Integrating physics‐informed symbolic regression with dimensional analysis for UHPC‐jacketed reinforced concrete columns

Abstract Ultra‐high‐performance concrete (UHPC) jacketing is an effective technique for enhancing the axial load capacity of reinforced concrete (RC) columns; however, current design codes do not provide calibrated analytical equations for such composite members. The strong interaction among geometry, material properties, and reinforcement complicates the development of reliable closed‐form design formulations. While machine learning (ML) models can achieve high predictive accuracy, their black‐box nature limits transparency and hinders adoption in structural design practice. This study proposes a physics‐informed symbolic regression framework aimed at deriving a code‐ready design equation for predicting the ultimate axial capacity of UHPC‐jacketed RC columns. Experimental data compiled from the literature were first transformed into mechanically consistent dimensionless parameters through dimensional analysis, ensuring proper physical scaling and reducing model redundancy. The resulting design equation demonstrates high accuracy on unseen data ( R 2 = 0.988, root mean square error [RMSE] = 194 kN), comparable to representative ML models, including eXtreme Gradient Boosting (XGBoost) ( R 2 = 0.98, RMSE = 290 kN) and Categorical Boosting (CatBoost) ( R 2 = 0.99, RMSE = 203 kN), while requiring fewer input variables and retaining full analytical transparency. When benchmarked against American Concrete Institute 318 (ACI 318) and Eurocode 2 (EC2) on the test set, the proposed formulation significantly improves predictive performance, reducing RMSE by approximately 71% and 78%, respectively, compared with ACI 318 (RMSE = 675 kN) and EC2 (RMSE = 865 kN). Shapley Additive Explanations‐based interpretation and Sobol sensitivity analysis further confirm the mechanical consistency of the equation, highlighting the dominant contributions of the RC core and UHPC jacket and the activating role of transverse reinforcement in confinement. The proposed formulation provides a transparent and mechanics‐consistent design equation suitable for calibration and potential incorporation into future design provisions for UHPC‐jacketed RC columns.