Comparative assessment of white-box and black-box machine learning models for predicting free-falling jet scour depth

Scour depth prediction downstream of hydraulic structures is an important task for maintaining their safety and long-term stability. The present study, for accurate modelling of scour depth caused by free-falling hydraulic jets, conducted a comparative investigation of the performance of various machine learning (ML) models. Black-box ML models were selected for their strong nonlinear learning capability. In addition, white-box ML models were chosen because they can provide explicit mathematical expressions. Several ML models, including Artificial Neural Networks (ANN), Support Vector Regression (SVR), Classification and Regression Trees (CART), Group Method of Data Handling (GMDH), Multi-Expression Programming (MEP), Multivariate Adaptive Regression Splines (MARS), and Stronger Variable Creator Machines (SVCM), were used. In addition, hybrid ML models were developed by combining Particle Swarm Optimization (PSO) with MARS, ANN, and SVR to improve the performance of standalone approaches. For the evaluation of the ML models, statistical indicators, the objective function (OBJ) criterion, uncertainty analysis (U95), and graphical plots were employed. The results revealed that the hybrid optimization ML approaches increased the accuracy compared to their standalone counterparts. The SVR-PSO model achieved the best accuracy with the lowest OBJ (0.07995) and U95 (0.0638) values, followed closely by MARS-PSO, MEP, and ANN-PSO. Comparison of the present ML methods with previous reported ML methods highlighted their superior performance for modelling of scour depth.