## 3 Performance Analysis of the Data-Driven Models  
Several configurations of the MLPNN representing the input layer, the hidden layer, and the output layer were tested in modeling the relationship between the textural properties and the BPA degradation from the wastewater. The performance of each of the MLPNN configurations as a function of the RMSE and R2 is depicted in Figure 3. The artificial neuron in the hidden layer of the MLPNN was varied from 1 to 15 to determine  
Figure 2: Interaction effect of (**a**) specific surface area and crystallite size, (**b**) pore diameter and crystallite size, (**c**) pore volume and crystallite size, and (**d**) pore volume and particle diameter on the BPA degradation. the best configuration. As shown in Figure 3a, the RMSE obtained varies with the changes in the number of artificial neurons in the hidden neuron. Similarly, the R\({}^{2}\) values also vary with changes in the artificial neurons in the hidden layer. The MLPNN with the configuration of 4 input nodes, 13 artificial neurons, and 3 output nodes displayed the best performance since the RMSE values are 4.2 and 4.6 for training and testing, respectively. R\({}^{2}\) of 0.902 and 0.992 were obtained for the 4-13-3 MLPNN configuration during training and testing, respectively. Using the best MLPNN configuration of 4-13-3, the performance of the model was tested as a function of the predictability of the targeted variable. As shown in Figure 4, the targeted variables to be tested were the BPA degradation and the rate of degradation of the BPA. The predictability of the MLPNN is a function of how well the nonlinear relationship between the input variables and the targeted variables can be trained and learned by the model. Figure 4 depicts the prediction of the BPA degradation and the rate of BPA degradation from the wastewater across the data points. It can be seen that at each data point, the actual values of the BPA degradation are consistent with MLPNN predicted values (Figure 4a). Similarly, the actual rate of BPA degradation at each data point is consistent with the MLPNN predicted values as shown in Figure 4b. A similar trend is observed for predicting the initial concentration of the BPA as shown in Figure 4c. Figure 3: (**a**) The RMSE of each of the MLPNN configurations; (**b**) the R\({}^{2}\) of each of the MLPNN configurations. This is an indication that the MLPNN model is robust in training and learning the nonlinear relationship between the input variables and the targets, resulting in a good prediction of the BPA degradation as well as the rate of BPA degradation. The robustness of the MLPNN model in predicting the BPA degradation and the rate of degradation can be attributed to the inbuilt features such as the back-propagation algorithms that help to minimize prediction errors [50]. The back-propagation algorithm helps the MLPNN model to improve its accuracy of the model [51]. With the help of the back-propagation algorithm, gradient descent is computed as a function of the weight [52]. Hence, the targeted outputs are compared with the predicted output, and the MLPNN network is positioned to adjust the associated connection weights with the hidden neurons in other to minimize the prediction errors [53; 54]. The performance of the MLPNN in the prediction of the targeted output is consistent with the literature. The performance of MLPNN in modeling hydrogen production by catalytic steam methane reforming has been reported by [PERSON] et al. [55]. The study revealed that the MLPNN robustly predicted hydrogen production with an R\({}^{2}\) of 0.988 and RMSE of 0.437. Similarly, nanofluid viscosity has been accurately predicted using MLPNN with an R\({}^{2}\) of 0.999. The MLPNN modeled the nonlinear relationship between the input parameters which include temperature, nanoparticle size, density, volume fraction and base fluid viscosity, and the nanofluid viscosity. [PERSON] et al. [56] reported a robust prediction of phenol degradation from wastewater using MLPNN.