## 4 Conclusions  
Numerical analysis and group method of data handling is used in the present study to present an equation for estimating the mean velocity (V*) in open channel intakes. The diversion angle with the longitudinal direction of the main channel (\(\theta\)), the longitudinal coordinates in the intake channel (y*), and the ratio of branch channel width to the main channel (W\({}_{r}\)), and experimental data dimensionless parameters were utilized to predict this parameter. The experimental model presented by [PERSON] et al. (2015) has been first numerically simulated by using ANSYS-CFX. Different simulations were then carried out with regard to the numerical model's ability to simulate the flow field at 30- and 60-degree intake angles and different ratios of branch channel width to the main channel. The results were used to present an equation for the purposes of predicting the main velocity. The results of the carried out verifications, (MAPE (mean) = 5% and RMSE (max) = 0.017, R\({}^{2}\) = 0.95, SI = 0.025), indicated that the simulation was fairly accurate. Therefore, with regard to the fact that the numerical model performed fairly accurately in simulating the experimental conditions, the numerical model's data were used to present a model by using GMDH to estimate the mean velocity. The results of the statistical indexes used to quantitatively examine this model, (R\({}^{2}\) = 0.86, MAPE = 10.44, RMSE = 0.03, and SI = 0.12), indicated the accuracy of this model in predicting the mean velocity of the flow within open channel intakes. Like the training mode, as the width ratio increases the prediction accuracy decreases. The velocity prediction results at the model's test mode (R\({}^{2}\) = 0.88, MAPE = 9.72, RMSE = 0.03, and SI = 0.11) also follow a similar trend to training mode of the model which indicates the flexibility of the presented model under different hydraulic conditions. It is, therefore, advisable to use the model presented in this study (Equation (23)), which is reasonably accurate. It could also be seen at different width ratios that the predictions made have a relative error of less than 10% at the width ratio of approximately 90%. The maximum error values are related to a 1.4 width ratio. It is worth mentioning that almost 70% of the predictions have a relative error  
Figure 9: Error distribution of GMDH for (**a**) different angle (\(\theta\)) (**b**) different relative width of branch channel to main channel (W\({}_{b}\)*/W\({}_{m}\)*).  
less than 15% in this state, which reveals that the proposed model performs with high performance. Although the manuscript brings significant novelty in predicting velocity in channel intake through a hybridized CFD model, other data-driven methods' applicability is yet to be explored. Future research can immensely benefit from the involvement of advanced machine learning and deep learning techniques hybridized by the CFD codes.  
Data curation, S.S.B., I.A.-S., H.K., S.K., J.E., and A.M.; formal analysis, S.S.B., I.A.-S., H.K., S.K., J.E., and A.M.; investigation, S.S.B., I.A.-S., H.K., S.K., J.E., and A.M.; project administration, S.S.B., I.A.-S., H.K., S.K., J.E., and A.M.; software, S.S.B., I.A.-S., H.K., S.K., J.E., and A.M.; supervision, S.S.B. and A.M.; validation, H.K.; visualization, S.S.B., I.A.-S., H.K., S.K., J.E., and A.M.; writing--original draft, H.K.; writing--review and editing, S.S.B., I.A.-S., H.K., S.K., J.E., and A.M. All authors have read and agreed to the published version of the manuscript.  
This research in part is supported by the Hungarian State and the European Union under the EFOP3.6.2-16-2017-00016 project.  
The authors declare that there is no conflict of interests regarding the publication of this paper.