Prediction of Depth-Averaged Velocity for Flow Though Submerged Vegetation Using Least Squares Support Vector Machine with Bayesian Optimization

Considering the limited accuracy of classical empirical formulas and traditional Machine Learning (ML) models for predicting the depth-averaged velocity of flow through submerged vegetation, in this article, a novel hybrid ML model named BO-LSSVM is developed that incorporates Bayesian Optimization (BO) into Least Squares Support Vector Machine (LSSVM). Comparing with standalone LSSVM, BO helps LSSVM to find the optimal hyperparameter combination and thus promotes its prediction accuracy. To further enhance the prediction performance, two different preprocessing methods including nondimensionalization and standardization are adopted to process the input parameters with nondimensionalization observed that better improves the performance of the ML predictions. Furthermore, comparisons with the other frequently used ML models (i.e., standalone LSSVM, Support Vector Machine (SVM) and Multilayer Perceptron (MLP)) and the previously proposed empirical formulas are also carried out. Best performance of BO-LSSVM with RMSE of 0.0188 and MAE of 0.0128 indicates its superiority when dealing with the prediction of the depth-averaged velocity. Besides, the highest prediction reliability of BO-LSSVM is further emphasized in the uncertainty analysis with uncertainty bandwidth of 0.008. Lastly, sensitivity analysis is conducted to figure out the relative importance of the involved input parameters, which turns out that the parameters about the frictional resistance demonstrate relatively higher importance than those regarding the bed slope.