## 3 Results and Discussion
### Predictive Modeling of Cutting Forces  
ML algorithms have become pivotal tools for predicting machining responses, such as cutting forces, across various manufacturing processes. Several studies have demonstrated that models like SVR, ANN, RFR, and GBR can provide high accuracy in predicting complex, nonlinear interactions between process parameters and output responses [19; 21; 26]. The current study builds upon this foundation by evaluating the predictive performances of RFR, GBR, LightGBM, CatBoost, and KNN models in estimating the cutting force components Fx, Fy, and Fz in micro-milling processes. Figure 7 illustrates the models' performance in predicting the Fx force component. Among all, CatBoost achieved the highest predictive accuracy, yielding an R\({}^{2}\) value of 0.9990 for training and 0.9642 for testing, coupled with the lowest mean absolute error (MAE) of 0.3889 and root mean square error (RMSE) of 0.6073 in testing. These results suggest strong generalization ability with minimal overfitting. Notably, LightGBM and KNN also performed well, with test R\({}^{2}\) values of 0.9698 and 0.9707, respectively, although their higher MAE values suggest comparatively less robustness. This observation aligns with findings reported in previous research [19], which indicated that CatBoost and ANN outperformed other models in predicting cutting force in AISI 4340 alloy turning. Such predictive precision is crucial for real-time process monitoring and adaptive control systems, where anticipating cutting forces can help avoid tool breakage, improve surface finish, and optimize machining efficiency. In the prediction of the Fy component (Figure 8), CatBoost once again showed the best performance with R\({}^{2}\) values of 0.9987 (training) and 0.9563 (testing). Its RMSE and MAE values (0.6481 and 0.4607, respectively) indicate a slightly increased error, potentially due to model sensitivity to minor outliers. RFR and LightGBM also yielded competitive results, both exceeding 0.96 in test R\({}^{2}\), which is consistent with previous studies [26], where RFR and SVR effectively captured milling force variations across different cutting speeds and feed rates. Despite slightly higher errors in Fy prediction, the models still demonstrate acceptable performance levels for integration into smart manufacturing platforms where force feedback is essential for closed-loop control. Figure 9 shows that all models performed exceptionally in predicting the thrust force (Fz). CatBoost attained the best balance, with the highest test R\({}^{2}\) (0.9763) and lowest MAE (0.1126) and RMSE (0.1688). While KNN slightly surpassed CatBoost in R\({}^{2}\) (0.9818), its  
Figure 8: Predictive performance of regression models for Fy based on actual and predicted values with corresponding R\({}^{2}\) scores. Figure 7: Predictive performance of regression models for Fx based on actual and predicted values with corresponding R\({}^{2}\) scores. higher error values suggest that CatBoost achieved better overall accuracy. This aligns with the findings reported in [22], which highlighted that advanced ML models exhibit superior predictive stability and robustness for cutting force estimations in high-speed machining. As detailed in Table 6, CatBoost consistently provided superior performance across all cutting force components, with training R\({}^{2}\) values exceeding 0.998 and balanced test accuracy, underscoring its strong generalization ability. This finding supports earlier work [21], which demonstrated that ANN and SVR, when properly tuned, can yield high-fidelity cutting force predictions. Nevertheless, models like RFR and GBR also offered competitive results, though with relatively higher error metrics in Fx and Fy predictions.