Explicit modelling of lift characteristics for high-lift devices based on knowledge-guided symbolic regression using large language model

The High-Lift Device (HLD) plays a critical role in determining the low-speed aerodynamic performance of aircraft during takeoff and landing phases. However, its aerodynamic performance prediction and design optimisation often involve costly high-fidelity simulations and complex black-box surrogate models. To achieve an explicit and accurate prediction of the lift increment with respect to the geometric parameters of the HLD, a knowledge-guided symbolic regression framework is proposed. First, key parameters that dominate the lift increment of HLD are selected and data are generated using a high-fidelity simulation method. Subsequently, mathematical features are extracted from the multimodal representation of the simulation results. These features and prior physical knowledge are embedded in natural language prompts to guide Large Language Models (LLMs) to design formulas in an evolutionary search framework. The designed formula achieves a lower mean square error with a simpler structure compared to that derived from conventional symbolic regression methods. It provides predictions with a deviation of less than 2% from wind tunnel test data, demonstrating accuracy comparable to Computational Fluid Dynamics (CFD) but with a significantly reduced computational budget. These results confirm the practicality and reliability of the proposed formula for engineering applications.