In this study, a new 3-stage approach that consists of clustering, simulation, and optimization stages is proposed for the simulation of groundwater level (GWL) in an arid region of eastern Iran. In the first stage, K-means clustering was used to divide the study aquifer into five different clusters based on precipitation, water recharge, water discharge, transmissivity, earth level, and water table. In the second stage, to simulate GWL in each cluster, several input variables, such as water level at the previous month, aquifer discharge, aquifer recharge, evaporation, temperature, and precipitation, were used in the form of various input patterns that were fed to an artificial neural network (ANN). Finally, in the third stage, two advanced optimization methods, i.e., particle swarm optimization (PSO) and whale optimization algorithm (WOA), were utilized to optimize the ANN results. Various patterns were identified as suitable clusters based on the studied models. A pattern including water level at the previous month, aquifer discharge, aquifer recharge, and precipitation was identified as the best model for four clusters, except for cluster 3. The validation with root mean squared error (RMSE), mean absolute percentage error (MAPE), and Nash Sutcliffe index (NSE) revealed RMSE = 0.01, NSE = 0.97, and MAPE = 0.13 for the first cluster, RMSE = 0.011, NSE = 0.99, and MAPE = 0.22 for the second cluster, RMSE = 0.003, NSE = 0.99, and MAPE = 0.30 for the fourth cluster, and RMSE = 0.001, NSE = 0.98, and MAPE = 0.05 for the fifth cluster. For the third cluster, a pattern including water level at the previous month, aquifer discharge, and aquifer recharge was identified as the best model resulting in RMSE = 0.006, NSE = 0.99, and MAPE = 0.05. Finally, according to the results, the ANN–PSO model was applied to three clusters, while the ANN–WOA model was applied to the remaining clusters. In general, this study showed that optimization algorithms can improve the simulation accuracy of ANN, and the efficient use of each method depends on the clustering type. The application of the approach proposed here can be extended to other aquifers that have a relatively large area and limited data availability.

在这项研究中，提出了一种由聚类、模拟和优化阶段组成的新的 3 阶段方法，用于模拟伊朗东部干旱地区的地下水位 (GWL)。在第一阶段，K-means 聚类用于根据降水、水补给、排水、导水率、地球水平和地下水位将研究含水层分为五个不同的聚类。在第二阶段，为了模拟每个集群中的 GWL，以各种输入模式的形式使用了几个输入变量，例如上个月的水位、含水层流量、含水层补给量、蒸发、温度和降水量。人工神经网络（ANN）。最后，在第三阶段，两种先进的优化方法，即粒子群优化（PSO）和鲸鱼优化算法（WOA），被用来优化人工神经网络的结果。基于所研究的模型，各种模式被确定为合适的集群。包括上月水位、含水层排放、含水层补给、和降水被确定为四个集群的最佳模型，除了集群 3。 均方根误差 (RMSE)、平均绝对百分比误差 (MAPE) 和纳什萨特克利夫指数 (NSE) 的验证显示 RMSE = 0.01，NSE = 0.97，第一个簇的 MAPE = 0.13，第二个簇的 RMSE = 0.011，NSE = 0.99 和 MAPE = 0.22，第四个簇的 RMSE = 0.003，NSE = 0.99 和 MAPE = 0.30，RMSE = 0.001，对于第五个集群，NSE = 0.98，MAPE = 0.05。对于第三个集群，包括上个月水位、含水层排放和含水层补给的模式被确定为最佳模型，导致 RMSE = 0.006、NSE = 0.99 和 MAPE = 0.05。最后，根据结果，ANN-PSO 模型应用于三个集群，而ANN-WOA 模型应用于其余集群。一般来说，本研究表明，优化算法可以提高人工神经网络的模拟精度，每种方法的有效利用取决于聚类类型。这里提出的方法的应用可以扩展到其他面积相对较大且数据可用性有限的含水层。