Accurate calculation of the longitudinal dispersion coefficient (K_x) of pollution is important in modeling the status of river pollution. Various equations are presented to calculate the K_x using experimental, analytical, and mathematical methods. Although machine learning models are more reliable than experimental equations in the presence of uncertainties missing data, they have not been widely used in the prediction of the K_x. In this study, the K_x of the river was predicted using machine learning methods, including least square-support vector machine (LS-SVM), adaptive neuro-fuzzy inference system (ANFIS), and ANFIS optimized by Harris hawk optimization (ANFIS-HHO), and the results were compared with that of the experimental methods. Several scenarios were designed by different combinations of input variables (B, H, U, u_⁎, B/H, U/u_⁎, β, and σ). The results showed that machine learning models had a more efficient performance to predict the K_x compared to experimental equations. The ANFIS-HHO with a scenario containing all the input variables, performed better than the other two models (RMSE = 17.0, MAPE = 0.22, and R² = 0.97). Furthermore, the HHO algorithm slightly increased the prediction performance of the ANFIS. The DR evaluation criteria showed that experimental equations overestimated the values of K_x, while the machine learning models resulted in higher precision. Also, the results of Taylor's diagram showed the acceptable performance of the ANFIS-HHO model compared to other models. Given the promising results of the present study, it is expected that the proposed approach can be efficiently used for similar environmental modeling problems.

准确计算污染的纵向弥散系数（K _x）对于模拟河流污染状况非常重要。提出了各种方程式，以使用实验，分析和数学方法来计算K _x。尽管在缺少数据不确定性的情况下，机器学习模型比实验方程更为可靠，但它们尚未广泛用于K _x的预测。在这项研究中，K _x使用机器学习方法（包括最小二乘支持向量机（LS-SVM），自适应神经模糊推理系统（ANFIS）和通过哈里斯霍克优化（ANFIS-HHO）优化的ANFIS）对河流进行预测。与实验方法相比。几种情况是由输入变量（的不同组合设计乙，ħ，ü，ü _⁎，B / H，U /ù _⁎，β，和σ）。结果表明，机器学习模型可以更有效地预测K _x与实验方程相比。具有包含所有输入变量的方案的ANFIS-HHO的性能优于其他两个模型（RMSE = 17.0，MAPE = 0.22和R ²  = 0.97）。此外，HHO算法略微提高了ANFIS的预测性能。DR评估标准表明，实验方程式高估了K _x的值，而机器学习模型则提高了精度。此外，泰勒图的结果表明ANFIS-HHO模型与其他模型相比具有可接受的性能。鉴于本研究的有希望的结果，可以预期所提出的方法可以有效地用于类似的环境建模问题。