## 3 Results
### Residual Stress Prediction Based on UNet Architecture
To study the influence of the number of measurement points on the full-field residual stress prediction, four cases were considered with the number of measurement points (elements) equal to 1024, 768, 512 and 448, respectively. The positions of these measurement points are shown in Table 1. Row and Column represent the positions of elements with known residual stresses at their integration points according to the rule of \"start:step:end\". For example, \"1:2:16\" in Row represents the elements in the 1 st row, the 3 rd row (...) and the 15 th row of the mesh (Figure 3a). Figure 6 shows the inversely determined residual stress fields based on different numbers of measurement points. It can be observed that the four cases with different numbers of measurement points yielded quite similar residual stress contours to  
Figure 4: Sub-images in task decomposition:1  
the simulated experimental result in Figure 3b, except for the stress distribution at the edges of the model. The reason for the relatively large errors at the edges may be that, during the network training process, the pixels near the edges were lost in each convolution, resulting in insufficient learning of the features. Further, to compare the predicted residual stress field with the simulated experimental result more intuitively, the relative error among them is shown in Figure 7. The relative error is defined as the difference between the predicted and experimental values divided by the experimental value. In Figure 7, the abscissa represents the actual residual stresses of all elements in Figure 3b, while the ordinate represents the relative error. It is evident that the larger the absolute value of residual stress, the smaller the error and the residual stresses of most elements with error greater than 20% were close to zero. This is reasonable because, for a small residual stress, a small deviation yields a huge relative error. Figure 8 shows the relative errors of elements with stress exceeding 20 MPa versus the proportion of elements with relative errors larger than a specified value. It can be observed that, with the decrease in the number of measurement points, the relative error increased sharply. For 1024 measurement points, the ratio of elements with relative error larger than 20% was only 1.42%. However, when the number of measurement points was reduced to 448, the ratio of elements with relative error larger than 20% increased to 12.56%. In fact, the elements with large errors were mainly located at the edges of the model. This is mainly due to the insufficient learning caused by the lack of pixels when the neural network learned the edge features. Some image processing methods could be used to improve this in the future. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Measurement Points** & **1024** & **768** & **512** & **448** \\ \hline Row & 1:1:16 & 1:2:16; 2:2:16 & 1:1:16 & 1:1:16 \\ Column & 1:1:64 & 1:1:64; 1:2:64 & 1:2:64 & 1:2:40; 41:3:64 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Locations of measurement points (elements). Figure 6: Residual stress fields (\(\sigma_{x}\)) by inverse identification: (**a**) 1024 measurement points, (**b**) 768 measurement points, (**c**) 512 measurement points and (**d**) 448 measurement points.