## 4 Results and Discussion
### Neural Networks in Adsorptive Processes
applied the MLPNN Feedforward ANN, and the software Matlab, for predicting the performances of competitive adsorption of phenol (Ph) and resorcinol (Re) from an aqueous solution by conventional and low-cost carbonaceous adsorbents such as AC (Model A), wood charcoal (Model B), and rice husk ash (Model C) (Table 3) [10]. The input parameters used to train the ANN were the adsorbent concentration (g/L), the initial Ph and RE concentrations (mg/L), the contact time (h) and the pH, and, as outputs, the removal efficiencies of these pollutants. The statistical performance of the models was assessed using the ME, MSE, and RMSE. They also carried out a linear regression analysis with the values predicted by the network and the actual experimental values of the pollutant removal efficiencies in a bi-solute mixture of Ph and Re. The efficiency achievements fairly validated the experimental results. The great potential of ANNs in predicting the efficiency of pollutant removal in a competitive adsorption process was verified. [PERSON] et al. also used MLPNN Feedforward ANN for predicting the performances of the competitive adsorption of Crystal Violet onto the composite Chitosan/Nanodiopside (Table 3) [47]. The GA-ANN architecture has also been used (Table 3). The optimization and prediction of the behavior of Au-NP-AC and TiO\({}_{2}\)-NP-AC materials in the adsorption of phenol red (PR) dye was carried out by applying the GA-ANN model based on the Levenberg-Marquardt algorithm (LMA), consisting of a linear transfer function (purelin) at the output layer and a tangent sigmoid transfer function (tansig) at the hidden layer, with 15 neurons for Au-NP-AC and 19 neurons for TiO\({}_{2}\)-NP-AC [44]. The input variables were the initial pH, the colorant concentration, the adsorbent dosage, and the contact time with the ANN. The applicability of this model was judged by the MSE and R\({}^{2}\) and the following results were obtained: MSE = 3.19 \(\times\) 10\({}^{4}\) and R\({}^{2}\) = 0.9962 for the removal efficiency by Au-NP-AC and MSE = 0.0022 and R\({}^{2}\) = 0.9729 for TiO\({}_{2}\)-NP-AC. The data predicted by the model were found to be in good agreement with the experimental values. [PERSON] et al. evaluated the impact of temperature, the amount of adsorbent, the initial concentration of the pharmaceutical Triamterene, and the contact time on the adsorption efficiency of this drug by multi-walled carbon nanotubes (MWCNTs) and single-walled carbon nanotubes (SWCNTs) using the multiple linear regression (MLR) model and ANN-GA [61]. To select the optimal topology for ANN-GA, 1-25 neurons were applied at the hidden layer, and the best was 3-3-1 for MWCNT and 3-7-1 for SWCNT. The results revealed that the applicability of the ANN model was more suitable for a more accurate and repeatable prediction of the experimental adsorption data compared to the MLR model (Table 3). An example of applying other ANN architectures (ANNs integrated with differential evolution optimization (DEO)) was in the work by [PERSON] et al., where the performance of a polyaniline-based nano adsorbent for the removal of methyl orange dye from wastewater in a batch adsorption process was studied [45]. To minimize the number of experiments and obtain optimal conditions, the authors developed a multivariate predictive model based on response surface methodology (RSM) and compared it with data-driven modeling using ANN-DEO for predicting the adsorption of the dye. The authors found that the optimal ANN-DEO architecture was the 5-12-1 topology and that the maximum number of iterations in the ANN-DEO implementation was 500, giving a higher R\({}^{2}\) and a lower MSE with 12 neurons in the hidden layer. The optimized trained neural network well represented the test data (R\({}^{2}\) = 0.964) and the validation data (R\({}^{2}\) = 0.973). [PERSON]'s chi-square evaluation of the quality of the fit was 0.005 for RSM and 0.038 for ANN-DEO, indicating the superiority of the ANN-DEO model for predictions over the quadratic model predictions provided by RSM.