## 4 ANN Modeling
### Weighted Sum Model (WSM)  
The design parameters of non-dimensional plate length and inclined angle were optimized to minimize the averaged reflection coefficient (\(R_{f}\)) and the spatial footprint  
\begin{table}
\begin{tabular}{c c c c} \hline  & _H/\(\lambda\)=0.01_ & _H/\(\lambda\)=0.02_ & _H/\(\lambda\)=0.03_ \\ \hline MSE & 0.00001 & 0.00003 & 0.00003 \\ MAE & 0.00241 & 0.00439 & 0.00429 \\ \(R^{2}\) score & 0.9817 & 0.9831 & 0.9872 \\ \hline \end{tabular}
\end{table}
Table 2: The evaluation metrics of the predicted output feature of the ANN model.  
Figure 6: The true values against the predicted values of the averaged reflection coefficient.  
Figure 7: The input dataset for the prediction of the (**a**) non-dimensional plate length and (**b**) inclined angle of an inclined porous plate.  
(\(l\cos\theta/h\)). The reflection coefficient was predicted using the trained ANN model outlined in the previous section, while the spatial footprint was calculated based on the plate length and the inclined angle, utilizing the larger dataset. To address the two objectives in the optimization process, a weighted sum model (WSM) was applied, and weighting factors were incorporated to represent their relative importance. The WSM is a well-known and simple multi-criteria decision-making approach used to evaluate multiple alternatives based on various decision criteria. Criteria are the attributes or factors taken into account during the decision-making process. This study has multiple criteria, such as the averaged reflection coefficient and the spatial footprint. Each criterion may carry a different level of importance or weight based on the context. Alternatives represent the various options or solutions available for evaluation, with each alternative assessed on how effectively it meets the criteria. The generated dataset of the reflection coefficient and the spatial footprint were utilized to prepare these alternatives. Weighting involves assigning relative importance to each criterion, representing its significance in the decision-making process. Scoring evaluates each alternative against each criterion, resulting in a numerical score that indicates how well the alternative fulfills the criterion. Finally, aggregation combines the scores and weights to yield an overall assessment of each alternative. The formula is given below:  
\[S^{i}=w_{1}R^{i}_{f}+w_{2}((l\cos\theta)^{i}/h) \tag{29}\]  
where \(S^{i}\) is the overall score of the alternative \(i\), \(w_{1}\) is the weighting factor for \(R_{f}\), \(w_{2}\) is the weighting factor for \(l\cos\theta/h\), and \(R^{i}_{f}\) and \((l\cos\theta)^{i}/h\) are the normalized values of alternative \(i\). The normalization is carried out using the MinMaxScaler as given in Equation (26). The weighting factor ratios (\(w_{1}:w_{2}\)) are assigned as 100% : 0, 80% : 20%, and 60% : 40%, where the ratio 100% : 0 denotes the optimization is based solely on the reflection coefficient, the ratio 80% : 20% indicates that the reflection coefficient is significantly prioritized over the spatial footprint, and the ratio 60% : 40% means both are given nearly equal importance with a 20% preference for the reflection coefficient.