# Machine Learning Prediction of Airfoil Aerodynamic Performance Using Neural Network Ensembles
## 3 Results
### Group B--Diverse Single Seeds  
Group B is designed to stress-test the model's sensitivity to random initialization by breaking away from uniform sampling, unlike Group A's structure. By introducing nonlinear, uncorrelated seed values, this group probes how much variability exists in performance when the seed space is sampled with no continuity, thereby evaluating the stability and generalization consistency of the model.  
As presented in Table 5, the results show a good degree of stability in both lift and drag predictions across the group. In terms of lift, the model maintains a MAPE between 1.08% and 1.97%, with seed 123 achieving the lowest error (1.08%) and seed 1 the highest (1.97%). For drag, prediction error remained largely controlled, with seed 0 and seed 999 achieving strong results (0.57%, respectively 0.58%).  
These findings, presented in more detail in Table 6, suggest that the model exhibits a high level of resilience to initialization-induced variance. While some fluctuation is present, especially in seeds 1 and 777, the network consistently converges to low-error predictions. The three airfoils that previously had notable drag prediction insta  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**N.crct.** & **Airfoil** & **Seed** & \begin{tabular}{c} **MAPE** \\ \(C_{L}\) \\ \end{tabular} & \begin{tabular}{c} **MAPE** \\ \(C_{D}\) \\ \end{tabular} & \multirow{4}{*}{13} & \multirow{4}{*}{20} & 42 & 2.37 & 1.14 & & 42 & 1.01 & 1.31 \\ \cline{5-10} \multirow{4}{*}{6} & \multirow{4}{*}{\begin{tabular}{c} NACA \\ 1512 \\ \end{tabular} } & 43 & 0.90 & 1.53 & & 43 & 1.04 & 2.33 & 43 & 1.71 & 1.89 \\ \cline{5-10} \multirow{4}{*}{7} & \multirow{4}{*}{\begin{tabular}{c} NACA \\ 1615 \\ \end{tabular} } & 44 & 1.04 & 0.61 & & 44 & 1.91 & 0.72 & 44 & 0.75 & 1.58 \\ \cline{5-10} \multirow{4}{*}{7} & \multirow{4}{*}{\begin{tabular}{c} NACA \\ 415 \\ \end{tabular} } & 45 & 3.03 & 2.25 & & 45 & 2.84 & 2.22 & 45 & 0.81 & 2.08 \\ \cline{5-10} \multirow{4}{*}{7} & \multirow{4}{*}{\begin{tabular}{c} NACA \\ 1615 \\ \end{tabular} } & 46 & 1.70 & 1.28 & & 46 & 0.77 & 1.30 & 46 & 0.76 & 1.22 \\ \cline{5-10} \multirow{4}{*}{7} & \multirow{4}{*}{\begin{tabular}{c} NACA \\ 44 \\ \end{tabular} } & 42 & 1.81 & 0.90 & & 42 & 1.07 & 1.21 & 42 & 0.66 & 1.17 \\ \cline{5-10} \multirow{4}{*}{7} & \multirow{4}{*}{\begin{tabular}{c} NACA \\ 4314 \\ \end{tabular} } & 43 & 2.53 & 1.39 & & 43 & 3.34 & 1.82 & 43 & 1.43 & 3.80 \\ \cline{5-10} \multirow{4}{*}{7} & \multirow{4}{*}{\begin{tabular}{c} NACA \\ 44 \\ \end{tabular} } & 44 & 1.28 & 0.76 & & 44 & 1.93 & 1.08 & 44 & 1.02 & 0.73 \\ \cline{5-10} \multirow{4}{*}{7} & \multirow{4}{*}{\
\begin{tabular}{c} NACA \\ 4314 \\ \end{tabular} } & 45 & 5.09 & 1.69 & & 45 & 2.78 & 1.25 & 45 & 0.85 & 2.17 \\ \cline{5-10} \multirow{4}{*}{7} & \multirow{4}{*}{
\begin{tabular}{c} NACA \\ 4314 \\ \end{tabular} } & 46 & 2.81 & 1.01 & & 46 & 1.59 & 1.31 & 46 & 0.52 & 0.83 \\ \hline \hline \end{tabular}
\end{table}
Table 4: _Cont_.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Single** & **Training Time** & \begin{tabular}{c} **MAPE** \\ \(C_{L}\) \\ \end{tabular} & \begin{tabular}{c} **MAPE** \\ \(C_{D}\) \\ \end{tabular} & \
\begin{tabular}{c} **R2** \\ \(C_{L}\) \\ \end{tabular} &
\begin{tabular}{c} **R2** \\ \(C_{D}\) \\ \end{tabular} \\ \hline
0 & 564.94 s (9.42 min) & 1.10\% & 0.57\% & 0.9998 & 0.9954 \\
1 & 710.68 s (11.84 min) & 1.97\% & 0.99\% & 0.9998 & 0.9938 \\
123 & 567.39 s (9.46 min) & 1.08\% & 1.54\% & 0.9999 & 0.9855 \\
777 & 361.83 s (6.03 min) & 1.78\% & 1.70\% & 0.9998 & 0.9861 \\
999 & 681.81 s (11.36 min) & 1.65\% & 0.58\% & 0.9998 & 0.9974 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Group B—Overall model performance for diverse single seeds.  
lead to more stable learning, particularly for drag, which is typically harder to predict due to higher noise.