Heavy-ion fusion reactions, as the exclusive means to synthesize superheavy elements and novel nuclides, hold paramount significance in nuclear physics. However, conventional physical models demonstrate limitations in characterizing the fusion cross section (CS) of heavy-ion reaction, while experimental measurements for numerous systems remain incomplete or lack sufficient precision. Machine learning (ML), which has been widely applied to scientific research in recent years, can be used to investigate the inherent correlations within a large number of complex data.

This study aims to establish the relationship between fusion reaction features and CS by training the dataset using LightGBM (Light Gradient Boosting Machine).

Several basic quantities (e.g., proton number, mass number, and the excitation energies of the 2⁺ and 4⁺ states of projectile and target) and the CS obtained from phenomenological formulas were fed into the LightGBM algorithm to predict the CS. Meanwhile, to evaluate the impact of different features on model predictions, the Shapley additive explanations (SHAP) method was employed to rank the importance of input features. A visual analysis was also conducted to illustrate the relationships between each feature and the CS, enabling the identification of key features that are highly sensitive to the CS and helping to uncover the underlying physical mechanisms.

On the validation set, the mean absolute error (MAE) which measures the average magnitude of the absolute difference between log10 of the predicted CS and experimental CS is 0.138 by only using the basic quantities as the input, this value is smaller than 0.172 obtained from the empirical coupled channel model. MAE can be further reduced to 0.07 by including an physical-informed input feature. The MAE on the test set (it consists of 175 data points from 11 reaction systems that not included in the training set) is about 0.17 and 0.45 by including and excluding the physical-informed feature, respectively. By analyzing the predicted CS for systems 18O+S116n and 36S+T50i in the test set, the fusion barrier distributions were further extracted. The results demonstrate that the incorporation of physics-informed features significantly enhances the agreement between calculated barrier distributions and experimental data. In addition, the SHAP method was used in the study to construct a visual correlation map between input feature parameters and CS. Through feature importance ranking, it revealed that the excitation energies of the 2⁺ and 4⁺ states of the target nucleus play an important role in predicting the CS.

Physical information plays a crucial role in machine learning studies of heavy-ion fusion reactions.