## 5 ANN Validation  
Three additional input combinations that differed from the initial DOE but still adhered to the input ranges, presented in Table 7, were generated after completing training and evaluation. Each combination was printed with five repetitions and subjected to tensile testing.  
The selection of three additional combinations was motivated by the need to test the ANN's ability to generalize to process conditions not yet observed during training. This approach helps ensure that the model can make accurate predictions over a wide range of printing scenarios, increasing its practical utility and reliability. The assessment evaluated the ability of the ANN to predict and generalize scenarios, even when there are minor differences in printing circumstances. The three considered cases take into account the values of the layer height and fan speed that are different from those used for the training. The height of each layer has an impact on both the strength and surface quality of the printed component. Additionally, the speed of the fan can affect the cooling of the material during the printing process, which can ultimately impact the mechanical properties of the material, including its strength and ductility [11; 15; 16].  
Table 8 displays the neural network's ability to predict new data. The R\({}^{2}\) value is above 70%, indicating good capabilities, considering the limited number of data points used for the training part of the network.  
\begin{table}
\begin{tabular}{c c c} \hline
**Input** & **Relative Importance in \%** & **Rank** \\ \hline A & 16.9 & 3 \\ B & 20.2 & 1 \\ C & 13.3 & 4 \\ D & 20.1 & 2 \\ E & 11.4 & 5 \\ F & 10.0 & 6 \\ G & 8.1 & 7 \\ Sum & 100.0 & \\ \hline \end{tabular}
\end{table}
Table 6: Connection weight approach.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Combination** & **A** & **B** & **C** & **D** & **E** & **F** & **G** \\ \hline C1 & 3 & 0 & 2 & 1 & 0 & 0 & 0 \\ C2 & 3 & 0 & 2 & 1 & 3 & 0 & 0 \\ C3 & 3 & 0 & 2 & 0 & 3 & 0 & 0 \\ \hline \end{tabular}
\end{table}
Table 7: Additional combination for ANN test.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Neuron 1** & **Neuron 2** & **Neuron 3** & **Neuron 4** & **Neuron 5** & **Neuron 6** & **Neuron 7** \\ \hline A & \(-0.395\) & \(-0.751\) & \(-0.341\) & \(-0.231\) & \(0.362\) & \(-0.151\) & \(-0.328\) \\ B & \(-0.414\) & \(-0.332\) & \(-0.347\) & \(-0.224\) & \(-0.330\) & \(-0.318\) & \(-0.383\) \\ C & \(-0.362\) & \(-0.166\) & \(-0.071\) & \(-0.187\) & \(-0.117\) & \(-0.131\) & \(-0.184\) \\ D & \(-0.465\) & \(-0.310\) & \(-0.330\) & \(-0.682\) & \(-0.524\) & \(-0.574\) & \(-0.570\) \\ E & \(-0.022\) & \(-0.036\) & \(0.377\) & \(0.624\) & \(0.279\) & \(0.521\) & \(0.521\) \\ F & \(-0.017\) & \(-0.024\) & \(-0.025\) & \(0.072\) & \(-0.379\) & \(0.064\) & \(-0.305\) \\ G & \(-0.014\) & \(-0.022\) & \(-0.023\) & \(0.013\) & \(-0.287\) & \(-0.016\) & \(-0.129\) \\ UTS & \(0.557\) & \(0.969\) & \(-0.357\) & \(-0.185\) & \(0.739\) & \(-0.108\) & \(-0.257\) \\ \hline \end{tabular}
\end{table}
Table 5: Input–hidden–output connection weights.  
The other performance metrics demonstrate a low prediction error, with an MAE and MSE of 0.070 and 0006, respectively. The low standard deviation values indicate a low variability and high repeatability. Finally, the results show that an excellent prognosis quality can be achieved by using the optimal meta-model, and the estimated prognosis from the COP of 99.20% indicates that the actual data closely match those of the verification dataset. Thus, the percentage difference between the data predicted by the ANN and the data obtained during the experimental campaign was calculated using the following formula:  
\[Variation=\frac{UTS_{pred}-UTS_{real}}{UTS_{real}}.100\% \tag{6}\]  
Table 9 shows that the variations are minimal, ranging from \(-1.17\%\) to \(2.56\%\), indicating a low margin of error.