## 3 Results and Discussion
### Results of MLP-Based Models  
The neural network models based upon MLP were executed by employing MATLAB software. The selection of input variables is the initial step in soft computing-based models' development. In this study, models were developed using pH, P, Ca, Mg and C variables. Figure 4: 3D surface plot of Co (**a**), Cu (**b**) and Pb (**c**) versus pH and P showing a three-dimensional functional relationship between designated dependent variable (Z = Co, Cu and Pb) and two independent variables (X = pH, Y = P). Model development is a trial-and-error process. A larger dataset was used for model preparation, and other (smaller) datasets were used for model testing and validation. Different input combinations were used to be developed for predicting the Co, Cu and Pb. After analyzing [PERSON]'s correlation matrix, five different models were developed. The different models are developed using a number of neurons in the hidden layer, and number of runs for output variables are Co, Cu and Pb. Figure 4 indicates the scatter plot of target and predicted values of Co using various MLP models. MLP-2-8-1 lies significantly closer to the line of perfect agreement (1:1) with lesser deviation. The model MLP-2-8-1 is best for predicting Co content, and the 2 signifies the number of input combinations (pH and phosphorus), while the 8 represents the number of neurons in a single hidden layer. Table 2 indicates the values of coefficient of correlation and RMSE for all developed models for Co. Table 2 and Figure 5 suggest that that Model 4 that has the structure 2-8-1 is the best performing of all the developed models for all stages of model development with CC values in training (0.8547), testing (0.7186) and validation (0.5119), compared to the RMSE values obtained in training (0.0474), testing (0.0193) and validation (0.0060). Figure 6 shows the scatter plot of target vs. output Cu using various models for the validation stage. MLP-2-10-1 lies closer to the line of perfect agreement (1:1), while deviation is much less. Table 3 indicates the values of coefficient of correlation and RMSE for all developed models for Cu. This table suggests that Model 2, which has the structure 2-10-1 \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{3}{c}{**Training**} & \multicolumn{3}{c}{**Testing**} & \multicolumn{3}{c}{**Validation**} \\ \cline{2-9}  & **Run** & **CC** & **RMSE** & **CC** & **RMSE** & **CC** & **RMSE** \\ \hline MLP 2-8-1 & 10 & 0.8676 & 0.0453 & 0.7226 & 0.0416 & 0.4026 & 0.0082 \\ MLP 2-5-1 & 10 & 0.8574 & 0.0469 & 0.7107 & 0.0162 & 0.4582 & 0.0070 \\ MLP 2-5-1 & 25 & 0.9075 & 0.0383 & 0.7645 & 0.0148 & 0.3138 & 0.0125 \\ MLP 2-8-1 & 25 & 0.8547 & 0.0474 & 0.7186 & 0.0193 & 0.5119 & 0.0060 \\ MLP 2-6-1 & 25 & 0.8511 & 0.0479 & 0.6662 & 0.0144 & 0.4769 & 0.0070 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Correlation coefficients and RMSE for different MLP topologies in all stages for Co.  
Figure 5: Scatter plot of target vs. output Co using different neural networks models dependent on MLP in validation stage. is the best performing of all the developed models for training and validation stages and shows comparable results in the testing stage with CC values in training (0.9488), testing (0.7366) and validation (0.8626), compared to the RMSE values obtained in training (0.0519), testing (0.0891) and validation (0.0943). The model MLP-2-10-1 is best for predicting the Cu concentration, and the 2 indicates the number of input variables used to build the model (pH and P) and the 10 indicated the number of neurons in a single hidden layer. Figure 7 shows the scatter plot of target vs. output Pb using various models for the validation stage, and the MLP-2-10-1 model lies closer to the line of perfect agreement (1:1), while deviation is much less.