## 6 Results and Discussion
underestimated the predictions (mean residuals +3.20, +1.2, and +5.64 kPa, respectively), while PySR demonstrated near-zero bias (\(-\)0.16 kPa). PySR also exhibited the lowest standard deviation (STD) among the models (27.34 kPa), whereas PGSR showed the highest dispersion (STD = 30.94 kPa). Considering this global analysis, PySR emerged as the most robust model, exhibiting minimal bias and the lowest variability in residuals. Based on the same residual and prediction data shown in Figure 7, a comparative summary of model performance was constructed using standard evaluation metrics, as shown in Figure 8. The evaluated metrics included Mean Absolute Error (MAE), Coefficient of Determination (R\({}^{2}\)), Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), Root Mean Square Logarithmic Error (RMSLE), and Explained Variance (EVS). The results of this analysis are included in Figure 8 as a radar chart. The performance analysis of the four models revealed differences across the considered metrics. PySR exhibited superior accuracy, with the lowest MAE (20.49 kPa) and RMSE (27.34 kPa), alongside the highest R\({}^{2}\) (0.933) and EVS (0.933), indicating a strong ability to capture data variability. PhySO, with an MAE of 20.66 kPa and RMSE of 29.63 kPa, performed competitively and achieved the lowest MAPE (13.95%) and a low RMSLE (0.174), making it particularly reliable in terms of relative errors. PhySO prioritized relative accuracy and performance across different data scales, while PySR optimized overall accuracy more effectively and demonstrated greater robustness against outliers. MOOSR displayed intermediate results, with an MAE of 21.47 kPa and RMSE of 30.54 kPa, and lower R\({}^{2}\) (0.916) and EVS (0.917), indicating that it explained less variance compared to PySR and PhySO. The PGSR model registered the highest error levels, MAE (22.65 kPa), RMSE (31.45 kPa), MAPE (16.60%), and RMSLE (0.205), along with the lowest R\({}^{2}\) (0.911) and EVS (0.914), suggesting it was less effective in capturing data variability. In summary, while all models demonstrated reasonable predictive capabilities, PySR and PhySO led in accuracy and consistency, with MOOSR being moderately effective and PGSR performing in a less robust manner. After completing the global analysis, a comparative analysis of the four SR regression models was conducted across different ranges of p\({}_{\text{s}}\). The dataset was then divided into several ranges of p\({}_{\text{s}}\): below 100 kPa, between 100 and 200 kPa, and above 200 kPa. For this analysis, MAPE, MAE, the mean, and the STD of the residuals were calculated. The results of this analysis are presented in Figure 9.  
This analysis revealed distinct strengths for each model depending on the p\({}_{\text{s}}\) interval. PhySO showed the best overall performance in relative terms, achieving the lowest MAPE on the full dataset and in the 100-200 kPa range (12.96%), and nearly the best in the \(<\)100 kPa segment. It also recorded the lowest residual STD in the \(<\)100 kPa range (8.27 kPa) and was close to the best in the 100-200 kPa range, indicating high precision at low to mid p\({}_{\text{s}}\). However, it exhibited notable bias in the extreme pressure ranges, particularly in \(>\)200 kPa (mean residuals = 18.20) and \(<\)100 kPa (\(-\)3.36 kPa), and its dispersion at high p\({}_{\text{s}}\) (STD = 42.06 kPa) was among the highest. PySR minimized global bias most effectively (mean residuals = \(-\)0.16 kPa) and achieved the lowest MAPE (11.81%) and STD (37.79 kPa) in the \(\geq\)200 kPa range, making it particularly well-suited for high p\({}_{\text{s}}\) applications. However, its performance in the \(<\)100 kPa range was not among the best, with the second highest MAPE (20.88%) and residual bias (\(-\)4.60 kPa). MOSR was the most robust in reducing residual bias at the extremes, with near-zero mean residuals in \(<\)100 kPa (\(-\)0.74 kPa) and the best bias in \(\geq\)200 kPa (9.36 kPa).