# Physics-Based Data Augmentation Enables Accurate Machine Learning Prediction of Melt Pool Geometry
## 3 Results and Discussion
### Calibration of the Explicit Model  
This study enhances the original explicit model by replacing its fixed constant term with a calibratable variable coefficient. This dynamic coefficient is calibrated against experimental data to account for complex physical mechanisms, including dynamic laser penetration depth and absorption variations. Calibration was performed using 18 experimentally validated datasets covering laser powers of 100-200 W and scanning speeds of 700-900 mm/s--selected for their parametric completeness. For each constant scanning speed, linear regression analysis established relationships between laser power and melt pool dimensions (width/depth). After calibration, the explicit model achieved an average coefficient of determination (\(R^{2}\)) of 0.925 for melt pool width and 0.965 for depth, with corresponding mean absolute errors of 1.53% and 5.23%, respectively. The predictive effec  
Figure 6: Microstructural and mechanical characterization of specimens produced under conduction, transition, and keyhole melt pool regimes. (**a**–**c**) Cross-sectional melt pool morphologies corresponding to (**a**) conduction (blue frame), (**b**) transition (green frame), (**c**) keyhole modes(red frame); (**d**–**f**) optical micrographs of etched metallographic cross-sections highlighting dominant defect types; (**g**) corresponding tensile properties of selected parameter sets across the three regimes.  
tiveness of the improved explicit model is illustrated in Figure 7. Based on the calibrated regression equations, constant values were computed for laser powers of 110 W, 130 W, 150 W, 170 W, and 190 W under scanning speeds of 700, 800, and 900 mm/s. These values were then substituted into the equations listed in Table 3 to generate 15 synthetic melt pool samples.  
Owing to its foundation on large-scale datasets across diverse metallic materials, the improved explicit model exhibits broad applicability and significantly enhanced predictive accuracy when calibrated against experimental measurements. The spatial distribution of both experimental and simulated data is presented in Figure 8. Notably, the synthetic data complement the experimental dataset by extending coverage into process regimes that are experimentally difficult to access--particularly at the transition-to-keyhole boundary (D/W \(\approx\) 0.6-1.2), where melt pool behavior is highly nonlinear and sensitive to process instabilities. These regions exhibit essential nonlinearities poorly represented in physical measurements. By encoding mechanisms like power-dependent absorption, the model generates physically consistent data with enhanced nonlinear features, enabling ML algorithms to capture behavioral transitions and inflection points critical for defect prediction [44; 45].  
Figure 7: The effect of the improved explicit model simulation data. (**a**) Experimentally obtained melt pool width data; (**b**) melt pool width data obtained from improved explicit model simulations; (**c**) experimentally obtained melt pool depth data; (**d**) Melt pool depth data obtained from improved explicit model simulations.  
As shown in Figure 9, the explicit model-generated data (yellow points) effectively supplement regions of the parameter space where experimental coverage is sparse, particularly near the conduction-to-keyhole transition. In both width and depth surfaces, these samples enhance the representation of nonlinear zones with steep geometric gradients, which are critical for learning melt pool morphological shifts. By enriching the dataset in these regions, the augmented data improve the model's ability to generalize and capture key transition behaviors.