## 3 Results  
Results consist of two parts. The first part is created by the results from the CFD analyses, which are subsequently used as the inputs for the ANN. The second part involves results with the predicted temperatures as the results from the ANN. In Figure 6, the temperature fields on the surface of the turbine blade estimated in the ANSYS CFX software are shown. The visualized results correspond to the first regime summarized in Table 1. Temperatures on the surface of the turbine blades are in the Kelvin units. The analysis was performed for 10 specified regimes, and the temperatures were recorded for the specific nodes with the corresponding x, y, and z coordinates. These coordinates also correspond to the points shown on the surface blade in Figure 6. The example from this record from the CFD analyses only for five chosen coordinates is shown in Table 2. The temperatures were calculated in 24 nodes for the purposes of the methodology verification. However, it is possible to perform temperature analyses for so many nodes as necessary [49]. Elapsed time for temperature fields prediction using CFD for one regime is 1 h, 42 min and 44.7 s.  
Figure 5: Architecture of the proposed artificial neural networks (ANN) for the temperature field prediction of the turbine blade. Temperatures at the specific nodes and corresponding coordinates were used for the ANN training. In our case, temperatures in 24 nodes with corresponding coordinates for each of the 10 runs representing 10 operational regimes (Table 1) were determined. It means that 240 temperatures for the training process of the ANN were used. In Figure 7, the data distribution and the corresponding linear approximation for the ANN training, validation and test process are shown. The data are divided for training 70% (blue line in Figure 7), 15% for validation (green) and 15% for the test (red part line in Figure 7). All values from the training, validation and testing process are shown in Figure 6 (black line). The results determined by the neural network are presented in Figure 8, where two types of data are shown. There are ten operation regimes of the iSTC-21v jet engine and the temperatures on the blade surface in the specific nodes. It means that each line corresponds to one operation regime of the jet engine, and each dot corresponds to a specific node. In Figure 8, results from the research based on the methodology described in Chapter 2.1 are presented. From the figure, the comparison between calculated temperatures in the specific nodes on the surface of the turbine blade is shown. The red lines correspond to the temperatures computed by the ANN, and the black lines are the temperatures calculated using the CFD method, whereby one pair of the black and red lines corresponds to one particular operation regime (according to Table 1) of the jet engine. Elapsed time for temperature fields prediction using ANN for one regime is 0.0027645 s. As it can be seen, the prediction time using ANN is almost immediate; thus, the methodology (Figure 1) applied in the iSTC-1v jet engine is really prompt. The peak in Figure 9 could be caused due to the mesh character in the trailing edge are (Figure 4), but there could be more reasons that have an impact on the results (Figure 9). The airfoil in the tail section of the \begin{table}
\begin{tabular}{c c c c} \hline
**Coordinate X** & **Coordinate Y** & **Coordinate Z** & **Temperature (°C)** \\ \hline
80.062 & 6.408 & 3.538 & 1044.510 \\
55.084 & 2.013 & 14.732 & 955.635 \\
60.602 & 2.115 & 13.566 & 964.962 \\
65.514 & 1.040 & 13.765 & 977.080 \\
72.748 & \(-\)0.077 & 13.519 & 998.633 \\ \hline \end{tabular}
\end{table} 
Table 2: Estimated temperatures using ANSYS CFX software for the chosen nodes of the blade. Figure 6: Temperature fields of the turbine blade of the iSTC-1v jet engine computed using ANSYS CFX software. turbine blade is the narrowest part, and in this area, the mesh could be finer; another reason can be nonuniform flow in this area, turbulence or geometrical phenomena.