## 4 Results and Discussion  
### Regression Model Results  
* Performance evaluation  
In the current study, 80% of the data was selected for training, while 20% of the data was used to validate the ML models as recommended by [PERSON] et al. [26]. The training and testing data were randomly selected to confirm that the datasets were typical samples of the original dataset. The MLAs performance was evaluated with the help of some of the most commonly used statistical indicators. The particulars of the statistical parameters are revealed in Table 3[27]. Table 4 depicts the configuration parameters for all the considered MLAs. The GridsearchCV tool in Scikit-learn was used to obtain the significant hyperparameters for each MLA. The hyper-parameters of ML models were calculated based on the fit accuracy. \begin{table}
\begin{tabular}{c c c} \hline \hline
**S. No.** & **Statistical Parameter** & **Equation** \\ \hline
1. & Correlation coefficient (R) & \(\mathrm{R}=\frac{\sum_{i=1}^{n}\left(M_{i}-M_{\mathrm{avg}}\right)\left(E_{i}-E _{\mathrm{avg}}\right)}{\sqrt{\sum_{i=1}^{n}\left(M_{i}-M_{\mathrm{avg}}\right) ^{2}\sum_{i=1}^{n}\left(E_{i}-E_{\mathrm{avg}}\right)^{2}}}\) \\ \hline
2. & Mean Bias Error (MBE) & \(\mathrm{MBE}=\frac{1}{\hbar}\sum_{i=1}^{n}\left(E_{i}-M_{i}\right)\) \\ \hline
3. & \(\begin{array}{c}\mathrm{Root\,Mean\,Square}\\ \mathrm{Error\,(RMSE)}\end{array}\) & \(\mathrm{RMSE}=\sqrt{\frac{1}{\hbar}\sum_{i=1}^{n}\left(E_{i}-M_{i}\right)^{2}}\) \\ \hline
4. & Mean Percentage Error (MPE) & \(\mathrm{MPE}=\frac{1}{\hbar}\sum_{i=1}^{n}\left(\frac{\left(E_{i}-M_{i}\right)}{ M_{i}}\right)\times 100\) \\ \hline
5. & \(\begin{array}{c}\mathrm{Mean\,Absolute\,Percentage}\\ \mathrm{error\,(MAPE)}\end{array}\) & \(\mathrm{MAPE}=\frac{100}{\hbar}\sum_{i=1}^{n}\left|\frac{\left(E_{i}-M_{i} \right)}{M_{i}}\right|\) \\ \hline
6. & \(\begin{array}{c}\mathrm{Maximum\,Absolute\,Relative}\\ \mathrm{Error\,(erMAX)}\end{array}\) & \(\mathrm{erMAX}=max\left(\left|\frac{\left(E_{i}-M_{i}\right)}{M_{i}}\right| \right)\right)\) \\ \hline
7. & \(\mathrm{Mean\,Absolute\,Error\,(MAE)}\) & \(\mathrm{MAE}=\frac{1}{\hbar}\sum_{i=1}^{n}\left(E_{i}-M_{i}\right)\) \\ \hline
8. & \(\mathrm{Uncertainty\,at\,95\%\,(U_{95})}\) & \(\mathrm{U_{95}=1.96\left(SD^{2}+RMSE^{2}\right)^{0.5}}\) \\ \hline
9. & \(\mathrm{T\,-Statistics\,(t\,\text{-stats})}\) & \(\mathrm{t}=\left[\frac{(n-1)\,\mathrm{MBE}^{2}}{\mathrm{RMSE}^{2}-\mathrm{MBE }^{2}}\right]^{0.5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Equations of statistical parameters. Figure 3 shows the performance of developed MLAs. There is a good agreement between the estimated and the measured (from CFD simulations) values for most MLAs. The deposition efficiency was estimated extremely well by all the MLAs. The MLP and GPR models performed exceptionally well, while the RF and \(k\)-NN models performed reasonably. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **MLAs** & **Hyper-Parameters** & \\ \hline \multicolumn{3}{c}{**Category 1**} & **Category 2** \\ \hline
1 & \(k\)-NN & No. of Neighbors: & 4 & 12 \\
2 & RF & No. of estimators: & 4 & 4 \\
3 & GPR & Kernel type: & DotProduct (sigma = 1) + & DotProduct (sigma = 1) + \\  & & RBF(length scale = 1), & RBF(length scale = 1), \\  & & No. of restarts optimiser & 2 & 2 \\  & & Sizes of hidden layer: & (100.) & (100,) \\  & & No. of hidden layers: & 1 & 1 \\
4 & MLP & Max iterations: & 10000 & 10000 \\  & & No. of hidden layers: & 0.001 & 0.001 \\  & & learning rate: & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Hyper-parameters of the MLAs used in the present work. Figure 3: _Cont._  
Table 5 shows the values of different statistical pointers, with the most significant value shown in bold. MBE values are in the range from \(-1.810\) to \(0.090\) for category 1 and \(0.066\) to \(-0.711\) for category 2. Most models have negative MBE values that suggest under-prediction, whereas the MLP model has a positive value that suggests over-prediction. The GPR model possesses the most significant value of MBE.