GMM-Enhanced Mixture-of-Experts Deep Learning for Impulsive Dam-Break Overtopping at Dikes

Impulsive overtopping generated by dam-break surges is a critical hazard for dikes and flood-protection embankments, especially in reservoirs and mountainous catchments. Unlike classical coastal wave overtopping, which is governed by long, irregular wave trains and usually characterized by mean overtopping discharge over many waves, these dam-break-type events are dominated by one or a few strongly nonlinear bores with highly transient overtopping heights. Accurately predicting the resulting overtopping levels under such impulsive flows is therefore important for flood-risk assessment and emergency planning. Conventional cluster-then-predict approaches, which have been proposed in recent years, often first partition data into subgroups and then train separate models for each cluster. However, these methods often suffer from rigid boundaries and ignore the uncertainty information contained in clustering results. To overcome these limitations, we propose a GMM+MoE framework that integrates Gaussian Mixture Model (GMM) soft clustering with a Mixture-of-Experts (MoE) predictor. GMM provides posterior probabilities of regime membership, which are used by the MoE gating mechanism to adaptively assign expert models. Using SPH-simulated overtopping data with physically interpretable dimensionless parameters, the framework is benchmarked against XGBoost, GMM+XGBoost, MoE, and Random Forest. Results show that GMM+MoE achieves the highest accuracy (R2=0.9638 on the testing dataset) and the most centralized residual distribution, confirming its robustness. Furthermore, SHAP-based feature attribution reveals that relative propagation distance and wave height are the dominant drivers of overtopping, providing physically consistent explanations. This demonstrates that combining soft clustering with adaptive expert allocation not only improves accuracy but also enhances interpretability, offering a practical tool for dike safety assessment and flood-risk management in reservoirs and mountain river valleys.