## 3 Results and Discussion
### Predictive Modeling of Surface Roughness  
ML has emerged as a powerful approach for predicting Ra, a key indicator of machining quality, across a wide range of manufacturing processes. Numerous studies [19; 21; 23; 27] have demonstrated the superiority of ML-based models over traditional statistical methods, particularly in handling nonlinear and multi-dimensional relationships among machining parameters. Unlike conventional modeling approaches that often rely on linear regression or simplified empirical formulas, ML algorithms can effectively learn complex, nonlinear patterns and subtle interactions among input features such as spindle speed, feed rate, and depth of cut, leading to more accurate and generalizable predictions of surface quality. In this study, five state-of-the-art ML algorithms, RFR, GBR, LightGBM, CatBoost, and KNN, were employed to predict surface roughness based on a dataset structured with [PERSON]'s experimental design. These models were selected based on their demonstrated predictive performance in the recent literature for similar applications [19; 22; 24]. The inclusion of both ensemble-based learners (e.g., CatBoost, LightGBM) and distance-based methods (e.g., KNN) allows for a comprehensive evaluation of different learning paradigms in capturing micro-milling behavior. The comparative performances of these models are presented in Figure 17, and detailed evaluation metrics are summarized in Table 7.  
Among the evaluated models, CatBoost achieved the highest accuracy, with R\({}^{2}\) values of 0.9977 for training and 0.9729 for testing, and the lowest test error metrics (MAE = 0.0731 \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Dependent Variable** & **Model** & **R\({}^{2}\) Train** & **R\({}^{2}\) Test** & **MAE Train** & **MAE Test** & **RMSE Train** & **RMSE Test** \\ \hline \multirow{8}{*}{SR} & RFR & 0.9854 & 0.9382 & 0.0418 & 0.0969 & 0.0778 & 0.1600 \\ \cline{2-8}  & GBR & 0.9906 & 0.9639 & 0.0449 & 0.0848 & 0.0640 & 0.1190 \\ \cline{1-1} \cline{2-8}  & LightGBM & 0.9611 & 0.9569 & 0.0791 & 0.0895 & 0.1303 & 0.1301 \\ \cline{1-1} \cline{2-8}  & CatBoost & 0.9977 & 0.9729 & 0.0238 & 0.0731 & 0.0315 & 0.1032 \\ \cline{1-1} \cline{2-8}  & KNN & 0.9676 & 0.9725 & 0.0674 & 0.0687 & 0.1188 & 0.1038 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Model performance metrics for surface roughness prediction. Figure 17: Predictive performance of regression models for surface roughness based on actual and predicted values with corresponding R\({}^{2}\) scores. and RMSE = 0.1032). These results reflect CatBoost's robust generalization capability and superior handling of nonlinear, high-dimensional relationships, aligning with findings from prior studies [19], which also reported a high performance from CatBoost in predicting Ra and cutting forces in AISI 4340 alloy steel turning. CatBoost's built-in capability to handle categorical variables, automatic feature interaction handling, and regularization features make it particularly well suited for modeling complex manufacturing processes where traditional parametric models fall short. KNN followed closely with a test R\({}^{2}\) of 0.9725. Despite its competitive performance, the model exhibited a slightly higher training error (MAE = 0.0674, RMSE = 0.1188), indicating potential limitations in modeling more complex nonlinear patterns. Similar observations have been made in previous research [26], where KNN performed well but was outperformed by ensemble methods. GBR showed a balanced performance with R\({}^{2}\) values of 0.9906 (train) and 0.9639 (test) and moderate RMSE (0.1190). This reflects its capacity to generalize well across the dataset, although its sensitivity to hyperparameter settings has been noted in several works [21; 23], making model tuning crucial for optimal performance.