming physically expected trends. Permutation feature importance identified relative freeboard and roughness factor as the dominant predictors. The integration of attention mechanisms improved model interpretability by identifying most influential input features. This work provides a reliable, computationally efficient framework that surpasses traditional methods, offering coastal engineers a tool for coastal infrastructure risk assessment, design optimisation, and climate adaptation planning.