## 5 Results and Discussion
### Model Training and Testing  
The parameters influencing illite wt.% as determined by the Pearson correlation coefficient and the PCA were embedded in an FF-ANN consisting of an input layer, two hidden layers, and an output layer (Figure 6). The training procedure was repeated using hidden layer neuron combinations from 5 to 50 with a step value of 5 to find the optimal model for the target parameters. The optimum results were recorded and are listed in Table 4.  
The overall performance of selected A.I. algorithms for FF-ANNs using the B.R. method with 30 and 15 neurons in the hidden layers, respectively, generates an R\({}^{2}\) value of 0.92 for the illite wt.% predictors (Table 4). For large models with sufficient representational capacity to overfit the task, it is frequently observed that the training error decreases consistently over time while the validation error begins to rise after a certain point. A popular regularization strategy known as early stopping can be employed to address this issue. In this strategy, the optimal parameter setting yielding the smallest validation error is reserved. Once training is terminated with the smallest training error, the model associated with the optimal parameter setting (smallest validation error), and not the most recent model, is selected. Figure 5: Petrophysical logs and the relationship with the illite wt.%. Figure 6: The MLP ANN structure shows the input, hidden, and output layers with sigmoid-sigmoid transform functions and the neurons in the hidden layers. As a result, the network in this study was calibrated by being trained on a separate test set. When calibrated, a network can deliver correct results once applied to new data since it has been tuned to its optimal parameters for the test set. The outcomes were quite promising after training to find the most optimal model for our goals. We aimed for a high R\({}^{2}\) and a low mean square (MSE) error between the predicted and the desired values. A scatter plot for the illite wt.% was created using an R\({}^{2}\) value of 0.92 from the best-fit model extracted during training (Figure 7). The neural network was trained using available data and subsequently tested against data from three wells distinct from those used in training and initial testing to determine the illite wt.%. The network's performance was evaluated based on its ability to accurately predict the illite wt.% for these unseen wells. The results demonstrated a favorable average coefficient of determination R\({}^{2}\) of 0.885 across the three evaluated wells. This indicates a strong correlation between the predicted and actual illite weight percentages, highlighting the effectiveness of the neural network model in accurately estimating this critical parameter (Figure 8). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Network**} & **Neurons in** & **Neurons in** & \multirow{2}{*}{**Training R\({}^{2}\)**} & \multirow{2}{*}{**Testing R\({}^{2}\)**} \\  & **Hidden Layer 1** & **Hidden Layer 2** & & \\ \hline
1 & 10 & 5 & 0.85 & 0.77 \\ \hline
2 & 15 & 5 & 0.81 & 0.86 \\ \hline
3 & 25 & 10 & 0.86 & 0.78 \\ \hline
4 & 25 & 15 & 0.79 & 0.63 \\ \hline
**5** & **30** & **15** & **0.92** & **0.885** \\ \hline
6 & 35 & 20 & 0.83 & 0.76 \\ \hline
7 & 45 & 25 & 0.84 & 0.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The optimum results from the different neuron combinations in the hidden layers. Figure 7: Linear regression graph shows the R\({}^{2}\) relation between measured and predicted illite wt.%. Using the petrophysical properties of conventional well logs and XRD data, this study provided optimistic predictions about the illite wt.% using a four-layer FFNN backpropagation algorithm and tangent sigmoidal hyperbolic transfer function. After applying the model to wells not part of the training and testing processes, the findings showed that it was excellent and dependable at predicting the value of illite wt.%.