## 3 Results and Discussion
### Results of the 2 nd Model Using CFD Inputs (Evaluating the 2 nd Model Independently)  
In this section, we focus exclusively on the finalized second model's results. Figure 17 presents the scatter plot of the second model's predictions (with the ground truth particle distribution on the substrate) on the entire test set. Additionally, Figures 18 and 19 show the ground truth and prediction results of a specific sample from the test set, respectively. This sample corresponds to the following configuration: an inlet pressure of 4 MPa, an inlet temperature of 800 \({}^{\circ}\)C, a substrate SOD of 20 mm, a mask SOD of 16 mm, a mask wire diameter of 0.46 mm, a mask opening size of 1.14 mm, and an open area of 51%. Figure 16: (**a**) Distribution of reallocated predictions vs. ground truth (y and z) for the test sample (inlet pressure: 4 MPa, inlet temperature: 800 \({}^{\circ}\)C, substrate SOD: 20 mm, mask SOD: 16 mm, wire diameter: 0.46 mm, opening size: 1.14 mm, and open area: 51%). Where the bars overlap, they appear as a purple. This indicates where the predicted distribution closely matches the ground truth; (**b**) local reallocation of under-estimated predictions for the mentioned test sample. A combined analysis of the scatter plots and the predicted velocity and temperature distributions demonstrates that the model effectively predicts key particle characteristics upon impact, particularly the normal impact velocity (\(u\)) and temperature (\(T\)) of each particle. The scatter plot of the \(x\)-direction velocity distribution (\(u\)) shows a strong correlation between the predicted and actual values, with most points closely following the ideal prediction line, indicating that the model successfully captures overall trends. Similarly, the scatter plot for particle temperature distribution exhibits a high degree of agreement between the predicted and actual values, further reinforcing the model's accuracy in predicting temperature characteristics. For the \(y\)-direction velocity (\(v\)), while the scatter plot generally follows the ideal prediction line, there are more dispersed points, particularly in the low-velocity and negative-velocity regions, indicating limited model capability in capturing local details for this direction. The scatter plot for the \(z\)-direction velocity (\(w\)) shows a similar trend. Figure 17: Scatter plot of the second model: predicted vs. actual values on the entire test set. Figure 18: Ground truth for the specific test sample: an inlet pressure of 4 MPa, an inlet temperature of 800 \({}^{\circ}\)C, a substrate SOD of 20 mm, a mask SOD of 16 mm, a mask wire diameter of 0.46 mm, a mask opening size of 1.14 mm, and an open area of 51%. It is important to note that the normal velocity and temperature (\(u\) and \(T\)) of the particle are the primary parameters influencing its adhesion. Deposition and no-deposition states as well as deposition rate are typically estimated by comparing the normal impact velocity (\(u\)) with the critical velocity, which is a function of particle temperature (\(T\)) and diameter [28,29]. In contrast, the velocity components in the \(y\)- and \(z\)-directions (\(v\) and \(w\)) are generally below 20 m/s, while \(u\) ranges from 300 to 750 m/s, making the effects of \(v\) and \(w\) negligible on coating buildup. Although these components (\(v\) and \(w\)) are less significant, their prediction can still be refined for further accuracy. Based on the distribution diagrams (Figures 18 and 19), the model accurately predicts each particle's \(x\)-direction velocity (\(u\)) and temperature (\(T\)), with local values, mean values  
Figure 19: Predictions of the 2 nd model for the specific test sample: an inlet pressure of 4 MPa, an inlet temperature of 800 \({}^{\circ}\)C, a substrate SOD of 20 mm, a mask SOD of 16 mm, a mask wire diameter of 0.46 mm, a mask opening size of 1.14 mm, and an open area of 51%. across all the particles, and overall distribution trends closely aligning with the ground truth.