In this research, the mean monthly groundwater level with a range of 3.78 m in Qoşaçay plain, Iran, is forecast. Regarding three different layers of gated recurrent unit (GRU) structures and a hybrid of variational mode decomposition with gated recurrent unit (VMD-GRU), deep learning-based neural network models are developed. As the base model for performance comparison, the general single-long short-term memory-layer network model is developed. In all models, the module of sequence-to-one is used because of the lack of meteorological variables recorded in the study area. For modeling, 216 monthly datasets of the mean monthly water table depth of 33 different monitoring piezometers in the period April 2002–March 2020 are utilized. To boost the performance of the models and reduce the overfitting problem, an algorithm tuning process using different types of hyperparameter accompanied by a trial-and-error procedure is applied. Based on performance evaluation metrics, the total learnable parameters value and especially the model grading process, the new double-GRU model coupled with multiplication layer (×) (GRU2× model) is chosen as the best model. Under the optimal hyperparameters, the GRU2× model results in an R² of 0.86, a root mean square error (RMSE) of 0.18 m, a corrected Akaike’s information criterion (AICc) of −280.75, a running time for model training of 87 s and a total grade (TG) of 6.21 in the validation stage; and the hybrid VMD-GRU model yields an RMSE of 0.16 m, an R² of 0.92, an AICc of −310.52, a running time of 185 s and a TG of 3.34.

In this study, the hydraulic features of the $SCVW$ (a novel type of sharp-crested V-notch weirs) were scrutinized in the popular vertex angles $\theta$ , i.e., 30°, 45°, 60°, 90°, 120°, 128°, and 150°, under aerated, steady and free overflow conditions in an open channel for large physical models. To assess the changes of the discharge coefficient of the $SCVW$ (i.e., $C_{\mathit{dSCVW}}$ ) versus weir height and $\theta$ , widespread laboratory works were performed by measuring the water head over the crest of the weir and the discharge. Special formulas for the $C_{dSCVW}$ in the $\theta =60°$ were checked, and an appropriate empirical equation was recommended. The calculated $C_{dSCVW}$ by the proposed equation was within 0%–10% of the measured values. Three types of nonparametric artificial intelligence (AI) methods, namely, support vector regression ($SVR$ ), gene expression programming ($GEP$ ), and a robust hybrid model entitled hybrid ($SVR\text{-}ACO$ ) were developed to estimate the $C_{\mathit{dSCVW}}$ . For the sake of modeling, 196 experimental datasets were applied in the mentioned methods to evaluate the $C_{dSCVW}$ by taking into consideration the dimensionless variables which impact the determining procedure of the $C_{dSCVW}$ . In this modeling, by varying the architecture and core factors of the aforementioned methods, several scenarios were defined. The generated mathematical equation of $C_{dSCVW}$ by the best scenario of the $GEP$ was compared with the corresponding measured values in which the results were in 0%–10%. According to the attained statistical indices, scatter plots, and the values of the total grade ($TG$ ) technique, the hybrid $SVR(RBF)\text{-}ACO$ model was determined as the superior and optimal method to estimate the $C_{dSCVW}$ with high performance and accuracy.