Scour depth downstream of weirs is considered one of the most important hydraulic problems, which greatly influences the stability of weirs. Recently, artificial intelligence (AI) methods have become increasingly popular in modeling hydraulic variables, especially scour depth, because they can capture nonlinear relationships between input variables and their associated objectives. Despite their importance, these models have problems with hyperparameter tuning in scour depth modeling due to their structures, so algorithms must be used to tune the hyperparameters. Moreover, these algorithms are usually tuned by using the trial-and-error method to select the hyperparameters such as the number of hidden nodes, transfer function, and learning rate, and in this case, the main problem is overfitting during the training phase. To solve these problems, the high-order response surface method (HORSM), an improved version of the response surface method (RSM), is used as an alternative approach for the first time in this study to predict the scour depth. The HORSM model is based on high-order polynomial functions (from two to six) compared with the artificial neural network model (ANN). The findings indicate that the fifth order of the HORSM polynomial function yields the most precise predictions, with a higher coefficient of determination (R²) of 0.912 and Willmott Index (WI) of 0.972 compared to the values obtained using ANN (R² = 0.886 and WI = 0.927). Moreover, the accuracy of the predictions is represented by a reduction of the mean square error by up to 44.17 and 29.01% compared to the classical RSM and ANN, respectively. The suggested model established an excellent correlation and accuracy with experimental values.

堰下游冲刷深度被认为是最重要的水力问题之一，极大地影响堰的稳定性。最近，人工智能（AI）方法在水力变量（尤其是冲刷深度）建模中变得越来越流行，因为它们可以捕获输入变量与其相关目标之间的非线性关系。尽管它们很重要，但由于其结构，这些模型在冲刷深度建模中存在超参数调整的问题，因此必须使用算法来调整超参数。此外，这些算法通常通过试错法来选择隐藏节点数量、传递函数和学习率等超参数，在这种情况下，主要问题是训练阶段的过拟合。为了解决这些问题，本研究首次使用响应面法（RSM）的改进版本高阶响应面法（HORSM）作为预测冲刷深度的替代方法。与人工神经网络模型 (ANN) 相比，HORSM 模型基于高阶多项式函数（从 2 到 6）。研究结果表明，与使用 ANN 获得的值 ( R ²  = 0.886)相比，五阶 HORSM 多项式函数可产生最精确的预测，其决定系数 ( R ² ) 更高，为 0.912，威尔莫特指数 ( WI ) 为 0.972 WI =  0.927）。此外，与经典 RSM 和 ANN 相比，预测的准确性表现为均方误差分别降低了 44.17% 和 29.01%。建议的模型与实验值建立了良好的相关性和准确性。