## 1 Introduction  
Laser cutting has become a fundamental technology in modern manufacturing due to its ability to deliver high precision and process a wide range of materials, including metals, polymers, and fiber-reinforced composites [1]. Despite these advantages, the industry is increasingly demanding tighter tolerances and better surface finishes. As a result, surface roughness (Ra) has become an important quality indicator, as it affects not only the aesthetic appeal but also the functional performance of components [2]. Even though laser cutting is a well-established technology, achieving good surface quality remains a challenge due to the complex and often nonlinear interactions between process parameters. For example, certain combinations of cutting speed and laser power can cause chaotic melt ejection [3; 4; 5]. Additional issues include gas pressure instabilities and material damage caused by overheating and resolidification [6]. These subtleties highlight the need for advanced modeling strategies capable of capturing the underlying physics while supporting robust process optimization. Response surface methodology (RSM) is often used to develop empirical models that describe the relationship between input process parameters and output performance metrics. For example, [PERSON] et al. successfully applied a Box-Behnken RSM design to optimize surface roughness (Ra) and kerf width in the laser cutting of Inconel 718 sheets [7]. Their regression models demonstrated high predictive accuracy, with an R\({}^{2}\) value of approximately 99%, identifying cutting speed and laser power as the most influential factors affecting cut quality. [PERSON] et al. used RSM to develop quadratic models based on four input process parameters--oxygen pressure, pulse width, pulse frequency, and cutting speed--and two output responses: average kerf taper and surface roughness (Ra) [8]. The analysis of variance (ANOVA) results indicated good agreement between the experimental data and the predicted nonlinear regression model, with R\({}^{2}\) values of approximately 97%. Similarly, [PERSON] et al. developed a multiple linear regression model to predict the maximum surface roughness height in CO\({}_{2}\) laser cutting of Ti-6 Al-4V alloys [9]. Their analysis showed that the cutting speed was the dominant factor for surface roughness, while the auxiliary gas pressure had a negligible influence within the investigated range. The model was validated using ANOVA and achieved a high coefficient of determination (R\({}^{2}\)) of 99.33%, confirming its appropriateness. Similarly, [PERSON] systematically investigated the effects of process parameters, such as cutting speed, focal length, and laser power, on the temperature adjacent to the cut kerf and cutting surface roughness using RSM [10]. A central composite design (CCD) was employed for the experimental setup and ANOVA, which revealed the significance of each factor's contribution to the responses. The resulting regression models demonstrated high accuracy in predicting both temperature distribution and surface roughness. Generally, these studies affirm RSM's value as a transparent and statistically sound tool for surface quality prediction in laser-based manufacturing processes. It is worth noting, however, that these models were developed using relatively large experimental datasets, which likely contributed to the high R\({}^{2}\) values. Recent advances in machine learning (ML) have enabled highly accurate modeling of surface roughness in laser cutting processes, often more successfully traditional statistical approaches in predictive performance. [PERSON] and [PERSON] evaluated the performance of three machine learning models--support vector regression, random forest, and extreme learning machine--for predicting kerf width in pulsed laser cutting [11]. They indicated that the vibration features selected from the optimal base wavelet selection combined with the random forest model are efficient for forecasting the straight kerf width of the workpiece by pulsed laser cutting.