## 1 Introduction  
In recent years, laser powder bed fusion (LPBF) additive manufacturing has attracted more and more interest from academia and industries due to its superior advantage in producing complex metallic parts than traditional manufacturing methods [1, 2, 3, 4, 5]. In LPBF, metallic parts are fabricated by melting metal powders in a layer-by-layer style [6]. The molten pool dimensions in the manufacturing process are important factors that affect the quality of the final products. The common defects, such as surface roughness, lack-of-fusion porosity, balling, and keyholing are all related to the molten pool behavior in LPBF [1, 7, 8, 9, 10]. Therefore, a good prediction model for the molten pool dimensions is necessary for quality control in LPBF. It was observed that there are three melting modes in the powder bed fusion process, which are the conduction mode at the low energy density regime, transition mode at the medium energy density regime, and keyhole mode at the high energy density regime [11, 12, 13]. Under different process conditions of LPBF, the laser power absorptivity is different due to the difference in melting modes. In the conduction melting mode, the vapor depression depth and molten pool depth are small, most laser power is reflected by the molten pool surface to the ambient, which induces low laser absorptivity in this process regime. In the transition mode, the vapor depression depth increases with the energy density, the laser has more reflections in the vapor hole, which induces an increase in laser absorptivity. When it comes to the keyhole mode melting regime, the absorptivity goes to the highest level and will not change much with the process conditions [11; 14; 15; 16]. Laser absorptivity has a significant influence on the energy input to the material in LPBF. Thus, the consideration of the difference in laser absorptivity is necessary for the prediction of molten pool under different process conditions. This paper focuses on the laser absorptivity in the transition mode and keyhole mode. Researchers have developed various methods to study the laser absorptivity and molten pool behavior in LPBF [17; 18; 19]. Plenty of experimental techniques have been used to measure the absorptivity and investigate the characteristics of the molten pool. [PERSON] et al. [10] employed a direct calorimetric technique to measure the laser absorptivity of 316L stainless steel substrate which is coated by a powder layer. [PERSON] et al. [20] used the same experimental technique to study the laser absorptivity of Tie\(\mathrm{\delta}\)Al4V powders. The sensitivity of absorptivity to laser beam size, the thickness of powder layers, laser power, and scanning speed were investigated. [PERSON] et al. [21] developed a calorimetric apparatus to investigate the laser absorptivity of Tie\(\mathrm{\delta}\)Al4V and stainless-steel powders. The effect of temperature on absorptivity was studied. [PERSON] et al. [22] employed optical micrographs to investigate the molten pool shapes and dimensions of Tie\(\mathrm{\delta}\)Al4V in single-track experiments of the selective laser melting process. [PERSON] et al. [23] used a SA2 Photon-Fastcam high-speed camera to monitor the molten pool behavior in LPBF. [PERSON] et al. [24] and [PERSON] et al. [1] employed the high-speed x-ray imaging technique to observe the molten pool shapes during the powder bed fusion process and measure the molten pool dimensions. These experimental investigations have made significant contributions to the research of the powder bed fusion process. However, the complex experimental procedure and high cost of experimental devices hinder the wide adoption of these techniques. Numerical methods have been an alternative for the experimental investigation for the study of absorptivity, temperature profile, and evolution of molten pools in LPBF. [PERSON] et al. [25] carried out ray-tracing simulations to compute the laser absorptivity of powder materials for additive manufacturing processes. [PERSON] et al.