## 3 Results and Discussion
### ANN Model Results  
After obtaining the optimal hyperparameters through the hyperparameter tuning process, an ANN model was constructed with the configuration illustrated in Figure 7. The structure of this base ANN model consisted of five input layers corresponding to the number of control parameters. The first hidden layer comprised 8 neurons, the second hidden layer consisted of 13 neurons, the third hidden layer also contained 13 neurons, and the final output layer consisted of 2 neurons, corresponding to the two predicted outputs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Level**} & \multicolumn{5}{c}{**Experiment 2**} \\ \cline{2-6}  & **Melt Temperature** & **Mold Temperature** & **Injection Speed** & **Packing Pressure** & **Screw Speed** \\  & (\({}^{\circ}\)**C**) & (\({}^{\circ}\)**C**) & **(mm/s)** & **(bar)** & **(rpm)** \\ \hline
**1** & 192 & 43 & 12 & 22 & 23 \\
**2** & 217 & 58 & 32 & 47 & 48 \\
**3** & 242 & 73 & 52 & 72 & 73 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Full factorial design for Experiment 2. Figure 7: Illustration of ANN model. To evaluate the performance of the constructed model against the test data, one metric to consider is the R\({}^{2}\) value. The R\({}^{2}\) value, or the coefficient of determination, measures how well a model predicts an outcome:  
\[\text{R}^{2}=1-\frac{\sum(y_{i}-\bar{y})^{2}}{\sum(y_{i}-\bar{y})^{2}} \tag{3}\]  
From Table 7, we can see that the model demonstrated excellent performance on the training set, achieving extremely low MSE and mean absolute error (MAE) values for both weight and energy consumption. The R\({}^{2}\) values were exceptionally high, indicating that the model explained 99.16% of the variance in weight and 95.99% of the variance in energy consumption. The combined R\({}^{2}\) total was 97.58%, reflecting strong predictive capability. On the validation set, the model maintained high accuracy for weight prediction, with an MSE of 8.22 \(\times\) 10\({}^{-6}\) and an R\({}^{2}\) value of 98.95%. However, the performance slightly decreased for energy consumption, with an MSE of 0.4354 and an R\({}^{2}\) value of 88.57%. The combined R\({}^{2}\) total was 93.76%, indicating that the model still performed well but with a slight reduction in accuracy compared with the training set. The test set results showed a slight increase in the MSE and MAE values, indicating some degradation in performance when the model was applied to new, unseen data. The MSE for the weight was 1.62 \(\times\) 10\({}^{-5}\), and for energy consumption, it was 0.7285. The R\({}^{2}\) values were 98.49% for the weight and 84.12% for energy consumption, with an overall R\({}^{2}\) total of 91.31%. Despite this decrease, the model still explained a significant portion of the variance for both responses, demonstrating robust generalization ability. Figure 8 displays the actual values of the weight and energy consumption on the \(X\) axis and the predicted values on the \(Y\) axis. A good predictive model will produce points which align closely with the reference prediction line. For weight prediction, the points generated from the predicted values closely resembled the ideal prediction line, with an R\({}^{2}\) value of 98.49%. In contrast, for energy consumption prediction, the predicted values were more dispersed and did not align as closely with the ideal line. There was even one predicted value which was significantly off, resulting in an R\({}^{2}\) value of 84.12% for energy consumption. When examining the distribution of error values, as shown in Figure 9, it was observed that the error distribution for weight prediction was fairly uniform, ranging from \(-\)0.006 to 0.009. In contrast, the error distribution for energy consumption prediction was more centralized, primarily between \(-\)1 and 1. However, there was one value with a significantly different error of five, which could notably shift the performance metrics.