Dynamic studies to test the copper (Cu2+) and manganese (Mn2+) adsorption efficacies on sodium dodecyl sulfate modified graphene (GN-SDS) were conducted. A fixed bed column adsorption performance was assessed by Thomas and Bed Depth Service Time (BDST) model. The adoption capacity of fixed bed was increased with increasing depth; while gradually increasing flow rate negatively affected the adsorption ratio. The optimal adsorption capacities for Cu2+ were 30.03, 41.01, and 48.83 mg/g and for Mn2+ were 29.84, 37.51 and 45.62 mg/g at bed depth of 1, 2 and 3 cm, at constant flow rate of 10 mL/min, respectively. The results of adsorption dynamics were fitted into Thomas model with a correction coefficient (R-2) of 0.996 for Cu2+ and 0.998 for Mn2+. The effect of operating parameters such as adsorbent dosage, initial pH, and temperature was studied by Artificial Neural Network (ANN) for optimizing the conditions required for maximum percentage removal of Cu2+ and Mn2+ ions. The ANN results showed that regimes related to the initial adsorbent dosage had the most importance effect (55 and 45%), among all, on the metals uptake. These results are very promising and, in our opinion, establish a milestone to a vital research field.