## 4 Results and Discussion
### The Performance of Conv1D Model at Validation Set  
The distribution of samples in the training set affected the training effect of the model. An unreasonable training set led to overfitting of the trained model, under which circumstances, the model's error in the training set was small; still, the model's performance in the validation set was poor. This means that the model had a poor understanding of the sample features and the robustness of the model was weak. In order to evaluate the robustness of the Conv1D model, we built up a validation set consisting of two cases, A (Figure 8c) and B (Figure 8d). Each consisted of sub-steps with a time interval of 0.2 s, and the validation set contained a total of 161 samples. The coefficient of determination, R\({}^{2}\) (Equation (11)) and MSE loss, were used to measure the fitness of the Conv1D model to the validation set data. \[R^{2}=1-\frac{\sum_{1}^{N}\left[\hat{T}(x,y)-T(x,y)\right]^{2}}{\sum_{1}^{N} \left[\right.T(x,y)-\overline{T}(x,y)\right]^{2}} \tag{11}\]  
Figure 7: Temperature distribution along the laser scanning track (y = 25 mm) at three different time steps in the deposition stage: (**a**) Absolute temperature and (**b**) temperature error. In Figure 8a, we can see that the model had a good performance on the validation set. The individual sample data in the validation set, which are shown as the blue dots in the figure, fit the red regression line very well. The overall R2 value of the validation set was 0.999963, which is very close to the ideal value of 1. The overall MSE loss of the model was maintained around 0-5, as shown in Figure 8b. We note that there were a few samples with large error numbers in Cases A and B, with the biggest error of 71.38 occurring at Sample A1. Figure 8c,d indicate that these samples were located at the end of each deposition process, where the workpiece's temperature continued to increase. Compared to those at the more stabilized manufacturing stage, the center of the heat source was close to the geometric boundary of the workpiece, and the shape of the high-temperature region changed due to the constraints of the geometric boundary of the workpiece. Therefore, new characteristics of the temperature distribution appeared. The new changes in the distribution characteristics of the temperature resulted in the precision of the model's reconstructed temperature distribution not being accurate enough. Figure 9 gives the absolute temperature errors for the A1 sample predicted by the model, with the true temperature and predicted temperature map listed on the bottom left. It can be seen from the figure that most of the prediction errors were concentrated in the high-temperature area, paralleled with the conclusion in Section 4.1. Furthermore, the model's prediction of the position of the heat source center was quite accurate, while the prediction of the temperature distribution at the geometric boundary had a higher tolerance, where the maximum error exceeded the number of 110 \({}^{\circ}\)C and reached a relative error of 7.3%. This is consistent with the conclusion we made in the previous paragraph. Figure 8: Scheme of (**a**) R\({}^{2}\) values of validation sets, (**b**) MSE loss of validation sets, (**c**) temperature gradient rising at geometry boundary of case A, and (**d**) temperature gradient rising at geometry boundary of case B. In order to improve the performance of the neural network model on the validation set, transfer learning is proposed to enhance the model's prediction ability. The blue curve in Figure 10 shows the training loss (log) curve for the validation set; compared to the training loss in the base training, the value of the validation set's initial loss was only \(1\times 10^{2}\). The training loss increased the first time due to the gradient value being too large in the first few iterations. Then, the value of the training loss continued to drop, as in the general case. After about 30 iterations, the loss dropped below 1, achieving the effect of 2000 iterations in the basic training.