Unsteady aerodynamic modeling of aircrafts at high angles of attack assisted by large language model

Compared with data-driven models, expert’s experience-informed models are widely preferred in engineering for unsteady aerodynamic modeling due to their explicit analytical expressions and strong generalization capability. However, constructing such models typically involves manually defining a candidate regressor pool based on prior knowledge, followed by extensive trial-and-error adjustments. This manual process is not only labor-intensive but often leads to suboptimal model structures, as determining the most effective functional forms from limited experience is challenging. To address this issue, this article proposes a novel symbolic regression approach based on a pre-trained large language model (LLM) within an evolutionary framework for unsteady aerodynamic modeling. The core idea is to leverage the generative and reasoning capabilities of the LLM to automatically discover and optimize physically meaningful expressions through prompt-driven interactions, eliminating the need for predefined candidate pools or manual tuning. This method is applied to the automated discovery of the forcing function representing unsteady aerodynamic effects within a differential equation model (DEM), and is referred to as DEM-LLM. Its effectiveness is validated by the unsteady aerodynamic modeling of the F/A-18 configuration undergoing single-degree-of-freedom (1-DoF) constant pitch-rate motions and further demonstrated on the standard dynamic model performing large-amplitude 2-DoF coupled oscillatory motions. Results indicate that the optimized expressions achieve significantly higher prediction accuracy than traditional manually designed models such as Taylor series expansions. Furthermore, they exhibit superior generalization capability compared to data-driven black-box models like long short-term memory networks, while maintaining a slight accuracy advantage.