A symbolic regression approach for crosswind response evaluation of rectangular cylinders

Crosswind vibration of rectangular cylinders is a long-standing problem in wind engineering, characterized by multiple coexisting flow-induced vibration mechanisms and strong nonlinear interactions among governing parameters. In this study, symbolic regression (SR) is employed to derive explicit and explainable formulas for the crosswind response of rectangular cylinders. A comparative investigation is conducted using two representative algorithms, i.e. the Python Symbolic Regression (PySR) and Physical Symbolic Optimization (PhySO), based on a comprehensive experimental database covering different turbulence intensities, side ratios, Scruton numbers, and reduced wind speeds. Model performance is evaluated in two reduced wind speed ranges ( 6 ≤ U r ≤ 15 and U r > 15 ). This partition helps the symbolic regression models better capture distinct response patterns, including VIV, galloping, and their coupling effects, while avoiding an overly complex single expression over the full range. PySR achieved R 2 values of 0.93 and 0.96 in the low and high speed regimes, respectively, compared with 0.54 and 0.92 for PhySO, with the largest performance difference occurring in the strongly nonlinear low speed regime. Finally, Sobol and partial-dependence analyses indicate that the derived expressions reproduce several dependencies consistent with established aerodynamic trends within the fitted domain. Therefore, this study demonstrates that the symbolic regression provides an effective and explainable framework for evaluating crosswind responses of rectangular cylinders.