Explicit Modeling Method for Lift Coefficient of High-Speed Vehicle Based on Symbolic Regression

Rapid prediction of vehicle lift coefficient is an important issue in aerodynamic design. Traditional CFD/DSMC methods have high computational costs. Although commonly used machine-learning surrogate models offer high prediction efficiency, they struggle to provide explicit mathematical expressions. To balance prediction accuracy and model interpretability, this paper introduces the symbolic regression method and establishes an explicit modeling process for the lift coefficient. Using Mach number, angle of attack, and related flow parameters as inputs, validation is conducted on two-dimensional blunt body DSMC data and three-dimensional missile aerodynamic data, with comparisons against linear regression, quadratic polynomial regression, Kriging, random forest, XGBoost, and multilayer perceptron. The results show that symbolic regression can obtain high-precision explicit expressions on the two-dimensional blunt body data and can also build analytical models with certain predictive capability on the three-dimensional missile data with limited samples. Compared with traditional explicit regression methods, symbolic regression does not require a pre-specified fixed functional form; compared with black-box models, its advantage lies in providing interpretable and editable algebraic expressions. The findings indicate that symbolic regression has application potential in rapid explicit modeling of the lift coefficient.