## 1 Introduction
[PERSON] et al. proposed a hybrid machine learning approach that combines clustering and classification to support laser cutting process planning by extracting meaningful patterns from time-consuming simulation data [12]. Their method enables designers to identify key parameter regions associated with high-quality cuts and gain valuable insights through interpretable models and visualization techniques. [PERSON] et al. developed predictive models using decision trees, random forests, and support vector machines for surface roughness in the fiber laser cutting of aluminum, based on 81 experimental points [13]. Among the tested algorithms, the random forest model achieved the best performance, with an R\({}^{2}\) of 0.981 and RMSE of 0.206, outperforming support vector regression (R\({}^{2}\) = 0.959, RMSE = 0.298) and gradient boosting (R\({}^{2}\) = 0.968, RMSE = 0.260). [PERSON] et al. proposed a high-precision roughness prediction model for high-power laser bevel cutting based on a least-squares support vector machine augmented by a whale optimization algorithm [14]. The optimized model achieves a reasonable coefficient of determination of 0.9576 and shows great potential for the effective prediction of level surface roughness. These developments underscore the growing role of machine learning in predicting laser processing performance characteristics. Despite its predictive power, full industrial adoption remains limited. This is because of the transparency of the methods and explainability. Most importantly, studies to date have relied predominantly on purely data-driven machine learning models, without considering the underlying physical or mathematical relationships. Several critical gaps in the current literature motivate the development of a hybrid RSM-ML framework, which is particularly suitable for applications with limited datasets. First, stand-alone RSM models are often unable to capture the nonlinear behavior of modern manufacturing processes. For example, [PERSON] and [PERSON] highlighted the limitations of RSM in modeling complex interactions in wire EDM of hybrid titanium-matrix composites, suggesting that RSM alone may not provide sufficient accuracy in such complicated processes [15]. Similarly, comprehensive reviews emphasized the shortcomings of RSM in high-dimensional and nonlinear problem spaces, advocating the integration of intelligent algorithms to enhance modeling flexibility and accuracy [16; 17]. Secondly, integrating RSM with ML techniques has shown promise in enhancing predictive accuracy. [PERSON] et al. demonstrated that a hybrid model combining RSM with a whale optimization algorithm-optimized back-propagation neural network outperformed traditional RSM in optimizing laser-induced hybrid hardening processes, indicating the efficacy of such hybrid approaches in capturing complex process dynamics [18]. These findings align with those in the review by [PERSON] et al., who observed that hybrid RSM-ML models consistently deliver better performance in process optimization across various advanced manufacturing domains [19]. Finally, rigorous validation strategies are essential to ensure the generalizability of prediction models [20; 21]. Leave-one-out cross-validation is widely used in structural optimization and reliability analysis, as it provides nearly unbiased error estimates especially useful for small datasets [22]. However, the aforementioned method can be very computationally intensive. To overcome this, improved leave-one-out cross-validation techniques have been developed that incorporate hyperparameter tuning from the full training dataset to improve both the accuracy and efficiency of model evaluation [23]. This study presents a hybrid RSM-ML framework for predicting the surface roughness of laser-cut EN 10130 steel. By integrating the interpretability of the RSM with regression tree-based residual correction, the framework achieves significantly improved prediction accuracy.