In this study, branched polyethylenimine (PEI) loaded on magnetic multiwalled carbon nanotubes (MWCNT/CoFe₂O₄) was synthesized and characterized by transmission electron microscopy (TEM), field emission scanning electron microscopy (FESEM), X-ray diffraction (XRD), Brunauer–Emmett–Teller (BET) analysis and Fourier transform infrared spectroscopy (FTIR). The isotherms and kinetic behavior of the adsorption of Cu(II) and Cr(VI) onto MWCNT/CoFe₂O₄@PEI were explained by pseudo-second-order kinetic and extended Freundlich models. The adsorption performance was analyzed by an adaptive neuro-fuzzy inference system (ANFIS), a generalized regression neural network (GRNN) and response surface methodology (RSM) and compared. The influence of process variables (the sonication time, initial concentration of cations, and adsorbent mass) on the removal of Cu(II) and Cr(VI) was considered by central composite rotatable design using RSM, GRNN and ANFIS. All the models were statistically compared with the root mean square error (RMSE), coefficient of determination (R²), absolute average deviation (AAD) and mean absolute error (MAE) based on the validation dataset. The coefficients of determination (R²) calculated from the validation data for the ANFIS, GRNN and RSM models were 0.9995, 0.9978 and 0.9647 for Cu(II) and 0.9992, 0.9949 and 0.9567 for Cr(VI) ions, respectively. The ANFIS model was found to be more precise in comparison with the other models. However, it was demonstrated that GRNN is much easier than the ANFIS method and needs less time for analysis. Hence, it has good prospects in chemometrics, and it is feasible that the GRNN algorithm could be applied to model real systems. The monolayer adsorption capacities for Cu(II) and Cr(VI) ions were 510.200 and 490.220 mg g⁻¹, respectively.