Importance of physical information on the prediction of heavy-ion fusion cross section with machine learning

In this work, the Light Gradient Boosting Machine (LightGBM), which is a modern decision tree based machine-learning algorithm, is used to study the fusion cross section (CS) of heavy-ion reaction. Several basic quantities (e.g., mass number and proton number of projectile and target) and the CS obtained from phenomenological formula are fed into the LightGBM algorithm to predict the CS. It is found that, on the validation set, the mean absolute error (MAE) which measures the average magnitude of the absolute difference between $log_{10}$ of the predicted CS and experimental CS is 0.129 by only using the basic quantities as the input, this value is smaller than 0.154 obtained from the empirical coupled channel model. MAE can be further reduced to 0.08 by including an physical-informed input feature. The MAE on the test set (it consists of 280 data points from 18 reaction systems that not included in the training set) is about 0.19 and 0.53 by including and excluding the physical-informed feature, respectively. We further verify the LightGBM predictions by comparing the CS of $^{ 40,48}{\rm Ca }$+$^{78}{\rm Ni}$ obtained from the density-constrained time-dependent Hartree-Fock approach. Our study demonstrates the importance of physical information in predicting fusion cross section of heavy-ion reaction with machine learning.