## 4 Results and Discussion
### The Performance of Conv1D Model at Training Set  
The loss value during the training process can intuitively reflect the prediction ability of the model. Figure 5 shows the changes in the loss value after taking the logarithm of the MSE loss function for 2000 iterations. When calculating the training loss, we restored the normalized output values so that they reflected the difference with the true temperature. The loss value reached an order of magnitude of \(1\times 10^{5}\) at the beginning of the training stage, which means that the model failed to capture the characteristic relationship between the input and output. As the number of iterations increased, the training loss (log) gradually decreased to \(-0.046\) in the gradient descent session. Since we set the learning rate to a fixed value, the gradient of the training loss may have been too large at each regression, which led to oscillations in the loss curve. In this experiment, the training loss of the model decreased with an increase in the training iterations, which means that the predicted results of the model became more accurate. To improve the training efficiency after the training loss decreased to \(1\times 10^{3}\) and reduce the fluctuation amplitude so that the model could converge faster to the saddle point [38], it was necessary to reduce the value of the learning rate according to the training iterations [39]. After completing 2000 training iterations, the overall training loss of the Conv1D model was reduced to 0.8995 \({}^{\circ}\)C. Figure 6 lists the FEM temperature distribution (column 1), the predicted temperature distribution (column 2), and the absolute temperature error (column 3) at t = 4.5 s, t = 9 s, and t = 13.5 s, respectively. When the time step was 4.5 s, the peak temperature of the numerical simulation was 1707.4 \({}^{\circ}\)C and the predicted peak temperature was 1702.58 \({}^{\circ}\)C, with a minor difference of 4.82 \({}^{\circ}\)C. When deposition proceeded to the 9 s, the predicted result of the heat source moved in the same direction as the FEM result, and the error of the peak temperature was 4.35 \({}^{\circ}\)C. At 13.5 s, the peak temperature reached 1802.2 \({}^{\circ}\)C as deposition proceeded, at which point, the error of the peak temperature widened to 14.19 \({}^{\circ}\)C. We can see that the model's temperature prediction was basically consistent with the actual situation, and the prediction accurately captured  
Figure 5: Loss curve of the Conv1D model in the training process. the heat conduction phenomenon in the process. In the given cases, the MSEs between the predicted temperature field and the temperature field calculated via numerical simulation were 1.5022 \({}^{\circ}\)C, 0.7936 \({}^{\circ}\)C, and 0.7803 \({}^{\circ}\)C, respectively. Three individual prediction cases show that the prediction performance of the Conv1D model reached a high level of accuracy in general. By comparing the absolute temperature error between the FEM and the Conv1D model, it can be observed that most of the prediction errors were concentrated in the molten pool region, where the temperature gradient changed fiercely. The training results show that the Conv1D model was able to accurately predict the characteristics of the temperature distribution, including the direction of heat source movement and the size of the melt pool, in the deposition process. In the local temperature distribution, the neural network model still gave good results. Figure 7a shows the temperature distribution curves at the center of the path predicted by the Conv1D model and the numerical simulation at times t = 4.5 s, t = 9 s, and t = 13.5 s, respectively.