Quantifying Predictive Uncertainty and Feature Selection in River Bed Load Estimation: A Multi-Model Machine Learning Approach with Particle Swarm Optimization

Abstract

This study presents a comprehensive multi-model machine learning (ML) approach to predict river bed load, addressing the challenge of quantifying predictive uncertainty in fluvial geomorphology. Six ML models—random forest (RF), categorical boosting (CAT), extra tree regression (ETR), gradient boosting machine (GBM), Bayesian regression model (BRM), and K-nearest neighbors (KNNs)—were thoroughly evaluated across several performance metrics like root mean square error (RMSE), and correlation coefficient (R). To enhance model training and optimize performance, particle swarm optimization (PSO) was employed for hyperparameter tuning across all the models, leveraging its capability to efficiently explore complex hyperparameter spaces. Our findings indicated that RF, GBM, CAT, and ETR demonstrate superior predictive performance (R score > 0.936), benefiting significantly from PSO. In contrast, BRM displayed lower performance (0.838), indicating challenges with Bayesian approaches. The feature importance analysis, including permutation feature and SHAP values, highlighted the non-linear interdependencies between the variables, with river discharge (Q), bed slope (S), and flow width (W) being the most influential. This study also examined the specific impact of individual variables on model performance by adding and excluding individual variables, which is particularly meaningful when choosing input variables for the model, especially in limited data conditions. Uncertainty quantification through Monte Carlo simulations highlighted the enhanced predictability and reliability of models with larger datasets. The correlation between increased training data and improved model precision was evident in the consistent rise in mean R scores and reduction in standard deviations as the sample size increased. This research underscored the potential of advanced ensemble methods and PSO to mitigate the limitations of single-predictor models and exploit collective model strengths, thereby improving the reliability of predictions in river bed load estimation. The insights from this study provide a valuable framework for future research directions focused on optimizing ensemble configurations for hydro-dynamic modeling.