CST-LLM: Enhancing airfoil parameterization method with large language model

The airfoil parameterization method is pivotal for airfoil design optimization, as it transforms numerous discrete coordinate points into a concise and manageable set of parameters. The primary goal of the parameterization method is to achieve a more precise representation and control of airfoil geometry with fewer parameters. This paper proposes a symbolic regression method based on the pre-trained Large Language Model (LLM) for enhancing the performance of the airfoil parameterization method. The proposed method utilizes LLM to generate and evolve feature transformation functions for modifying the Class/Shape function Transformation (CST) method. By offering simple mathematical insights to the LLM through natural language, feature transformation functions are effectively designed and the CST-LLM parameterization method is proposed by modifying the CST parameterization method using designed function. In geometry recovery tests conducted on open source airfoil libraries, the CST-LLM parameterization method consistently outperforms other state-of-the-art parameterization methods, offering a more complete design space for airfoil design optimization by accurately representing a wider range of airfoil geometries. In design optimization of RAE 5214 airfoil, the CST-LLM parameterization method consistently achieved better results compared with the CST parameterization method. These improvements not only demonstrate the efficacy of the proposed LLM-based symbolic regression method, but also underscore the wide application potential of LLM in scientific research.