High-temperature compression behavior prediction of medium Mn steel: a comparative study of Arrhenius constitutive equation, machine learning, and symbolic regression models

Abstract

This study aims to accurately predict the compression stress–strain curves of medium Mn steel under high-temperature conditions. The Arrhenius constitutive equation with Zener–Hollomon, machine learning (ML), and genetic programming-based symbolic regression (GP-SR) was used to construct a prediction model for the high-temperature compression properties of medium manganese steel. The prediction performance of the three models was fairly compared by using the leave-one-out cross-validation dataset partitioning method. The average R² value of the Arrhenius constitutive equation on the training set is 0.855, and the average RMSE value is 12.14MPa. The ML dataset was constructed using the equidistant point method, and a new feature “strain level” was introduced. Combining support vector regression (SVR) with eXtreme gradient boosting (XGBoost) improved model performance, increasing R² from 0.824 to 0.907 and reducing RMSE from 10.70 to 8.28 MPa. The GP-SR method, combined with optimized hyperparameters and multiple iterations, produced a highly effective predictive formula with an average R² of 0.942 and an average RMSE of 7.87 MPa, and it demonstrated significant advantages. Compared with the ML models, this formula has excellent interpretability. Therefore, the formula obtained using the GP-SR method achieves higher accuracy compared to traditional equations and models. It provides an accurate reference for predicting stress–strain curves and selecting hot working parameters in the hot working process of medium Mn steel.