## 1 Introduction  
Plasma arc additive manufacturing (PAAM) technology utilizes an electric arc to melt powder or filament material and solidify it on a substrate or previous layer to create parts via layer-by-layer deposition [1]. It has the superior ability to directly print complex geometrical parts compared to traditional manufacturing techniques [2]. Titanium-aluminum alloys have the merits of material properties, while their usage is constrained due to their weak ductility at room temperature [3]. Therefore, additive technology like PAAW serves as an ideal process for manufacturing Ti-Al alloys [4]. A huge temperature gradient exists near the melt pool during the deposition process, which leads to significant thermal residual stress and deformation that affect the mechanical properties of the part [5]. The temperature distribution during the deposition process is a key factor in determining the quality of the printed components. In recent years, researchers have studied these temperature distribution features considering the factors of the heat source mode, print material delivery form, and print path [6; 7; 8]. At the same time, it is common to use finite element methods instead of experiments to study the characterizations of the deposition process [9]. The use of this method possesses advantages such as cost savings and reduced difficulty in parameter measurement [10]. However, trade-offs need to be made between computational accuracy and computational time [11; 12]. With the explosive growth of machine learning research, many scholars have tried to use in situ parameters to predict experiment results. [PERSON] et al. [13] predicted the producing quality by using molten pool, plume, and spatter images obtained from a high-speed camera. [PERSON] et al. [14] used acoustic signals to determine the producing quality during the deposition process. [PERSON] et al. [15] collected spectral data and used neural networks, support vector machines, and linear discriminant analysis to predict the manufacturing quality. [PERSON] et al. [16] collected infrared temperature data and used them to predict mechanical properties such as the maximum tensile strength of a component. Many scholars have found that the cost of data collection can be reduced through a numerical simulation approach. [PERSON] et al. [17] used an artificial neural network model that predicted thermal deformation by extracting the deformation nodes generated by the finite element model. [PERSON] et al. [18] used a machine learning algorithm to propose a fast surrogate model to replace the traditional numerical simulation methods for acquiring temperature cycle features during the deposition process. Data-driven methods can generate hundreds of thousands of data for further analysis [19], which are difficult to reach through experiments. [PERSON] et al. [20; 21] proposed a neural network approach for solving partial differential equations, which benefited from the popularization of the concept of Automatic Differentiation (AD) [22] in ML algorithms. [PERSON] et al. [23] applied such physics-informed neural networks (PINNs) to solve the partial differential equations of heat conduction and compared them with the traditional FEM, achieving ideal results. [PERSON] et al. [24] proposed an innovation in the structure of neural networks by combining residual block with PINN and achieved great results. However, restricted to the structure itself, this method can only perform point-to-point prediction, and there exists the problem of solving the partial differential equation logically under the physical law for 2D scenes [23]. To fit practical applications, ML approaches have also been used to investigate the effect of the deposition path on heat accumulation [19]. [PERSON] et al. [25] summarized previous research results and used model predictions to guide a metal component printing process, which achieved the expected results.