# Physics-Based Data Augmentation Enables Accurate Machine Learning Prediction of Melt Pool Geometry
## 3 Results and Discussion  
### Analysis of Experimental Data  
The melt pool depth-to-width ratio (D/W, denoted as N) serves as a critical dimensionless parameter for distinguishing melt pool modes. While prior studies have proposed conflicting threshold values for optimal N ranges--[PERSON] et al. [41] suggested N \(>\) 0.5 indicates keyhole mode through numerical simulations, whereas [PERSON] et al. [42] experimentally determined N = 0.37-0.6 for effective substrate bonding--this study systematically captured a comprehensive dataset spanning N = 0.34-1.29, encompassing conduction, transition, and keyhole modes across the parameter matrix.  
According to Figure 4, 36 sets of melt pool measurements were obtained experimentally. Figure 5a,b show their respective profiles under varying laser power at fixed scanning speeds, while Figure 5c,d illustrate the variation of melt pool width and depth as functions of laser power and scanning speed. It can be observed that both width and depth generally increase with rising laser power and decrease with increasing scan speed. Notably, the melt pool depth exhibits a larger dynamic range (24 \(\upmu\)m to 173 \(\upmu\)m) compared to width (72 \(\upmu\)m to 143 \(\upmu\)m), indicating its higher sensitivity to processing conditions. To account for experimental uncertainty, each data point in Figure 5c,d represents the mean value of 15 single-track measurements under identical processing conditions. The error bars denote one standard deviation (\(\pm\)1\(\sigma\)), calculated from these replicate measurements. These bars provide a quantitative indication of measurement repeatability and process stability. The increasing size of error bars at high laser power and low scan speeds suggests elevated thermal instability and inconsistent melt pool morphology in these regimes. Specifically, the melt pool width exhibits larger variability than depth under these conditions, implying greater susceptibility to fluctuation in lateral melt propagation.  
To further validate the rationality of the melt pool modes classification and its relevance to build quality, representative cross-sectional morphologies, pore characteristics, and tensile test results were examined across conduction, transition, and keyhole conditions (Figure 6). The tensile tests were conducted at room temperature using a Shimadzu AG-IC 100 kN testing machine(Shimadzu Corporation; Kyoto, Japan). Specimens were prepared in accordance with ASTM E8/E8M-15 standards and tested at a strain rate of 3 mm/min [43]. Conduction-mode samples showed shallow melt pools with lack-of-fusion defects, while keyhole-mode cases exhibited deep, unstable geometries with gas-induced porosity. By contrast, the transition regime featured stable, cup-shaped melt pools with minimal porosity. This trend is reflected in tensile performance: transition-mode specimens achieved the highest UTS and YS values, while conduction and keyhole modes suffered strength degradation due to insufficient fusion and instability-induced defects, respectively.  
with laser power and scanning speed; (**c**) variation of melt pool width with laser power at different scanning speeds and its error bars; (**d**) variation of melt pool depth with scanning speed at different laser powers and its error bars.