The environmental pollution caused by antibiotics such as amoxicillin and ibuprofen has gained increasing attention in recent years. These compounds should be eliminated from discharged effluents to prevent possible negative effects on humans, animals, and the environment. Recently, adsorption processes have gained more and more interest among the possible methods to remove emerging pollutants from water. In this study, activated carbon and potassium persulfate has been investigated for the adsorption of amoxicillin and ibuprofen from synthetic wastewater. Scanning Electron Microscopy (SEM), Fourier transform infrared (FTIR) and X-ray diffraction (XRD) analysis has been used in adsorbents characterization. Furthermore, the adsorption mechanisms, performance, kinetics and isotherm for amoxicillin and ibuprofen removal were evaluated. To optimize the experiment results by minimizing the final concentration and increasing the percentage of amoxicillin and ibuprofen removal efficiency, Response Surface Methodology-Central Composite Design (RSM-CCD) (statistical analysis) and Support Vector RegressionGenetic Algorithm models (SVR-GA) (machine learning) were used by Minitab and MATLAB software. The removal process was conducted using different pH values (3–9), adsorbent dosages of activated carbon and potassium persulfate (10–50 mg), contact time (5–120 min) and initial concentration of each antibiotic (5-200 mg/L). It was found that both adsorbents removed amoxicillin and ibuprofen effectively at pH 7 and the optimal contact time was 5 minutes. It has been demonstrated that the Langmuir isotherm model for both AMX and IBU removal accurately defines the isotherm data (R2 = 1). In addition, a pseudo-second-order model was used to describe the adsorption kinetics. As a consequence of these data, the maximum adsorption capacity of amoxicillin on activated carbon and potassium persulfate was 90.97 and 196.31 mg/g, respectively, while for ibuprofen it was 135.23 and 196.47 mg/g. In the modelling part, RSM and SVR-RBF models could be fitted to both models to predict the results of the final concentrations of amoxicillin and ibuprofen. The performance of these models is evaluated using mean absolute relative error (MARE%). Both prediction models have identical MARE equal to or less than 25%. In this case, the final concentration can be predicted using either the GA-SVR or the RSM model. On the other hand, the value of R2 obtained by RSM and SVR was close to 1, but the lowest mean absolute relative error (%) for all antibiotics and adsorbents is modelled by machine learning, which is better than RSM-CCD.