This study presents an approach that combines parametric modeling with a finite element (FE) simulation campaign, followed by post-processing of the results to generate generic data in the form of a matrix of varied geometric configurations along with their responses in linearized stress analysis. Using advanced Machine Learning techniques, this method aims to develop explicit formulas for evaluating the strength of mechanical structures. The selected industrial application concerns the integrity verification of the ligament between neighboring nozzles in critical areas of pressure vessel. The method relies on an algorithm called Recursive Multifactorial Regression (RMR), which integrates a Score-Learning strategy that maximizes a specific and adapted accuracy score. This approach optimizes variable selection through cross-validation and recursive pruning while limiting overfitting. An original Ordinal Correlation algorithm, using the Löwner order to identify dominance relationships between stress concentration zones, is structured in two stages: first, selection by inferiority, then regularization by superiority. It allows the identification of critical dimensioning areas from the dataset resulting from the numerical simulation campaign. The results have been validated through serval tests demonstrating an excellent correlation between the empirical formulas developed via RMR and theoretical formulas, thus confirming the robustness of the method. Therefore, RMR enables the derivation of interpretable and accurate empirical formulas, providing a practical alternative to systematically performing costly FE calculations during the design and sizing of mechanical structures.