## 4 Results of Prediction Accuracy Tests  
To evaluate the prediction accuracy of the surrogate models obtained from the RSM and ANN, 50 test samples randomly distributed inside the input variables' space were created for each prediction accuracy test. These samples were not utilized for surrogate model construction and optimization but were used only for a quantitative prediction accuracy comparison. If \(M\) is defined as the number of test samples, which is 50 in the current study, the quantity to measure the prediction accuracy of the constructed surrogate model is defined using the normalized root-mean-square deviation:  
\[E=\frac{\sqrt{\frac{1}{M}\sum_{i=1}^{M}(\phi_{i}-\hat{\phi}_{i})^{2}}}{\tilde{ \phi}}, \tag{6}\]  
where the variables \(\phi_{i}\) and \(\hat{\phi}_{i}\) are the output values of the \(i\)-th test set computed from XFOIL and constructed surrogate model, respectively, and the \(\tilde{\phi}\) is the mean value of \(\phi_{i}\), which can be computed from  
\[\tilde{\phi}=\frac{1}{M}\sum_{i=1}^{M}\phi_{i}. \tag{7}\]  
Tables 3 and 4 show the values of the normalized root-mean-square deviation \(E\) for the prediction accuracy tests with geometric variables and with geometric and operational variables, respectively. On the rightmost column of each table, the values of the variable \(\gamma\), defined as  
\[\gamma=\frac{E_{RSM}}{E_{ANN}}, \tag{8}\]  
are presented where \(E_{RSM}\) and \(E_{ANN}\) are the normalized root-mean-square deviation of the RSM-computed and ANN-computed surrogate models, respectively. If \(\gamma\) is greater than unity, the ANN-computed surrogate model is more accurate in predicting the lift-to-drag ratio than the RSM-computed surrogate model; otherwise, the latter surrogate model is more accurate. When the values of \(E\) are compared with respect to the number of input variables in Table 3, all \(E\) values increase as the number of variables increases except for the ANN-computed surrogate model with G-DLB-6-3 whose value is slightly smaller than the ANN-computed surrogate model with G-DLB-4-3. The growth of the nonlinearity with an increase in the number of input variables is thought to cause this phenomenon, so the prediction accuracy of the surrogate models obtained from the RSM and ANN decreases for the tests with geometric input variables. In addition, the fact that the values of \(E\) of the surrogate models with geometric input variables are smaller than the ones with geometric and operational input variables reveals that the lift-to-drag ratio prediction of wind turbine airfoils is more difficult to assess when the geometric variables and operating conditions are given as input parameters at the same time instead of when only geometric variables are presented. From Table 4, it is shown that the prediction accuracy of the ANN-computed surrogate models is higher than the ones computed from the RSM for the prediction tests with geometric and operational variables. However, for the cases with geometric variables, the opposite phenomenon is observed, except for the tests with 8 degrees of freedom. Note here that the general complexity of the datasets for the prediction accuracy tests with geometric and operational variables is higher than the one with geometric variables. From this, it can be deduced that the prediction accuracy of the surrogate model computed from the ANN is better than the RSM-computed model if the datasets for the surrogate model construction have a high complexity; however, the RSM-computed surrogate model will have a higher accuracy, otherwise. Among the prediction accuracy tests with geometric variables, the datasets used to predict lift-to-drag ratio with eight input variables have the highest complexity. In this context, the fact that the ANN-computed surrogate models' prediction accuracy for these tests is higher than the accuracy using the RSM-computed surrogate models is not a surprising phenomenon, and it can be explained by the complexity of the datasets.