The optimization of urban multi-source water supply systems is essential for addressing the growing challenges of water allocation, cost management, and system resilience in modern cities. This study introduces a graph-theory-based optimization model to analyze the structural and operational dynamics of urban water supply systems, incorporating constraints such as water quality, pressure, and system connectivity. Using Lishui City as a case study, the model evaluates three water allocation plans to meet the projected 2030 water demand. Advanced algorithms, including Floyd’s shortest path algorithm and the GA-COA-SA hybrid optimization algorithm, were employed to address constraints such as pipeline pressure, water quality attenuation, and nonlinear flow dynamics. Results indicate a 1.4% improvement in cost-effectiveness compared to the current allocation strategy, highlighting the model’s capability to enhance efficiency. Among the evaluated options, Plan 2 emerges as the most cost-effective solution, achieving a supply capacity of 4.5920 × 10⁵ m³/d with the lowest annual cost of 5.7015 × 10⁷ yuan, highlighting the model’s capability to improve both efficiency and resilience. This study prioritizes cost-efficiency tailored to regional challenges, distinguishing itself from prior research that emphasized redundancy and water quality analysis. The findings demonstrate the potential of graph-theoretic approaches combined with advanced optimization techniques to enhance decision-making for sustainable urban water management.

The prediction of debris flows is essential for safeguarding infrastructure and minimizing the economic losses associated with the hazards. Traditional empirical and theoretical models, while providing foundational insights, often struggle to capture the complex and nonlinear behaviors inherent in debris flows. This study aims to enhance debris flow prediction by integrating theoretical modeling with data-driven approaches. We model debris flow as a viscoplastic fluid, employing the Herschel–Bulkley rheological model to describe its behavior. By combining the kinematic wave model with lubrication theory, we develop a comprehensive theoretical framework that encapsulates the mechanical physics of debris flows and identifies key governing parameters. Numerical solutions of this theoretical model are utilized to generate an extensive training dataset, which is subsequently used to train a support vector regression (SVR) model. The SVR model targets slide depth and velocity upon impact, using explanatory variables including yield stress, material density, source area depth and length, and slope length. The model demonstrates high predictive accuracy, achieving coefficients of determination $R^2$ of 0.956 for slide depth and 0.911 for slide velocity at impact. Additionally, the relative residuals $\sigma$ are primarily distributed within the range of −0.05 to 0.05 for both slide depth and slide velocity upon impact. These results indicate that the proposed hybrid model not only incorporates the fundamental physical mechanisms governing debris flows but also significantly enhances predictive performance through data-driven optimization. This study underscores the critical advantage of merging physical models with machine learning techniques, offering a robust tool for improved debris flow prediction and risk assessment, which can inform the development of more effective early warning systems and mitigation measures.

Dam break problem-induced floods can trigger hazardous dike overtopping, demanding predictions that are fast, accurate, and interpretable. We pursue two objectives: (i) introducing a new alpha evolution (AE) optimization scheme to improve tree-model predictive accuracy, and (ii) developing a cluster-wise modeling strategy in which regimes are defined by wave characteristics. Using a dataset generated via physical model experiments and smoothed particle hydrodynamics (SPH) numerical simulations, we first group samples via hierarchical clustering (HC) on the Froude number $\left(\mathrm{Fr}\right)$, wave nonlinearity $\left(R\right)$, and relative distance to the dike $\left(D\right)$. We then benchmark CatBoost, XGBoost, and ExtraTrees within each cluster and select the best-performing CatBoost as the baseline, after which we train standard CatBoost and its AE-optimized variant. Under random train–test splits, AE-CatBoost achieves the strongest generalization for predicting relative run-up distance $H_m$ (testing dataset $R^2=0.9803$, $\mathrm{RMSE}=0.0599$), outperforming particle swarm optimization (PSO) and grid search (GS)-tuned CatBoost. We further perform TreeSHAP analyses on AE-CatBoost for global, local, and interaction attributions. SHAP analysis yields physics-consistent explanations: D dominates, followed by H and L, with a weaker positive effect of $\mathrm{Fr}$ and minimal influence of R; $H\times D$ is the strongest interaction pair. Overall, AE optimization combined with HC-based cluster-wise modeling produces accurate, interpretable overtopping predictions and provides a practical route toward field deployment.

Flash floods arise from the interaction of rugged topography, short-duration intense rainfall, and rapid flow concentration. Conventional risk mapping often builds empirical indices with expert-assigned weights or trains supervised models on historical event inventories—approaches that degrade in data-scarce regions. We propose a fully data-driven, unsupervised Geographic Information System (GIS) framework based on fractional order k-means, which clusters multi-dimensional geospatial features without labeled flood records. Five raster layers—elevation, slope, aspect, 24 h maximum rainfall, and distance to the nearest stream—are normalized into a feature vector for each 30 m × 30 m grid cell. In a province-scale case study of Zhejiang, China, the resulting risk map aligns strongly with the observations: 95% of 1643 documented flash flood sites over the past 60 years fall within the combined high- and medium-risk zones, and 65% lie inside the high-risk class. These outcomes indicate that the fractional order distance metric captures physically realistic hazard gradients while remaining label-free. Because the workflow uses commonly available GIS inputs and open-source tooling, it is computationally efficient, reproducible, and readily transferable to other mountainous, data-poor settings. Beyond reducing subjective weighting inherent in index methods and the data demands of supervised learning, the framework offers a pragmatic baseline for regional planning and early-stage screening.

Debris flows are highly unpredictable and destructive natural hazards that present significant risks to both human life and infrastructure. Despite advances in machine learning techniques, current predictive models often fall short due to the insufficient and low-quality historical data available for training. In this study, we introduce a hybrid approach that combines physical model experiments with a gradient boosting regression model to enhance the accuracy and reliability of debris flow predictions. By integrating experimental data that closely simulate real-world flow conditions, the gradient boosting regression model is trained on a more robust foundation, enabling it to capture the complex dynamics of debris flows under various conditions. Selecting slide mass, slope length, yield stress, and slope angle as explanatory variables, we focus on quantify two critical debris flow parameters—frontal thickness and velocity—at indicated locations within the flow. The model demonstrates strong predictive performance in forecasting these key parameters, achieving coefficients of determination of 0.938 for slide thickness and 0.934 for slide velocity. This hybrid approach not only simplifies the prediction process but also significantly improves its precision, offering a valuable tool for real-time risk assessment and mitigation strategies in debris flow-prone regions.

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 ($R^2=0.9638$ 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.