## Appendix B Interpolation-Based Data-Augmentation Protocol for Expanding Sparse Process Parameters  
To perform interpolation, it is first necessary to select endpoint data from two or more sets of CFD simulations. However, particles in different simulations typically occupy different spatial positions or almost it is not possible to find two particles that share the same coordinates in two simulations. As a result, direct interpolation and matching are not feasible. To address this issue, stratified clustering is applied to each dataset based on the particles' \(y\)-coordinates and sorted by \(z\)-coordinates within each \(y\)-based layer. This approach divides particles into multiple layers (strata) along the \(y\)- and \(z\)-axis. Assume a CFD dataset contains N particles, where the coordinates of the \(i\)-th particle at the substrate are \(\theta_{i}=(y_{i},z_{i})\), with \(y_{i}\) and \(z_{i}\) representing the \(y\)- and \(z\)-coordinates, respectively. To match particles within each layer, a relative difference distance based on the \(y\)-coordinate is defined to measure the similarity of particles in the horizontal direction (Equation (A13)). This ensures consistent stratification and enables effective interpolation within each corresponding layer. \[\Delta(i,j)=\frac{|y_{i}-y_{j}|}{\max\big{(}y_{i},y_{j}\big{)}}\] (A13)  
where \(y_{i}\) and \(y_{j}\) are the \(y\)-coordinates of particles \(i\) and \(j\). During the particle matching process, if the relative difference distance between two particles is less than or equal to 5%, they are considered to belong to the same group (Equation (A14)). \[\Delta(i,j)\leq 0.05\Longrightarrow Group(i)=Group(j)\] (A14)  
After completing the matching process, the particle set for each layer is represented as \(S_{l}\) (Equation (A15)). This set \(S_{l}\) contains all the particles within a specific layer that have been grouped based on the matching criteria, ensuring that particles in the same layer share similar horizontal characteristics. \[S_{l}=\Big{\{}\theta_{i}\mid y_{i}\in\Big{[}y_{l}^{\{\{min\}\}},\,y_{l}^{\{\{max\} \}}\big{)}\Big{\}},\,\,l=1,\,2,\ldots,k\] (A15)  
where \([y_{l}^{\{\{min\}\}},y_{l}^{\{\{max\}\}})\) represents the range of \(y\) in the layer \(l\), and \(k\) is the total number of layers. Furthermore, within each layer, particles are sorted by their \(z\)-coordinate to further divide the layer into \(y\)- and \(z\)-coordinate-based sublayers. Finally, particles from each dataset are matched based on these finalized sublayers, ensuring that each particle is spatially as close as possible to its counterpart in the other datasets. Linear Interpolation  
\[Y_{i}(X_{i})=Y_{start}+\frac{(X_{i}-X_{end})}{(X_{end}-X_{start})}\times(Y_{ end}-Y_{start})\] (A16)  
where \(X_{i}\) is the input feature value at the interpolation point \(i\) and \(Y_{i}\) is the interpolated output feature value at that point, \(X_{start}\) and \(X_{end}\) are the boundary input features, and \(Y_{start}\) and \(Y_{end}\) are the corresponding boundary output features. 4 Points Cubic Spline Interpolation  
\[\begin{array}{l}Y_{i}(X_{i})=a_{1}(X_{i}-X_{1})^{3}+b_{1}(X_{i}-X_{1})^{2}+ c_{1}(X_{i}-X_{1})+d_{1},X\in[X_{1},X_{2}]\\ Y_{i}(X_{i})=a_{2}(X_{i}-X_{2})^{3}+b_{2}(X_{i}-X_{2})^{2}+c_{2}(X_{i}-X_{2})+ d_{2},X\in[X_{2},X_{3}]\\ Y_{i}(X_{i})=a_{3}(X_{i}-X_{3})^{3}+b_{3}(X_{i}-X_{3})^{2}+c_where \(a_{n}\), \(b_{n}\), \(c_{n}\), and \(d_{n}\) are cubic spline coefficients, and \(X_{1}\), \(X_{2}\), \(X_{3}\), and \(X_{4}\) are the boundary points of the intervals. Finally, for the mask type, each mask design includes multiple attributes, and the differences between masks are non-monotonic. Therefore, a weighted interpolation method (Equation (A18)) is applied, which considers multiple mask attributes and their irregular variations simultaneously, ensuring a more accurate representation of the data. Inverse Distance Weighted (IDW)  
\[ \begin{array}{c}Y_{i}(X_{i})=\frac{\sum_{k=1}^{N}w_{k}\,Y_{k}}{\sum_{k=1}^{ N}w_{k}}\\ w_{k}=\frac{1}{|X_{i}-X_{k}|}\end{array}