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Abstract Side weirs are broadly used in irrigation channels, drainage systems and sewage disposal canals for controlling and adjusting the flow in main channels. In this study, a new artificial intelligence model entitled “self-adaptive extreme learning machine” (SAELM) is developed for simulating the discharge coefficient of side weirs located upon rectangular channels. Also, the Monte Carlo simulations are implemented for assessing the abilities of the numerical models. It should be noted that the k-fold cross-validation approach is used for validating the results obtained from the numerical models. Based on the parameters affecting the discharge coefficient, six artificial intelligence models are defined. The examination of the numerical models exhibits that such models simulate the discharge coefficient valued with acceptable accuracy. For instance, mean absolute error and root mean square error for the superior model are computed 0.022 and 0.027, respectively. The best SAELM model predicts the discharge coefficient values in terms of Froude number (F d), ratio of the side weir height to the downstream depth (w/h d), ratio of the channel width at downstream to the downstream depth (b d/h d) and ratio of the side weir length to the downstream depth (L/h d). Based on the sensitivity analysis results, the Froude number of the side weir downstream is identified as the most influencing input parameter. Lastly, a matrix is presented to estimate the discharge coefficient of side weirs on convergent channels.