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Deep symbolic regression method based on Transformer
Pengcheng XU, Lei HE, Chuan LI, Weiqi QIAN, Tun ZHAO
Journal of Computer Applications    2025, 45 (5): 1455-1463.   DOI: 10.11772/j.issn.1001-9081.2024050609
Abstract75)   HTML3)    PDF (3565KB)(23)       Save

To address the challenges of reduced population diversity and sensitivity to hyperparameters in solving Symbolic Regression (SR) problems by using genetic evolutionary algorithms, a Deep Symbolic Regression Technique (DSRT) method based on Transformer was proposed. This method employed autoregressive capability of Transformer to generate expression symbol sequence. Subsequently, the transformation of the fitness value between the data and the expression symbol sequence was served as a reward value, and the model parameters were updated through deep reinforcement learning, so that the model was able to output expression sequence that fitted the data better, and with the model’s continuous converging, the optimal expression was identified. The effectiveness of the DSRT method was validated on the SR benchmark dataset Nguyen, and it was compared with DSR (Deep Symbolic Regression) and GP (Genetic Programming) algorithms within 200 iterations. Experimental results confirm the validity of DSRT method. Additionally, the influence of various parameters on DSRT method was discussed, and an experiment to predict the formula for surface pressure coefficient of an aircraft airfoil using NACA4421 dataset was performed. The obtained formula was compared with the Kármán-Tsien formula, yielding a mathematical formula with a lower Root Mean Square Error (RMSE).

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