## 2 Datasets Building
### Finite Element Method Description  
Based on [PERSON]'s law, the general form of the heat transfer equation can be defined as:  
\[\rho c\frac{\partial T}{\partial t}=\frac{\partial}{\partial x}\left(k_{x} \frac{\partial T}{\partial x}\right)+\frac{\partial}{\partial y}\left(k_{y} \frac{\partial T}{\partial y}\right)+\frac{\partial}{\partial z}\left(k_{z} \frac{\partial T}{\partial z}\right)+Q \tag{1}\]  
where \(\rho\) is the material density, \(c\) is the specific heat capacity, \(T\) is the temperature, \(t\) is the time, and \(Q\) is the heat flux. In addition, the subscripts \(x\), \(y\), and \(z\) denote the horizontal arc motion, the vertical arc motion, and the direction perpendicular to the \(xy\) plane, respectively. Moreover, \(k_{x}\), \(k_{y}\), and \(k_{z}\) are the thermal conductivities as a function of \(T\) in the \(x\), \(y\), and \(z\) directions, respectively. The Gaussian cylindrical heat source is chosen as the Q heat source formula, as shown in Equation (2).  
\[Q(x,y,\ t)=\frac{3\eta P}{\pi r^{2}}\cdot\exp\left(\frac{-C(x-(vt+x_{0}))^{2}-C (y-y_{0})^{2}}{r^{2}}\right) \tag{2}\]  
\(C\) is the concentration of the heat source, \(\eta\) is the energy absorptivity, \(P\) is the laser power, and \(r\) is the plasma arc radius. The ambient temperature was 25 \({}^{\circ}\)C. For the initial temperature of the substrate, 300 \({}^{\circ}\)C was used. The boundary condition in the model was the convection with the air, which can be expressed as:  
\[-k\frac{\partial T}{\partial t}=h(T-T_{a}) \tag{3}\]  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Si** & **Cu** & **Zn** & **Mn** & **Fe** & **Al** \\ \hline ER1100 & 0.03 & 0.02 & 0.013 & 0.003 & 0.18 & Bal \\ \hline \end{tabular}
\end{table}
Table 1: Composition (at.%) of the Al alloy wire (ER1100).  
Figure 1: Schematic diagram of (**a**) the PAAW process; and (**b**) the thermal measure experiment.  
where \(h\) is the heat convection coefficient between the substrate and air, \(T_{a}\) is the ambient air temperature, and \(\overrightarrow{n}\) is the orientation vector at the substrate surface. In our FEM model, the geometry of the simulation domain was set to 50 mm \(\times\) 50 mm \(\times\) 5 mm, with a total of 83,603 nodes and 75,168 cells. The mesh size was uniformly set to 1 mm \(\times\) 1 m. Table 3 summarizes the other relevant parameters during the simulation. The simulation process was conducted by a solver based on the Lagrange-Galerkin finite element method.  
We used a Python script to extract the temperature data for each node from the FEM results. We designed 13 groups of single-track deposition with different time steps and different heat source locations to enrich the dataset. Each group was divided by time steps, and more than 1000 cases of temperature fields under different deposition times were collected. In total, 11 of these groups were training sets and 2 groups were validation sets, which represented short and long deposition times, respectively, and were not involved in the training stage. The training set and validation set vary in the total time used in the deposition process. Considering that the manufacturing parameters were defined values, the dominant factor that determined the temperature features was the variation in heat accumulation, which can be noted as the deposition time in our research. Each training set and validation set shared different deposition times. The volume of the validation set was 15% of the total dataset. We normalized the values of the temperature to 0\(\sim\)1 in order to train the neural network model efficiently. The training set for the model consisted of 2D temperature fields as the output and the 1D temperatures at the center path as the input. In this paper, we focused on the temperature variations in the melting stage of the deposition process, and the temperatures of the cooling stage were not considered.