MorphoGP: A Nonparametric Framework for Predicting Equilibrium Beach Profiles Under Tidal Influence
Abstract
The prediction of equilibrium beach profiles (EBPs) under tidal influence is of fundamental importance for sustainable coastal development, informing shoreline protection strategies and managing coastal ecosystems under changing environmental conditions. However, it remains challenging due to the highly nonlinear interactions among wave, tide, and sedimentary processes. Traditional empirical and numerical models often exhibit limited adaptability across diverse coastal environments, with especially pronounced limitations in beach systems where tidal processes are important. To improve data-driven prediction under these conditions, this study proposes MorphoGP, a unified category-specific Gaussian process (GP) framework for predicting EBPs under tidal influence. The framework first introduces a ContourCluster model based on contrastive learning to classify tide-influenced beach morphologies automatically. Within each morphological category, a specialized GP expert learns statistical associations between environmental descriptors including waves, tides, and sediments and the beach profile’s shape. A gating net then integrates the outputs of all experts through a probabilistic weighting mechanism to produce the final prediction. It should be noted that MorphoGP is a data-driven predictive framework and does not explicitly resolve the full wave–tide–sediment transport dynamics. Instead, it incorporates physically relevant descriptors to support prediction and model interpretation. Evaluated on data from over 180 beach profiles from tide-influenced coasts along the Chinese coast, MorphoGP achieves improved predictive performance compared with conventional and deep learning (DL) models, reducing the test root mean square error (RMSE) by about 59.3% compared with the best baseline and achieving a final RMSE of 0.297 m. Additionally, feature relevance analysis suggests that tidal parameters are strongly associated with equilibrium morphology, alongside wave and sediment characteristics. The proposed framework provides a physically informed, data-driven tool for equilibrium beach-profile prediction under tidal influence and coastal management, while stronger process-level physical coupling remains an important direction for future development. The source code is available at https://github.com/Ch1hyaAnon/MorphoGP.git
