# Physics-Based Data Augmentation Enables Accurate Machine Learning Prediction of Melt Pool Geometry
## 3 Results and Discussion
### Model Training Results and Discussion  
In this section, the predictive performance of the optimized machine learning (ML) models is assessed, with a focus on comparing melt pool width and depth predictions to evaluate the impact of data quality. The dataset simulated by the calibrated explicit model was integrated with the experimental data to form a hybrid training set. This augmented dataset was then used to retrain the ML models, and the results were benchmarked against  
Figure 8: Classification of melt pool regimes based on depth-to-width (D/W) ratio. (**a**) Experimental design layout of 36 parameter combinations across laser power (100–200 W) and scanning speed (400–1100 mm/s), with melt pool modes labeled as conduction (blue), transition (green), and keyhole (red); (**b**) depth-to-width and mode distribution of melt pools under each parameter set. Bubble color indicates melt pool mode, while size represents the corresponding depth-to-width. Figure 9: Melt pool width and depth for process parameters and explicit model simulations. (**a**) Melt pool width; (**b**) melt pool depths. (The colored graphs represent experimental data, and the yellow dots represent simulated data). models trained solely on experimental data. Details of the dataset composition are provided in Table 6. To ensure statistical consistency during fivefold cross-validation, the S0 dataset was excluded, resulting in a total of 50 samples with balanced partitions for training and testing. When trained on the original 35 experimental data points, the XGBoost model achieved the highest R\({}^{2}\) (0.864) for melt pool width prediction, while the MLP model yielded the lowest RMSE (5.877). For melt pool depth, the MLP model exhibited the best overall performance, attaining an R\({}^{2}\) of 0.977, MAE of 3.939, and RMSE of 5.197--substantially outperforming the other two models. The Random Forest model consistently underperformed in both tasks. The three machine learning models selected and optimized in this paper have different prediction performances due to different mathematical principles, but it can be observed that the changes in the three indicators--R\({}^{2}\), MAE and RMSE--are broadly consistent. The MLP and XGBoost models show excellent prediction performance for melt pool width after data augmentation with the improved explicit model. Compared with the Random Forest model, which has an R\({}^{2}\) value of only 0.814, the prediction accuracies of these two models are similar and above 0.9. The MLP model has the highest prediction accuracies, with an R\({}^{2}\), MAE, and RMSE of 0.919, 3.535, and 5.202, respectively, and outperforms the other two models in all three scoring criteria. The difference in prediction performance among the three models is even more obvious in melt pool depth prediction: the R\({}^{2}\) value of the MLP model is as high as 0.984, which is much higher than that of the remaining two algorithms, and its MAE and RMSE are close to each other, more than twice lower than those of the remaining algorithms. Meanwhile, the XGBoost model is also very effective in predicting the depth of the melt pool, with an R\({}^{2}\), MAE, and RMSE of 0.922, 6.308, and 10.131, respectively. Overall, in terms of performance on the data-enhanced hybrid dataset, among the three models proposed in this paper, the MLP model has the best predictive results, followed by the XGBoost model, and the Random Forest model delivers a comparatively average performance. Figures 10 and 11 demonstrate that, despite the dataset expansion using the explicit model, prediction accuracy remained sensitive to data distribution. Across all models, melt pool depth was more accurately predicted than width, regardless of dataset type. This may be attributed to greater experimental variability in melt pool width. Elevated prediction errors were observed under extreme energy conditions (e.g., S9 and S17 for width; S27, S32, and S37 for depth), further highlighting the influence of data quality.