## 3 Settings for Prediction Accuracy Tests
### Number of Input Variables  
The complexity of datatsets is not only affected by the characteristics of the input variables, but it is also influenced by the number of input variables. To investigate a change of prediction accuracy as a function of the number of input variables, surrogate models with different degrees of freedom are constructed for the following tests: \(n_{1}\)-degree of freedom prediction accuracy test with geometric variables and \(n_{2}\)-degree of freedom prediction accuracy test with geometric and operational variables. Here, \(n_{1}\) can be 2, 4, 6, and 8, and \(n_{2}\) can be 4 and 6. Because the values of \(n_{1}\) and \(n_{2}\) are less than or equal to 8, which is the total number of the movable control points presented in Figure 1, only some of these control points should be set as input geometric variables in the prediction accuracy tests. Therefore, a rule to choose input geometric variables from the candidates is needed.  
Table 2 shows the selection priority of the eight control points with their own upper and lower bounds. For example, the input variables at the 2- and 4-degrees of freedom prediction accuracy tests with geometric variables are the control points \(\{\mathbf{p}_{7},\mathbf{p}_{8}\}\) and \(\{\mathbf{p}_{7},\mathbf{p}_{8},\mathbf{p}_{2},\mathbf{p}_{3}\}\), respectively, meaning only these control points can move vertically within their own ranges during the tests. The selection priority of the control points here was defined under the expectation that the control points located in the middle of the airfoil profile \((\mathbf{p}_{2},\mathbf{p}_{3},\mathbf{p}_{7},\mathbf{p}_{8})\) has a greater impact on its aerodynamic property than the ones close to the leading and trailing edges \((\mathbf{p}_{1},\mathbf{p}_{4},\mathbf{p}_{6},\mathbf{p}_{9})\). Among the control points located in the same \(x\) position, the point located on the lower surface of the wind turbine airfoil is weighted more than the other. At a \(n_{2}\)-degree of freedom prediction accuracy test with geometric and operational input variables, the \((n_{2}-2)\) number of geometric input variables are selected because two variables are taken for the operational variables, Reynolds number and angle of attack. For example, four input parameters of the 4-degrees of freedom prediction accuracy test with geometric and operational variables are the control points \(\{\mathbf{p}_{7},\mathbf{p}_{8}\}\), Reynolds number, and angle of attack. The ranges of the Reynolds number and angle of attack here are defined as \(10^{5}\leq\mathrm{Re}\leq 10^{6}\) and \(0^{\circ}\leq\mathrm{AOA}\leq 15^{\circ}\), respectively. Here, because the range of Re is much larger than the other input variables, a logarithm of its value is given as the input in the prediction accuracy tests (Another way to deal this issue is normalizing the input parameters using the method, for example, with a batch normalization [45].). With the constructed surrogate model, the value of lift-to-drag ratio is predicted under the expectation that it is the simplest way to evaluate the aerodynamic performance of a wind turbine airfoil.