关键词: 关键词: 符号回归, Transformer, 深度强化学习, NACA4412, 卡门-钱学森公式

Abstract: Addressing the issues of reduced population diversity and sensitivity to hyperparameters in solving symbolic regression problems with genetic evolution algorithms, a Deep Symbolic Regression Technique (DSRT) based on Transformer was introduced. This approach leveraged the autoregressive capability of Transformer to generate expression symbol sequences. Subsequently, the transformed value of the fitness score between the data and the expression symbol sequence serves as a reward, which was employed to update the model parameters through deep reinforcement learning. This process enabled the model to output expression sequences that better align with the data, and as the model progressively converges, the optimal expression was identified. An evaluation of the DSRT method's effectiveness was conducted on the Nguyen symbolic regression benchmark dataset, where it was compared with DSR (Deep Symbolic Regression) and GP (Genetic Programming) algorithms within 200 iterations. Experimental results confirmed the validity of the DSRT approach. Additionally, the impact of various parameters on the DSRT method was discussed, and an experiment to predict the formula for the surface pressure coefficient of an aircraft airfoil using the NACA4421 dataset was performed. The obtained formula was compared with the Kármán-Tsien formula, yielding a mathematical formula with a lower RMSE.

Key words: symbolic regression, Transformer, deep reinforcement learning, NACA4412, Karman-Tsien formula