# Physics-Based Data Augmentation Enables Accurate Machine Learning Prediction of Melt Pool Geometry
## 4 Conclusions  
This study establishes a hybrid prediction framework that couples an improved explicit model with machine learning to predict melt pool geometry in L-PBF with high accuracy and enhanced interpretability. The explicit model was calibrated using experimental data and effectively simulates melt pool width and depth by accounting for variable absorptivity and penetration depth under different processing conditions. When integrated into a machine learning pipeline, the augmented dataset enables accurate interpolation across conduction, transition, and keyhole regimes.  
Model evaluation reveals that MLP outperforms other algorithms, especially in predicting melt pool depth. Data augmentation leads to a maximum R\({}^{2}\) improvement of 23.5%, with reductions of up to 27.1% in MAE and 17.8% in RMSE. These results confirm that the predictive performance of ML models is highly dependent on dataset characteristics, particularly in high- or low-energy regimes where experimental data are scarce or unstable. Notably, the model demonstrates superior generalization in transition zones, where abrupt melt pool morphology changes typically elude experimental capture.  
In summary, the explicit-model-augmented approach bridges the gap between physical interpretability and data-driven modeling. It enhances predictive robustness under small-sample constraints and offers a scalable strategy for real-time optimization in L-PBF. Despite its strong predictive performance, the model is subject to limitations related to dataset scope, lack of thermal field resolution, and material-specific calibration. These aspects can be addressed in future work by integrating physics-informed features and extending to multi-material datasets. This methodology provides a foundation for broader integration of hybrid modeling in metal additive manufacturing, supporting intelligent process control, in situ monitoring, and digital twin development.  
All authors contributed to the study conception and design. Material preparation, data collection, and analysis were carried out by [PERSON] [PERSON], [PERSON] and [PERSON] revised the manuscript  
Figure 12: (**a**) Predicted \(R^{2}\) values of melt pool width before and after data enhancement; (**b**) predicted MAE values of melt pool width before and after data enhancement; (**c**) predicted RMSE values of melt pool width before and after data enhancement; (**d**) predicted \(R^{2}\) values of melt pool depth before and after data enhancement; (**e**) predicted MAE values of melt pool depth before and after data enhancement; (**f**) predicted RMSE values of melt pool depth before and after data enhancement.  
with respect to language, interpretations, and figures. [PERSON] and [PERSON] supervised the research, critically reviewed the manuscript, and contributed to refining the interpretations and improving the overall quality of the paper. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Open Fund of Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering at Wuhan University of Science and Technology (MTMEOF2021B05).  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.