## 3 Results and Discussion
### Physical Field Reconstruction  
In this research, 70% and 30% of the off-design performance data set were selected as the training set and the verification set randomly for the neural network model training. The training process is shown in Figure 8. The cyan and purple lines indicate the field loss during the training process changes with the number of iterations. According to the figure, the field loss declines very quickly, and the loss of the training set and the verification set is similar in the late training period which can prove the model is well trained. The orange and blue lines indicate the R square value of the efficiency and power prediction, respectively, which can effectively represent the effect of the regression model. It can be seen from the figure that during the training process, the square R square value quickly rises from a large error area less than 0 to a small error close to 1 in the region. The final R-squared value is kept near 1, which means that all the real data in the validation set of the model we built predicts well. In this study, the surfaces of the stator blade and rotor blade were, respectively, expanded into the \(260\times 65\) rectangle as shown in Figure 9. The transverse direction is the chord direction, the longitudinal direction is the spanwise direction (0 for blade tip, 65 for blade root). Four key positions of leading edge (LE), trailing edge (TE), pressure surface (PS), and suction surface (SS) corresponding to rotor blade (R) and stator (S) blades were identified in the figure. For the rotor blade, area (12-40) \(\times\) 65 corresponds to R_TE, area (130-145) \(\times\) 65 corresponds R_LE, area (40-130) \(\times\) 65 corresponds to R_PS, and the rest of the area corresponds to R_SS. For the stator blade, areas (120-135) \(\times\) 65, (220-240) \(\times\) 65, and (135-220) \(\times\) 65 correspond to S_LE, S_TE, and S_PS respectively. The rest of the region corresponds to S_SS. Figure 8: The training process. Figure 9: Structure diagram of the field. The data obtained after the reconstruction of all the calculation examples were summarized. Then, the average relative error and maximum relative error of the temperature and pressure at the stator blade and rotor blade were obtained with the box chart, as shown in Figure 10. The results show that the average relative error of the field is less than 1.5%, and the error of the stator blade temperature and the rotor blade pressure is relatively small. The maximum relative error is less than 15%, and the prediction error of the stator blade pressure is small. The above description shows that the reconstructed field is in good agreement with the field calculated by CFD, and the reconstruction method is effective. The prediction results, 3-D CFD results and error distributions of Cases A and B are shown in Figures 11 and 12, respectively. It can be found that the cloud map distribution of the prediction results is basically the same as that of the CFD results, which is in good agreement. All kinds of key typical phenomena in turbine are captured and predicted, including:  
1. Stagnation phenomenon of high temperature and high pressure in the S_LE. 2. The local acceleration of S_LE due to the large curvature change results in a small area of low pressure and low temperature. 3. The tip clearance of rotor blade is affected by the pressure difference between both rotor blade sides and the larger negative impact angle. This causes the working fluid in the tip clearance to accelerate from the pressure side to the suction side. Therefore, the pressure and temperature near the tip of the rotor blade will be relatively low. 4. The flow separation due to deviation from the design condition. It is worth noting that the flow in these regions is very complex, so the corresponding prediction error will increase accordingly. However, the error is still small, completely within the acceptable range.