Real-time phase-resolved wave prediction over planar coastal bathymetries using U-Net convolutional neural networks

Real-time, phase-resolved forecasting of waves is essential for safe operations in the coastal zone, for example, by enabling early-warning systems to inform real-time decision-making. However, non-linear transformations, depth variations and wave breaking limit the accuracy of theoretical models. This study presents a data-driven alternative using convolutional neural networks to predict nearshore surface elevation time series. The proposed method is developed for long-crested waves over planar slopes, predicting surface elevations up to approximately 6 peak periods in advance. Specifically, a U-Net architecture with three encoding and three decoding stages and approximately 200,000 trainable parameters is used, with the prediction based on a short time window from a single offshore gauge. Laboratory experiments of long-crested waves propagating over sloping beds were used for training and testing, covering multiple bed slopes and a wide range of spectral shapes, peak periods, and steepnesses. Model performance was compared against predictions from linear and second-order wave theories with shoaling corrections. The neural network reproduced the measured wave evolution with consistently lower errors than the theoretical models, particularly in shallow water where nonlinearity and breaking become dominant. It also captured wave arrival times with higher accuracy than the theoretical models, and showed robustness when applied to unseen sea states or slightly noisy input signals. These results show that within this laboratory regime, neural networks can extend phase-resolved wave prediction into the coastal zone, complementing traditional theoretical approaches and offering a practical framework which, with further development, could provide real-time operational forecasting based on offshore wave data. • Accurate surface elevation predictions across a range of water depths and sea states. • Sensitivity of neural network to dataset size and measurement accuracy discussed. • Key non-linear effects, such as amplitude dispersion, accurately reproduced. • Robust neural network predictions for sea states beyond the range used for training.