## 3 Results
### Regression Learner Predicted vs. Actual Response  
The predicted versus actual regression learner plots are utilized to check model execution after preparing a model. An ideal regression model has an expected response equivalent to the true response, so all the values lie on a regression line. Variations from regression on the line are termed as prediction errors for that point. A reasonable model has minimum errors; thus, the forecasts dissipate close to the regression line. Typically, almost perfect modeled results are evenly spread around the regression line. The complete algorithm of linear regression, stepwise regression, tree (fine, medium, and coarse), SVM (quadratic, cubic, fine, medium, and coarse), ensembled (boosted tree, and bagged tree), and gaussian process regression (GPR) models (squared exponential GPR, Matern 5/2 GPR, exponential GPR, and rational quadratic GPR) are analyzed, whereas the response plot of these models is selected based on predicted versus actual results, which dissipate close to the regression line [31; 32]. A comprehensive examination of these models was evaluated in terms of root mean square error and R-squared error. Figure 7: Testing dataset unity plots for (**a**) mass flow rate, (**b**) pressure ratio, (**c**) temperature ratio, and (**d**) isentropic efficiency. Based on the minimum error, Figures 8-12 show various regression model learners and their selection for mass flow rate, pressure ratio, temperature ratio, and isentropic efficiency. Figure 8: Regression models for mass flow rate (**a**) Ensembled Bagged Tree, (**b**) Tree Fine, (**c**) SVM Medium, (**d**) Stepwise Linear, (**e**) GPR Matern, and (**f**) GPR Rational Quadratic. Figure 9: Regression models for pressure ratio (**a**) Ensembled Bagged Tree, (**b**) Tree Fine, (**c**) SVM Medium, (**d**) Stepwise Linear, (**e**) GPR Matern, and (**f**) GPR Rational Quadratic. Figure 10: Regression models for temperature ratio (**a**) Ensembled Bagged Tree, (**b**) Tree Fine, (**c**) SVM Medium, (**d**) Stepwise Linear, (**e**) GPR Exponential, and (**f**) GPR Rational Quadratic. Figure 11: Regression models for isentropic efficiency (**a**) Ensembled Bagged Tree, (**b**) Tree Fine, (**c**) SVM fine, (**d**) Stepwise Linear, (**e**) GPR Matern, and (**f**) GPR Rational Quadratic. On a 2.5-stage fully loaded axial compressor, a new Bezier surface modeling approach for the entire suction surface and pressure surface of blades was created, and the multi-island genetic algorithm was directly used for optimization. The smoothness of the blade surface can be ensured by the high-order continuity of control points [33]. The paper first adopted the novelty of extensive CFD analysis on distorted inlet flow, and then a different regression learner was applied to predict the compressor performance at variable conditions, as shown above. To achieve the optimum hyperparameters, two supervised learning methods, (SVR) and (GPR), had been used earlier to train the models with a Bayesian optimization algorithm. On five rotational speed lines, the qualified models are inserted into the through-flow code using the streamline curvature method (SLC) to estimate the overall output and internal flow field of the transonic compressor [34]. In the current research, sensitivity analysis has been applied to select the most influential features of the axial compressor at distorted inlet flow conditions and different RPM. The analysis had been conducted on linear regression, SVM, GPR, and tree regression learners. The Matern 5/2 kernel takes the spectral densities of the fixed component and applies Fourier  
Figure 12: Best Response Regression Models (**a**) Exponential GPR for mass flow rate, (**b**) GPR Matern for pressure ratio, (**c**) GPR Matern for temperature ratio, and (**d**) GPR Exponential for isentropic efficiency. modifications to the Radial Basis function kernel. On the other hand, it does not measure data in high-dimensional spaces.