Application of machine learning in the determination of impact parameter in the 132Sn+124Sn system

Here, 132Sn +124 Sn collisions at a beam energy of 270 MeV/nucleon were performed at the Radioactive Isotope Beam Factory (RIBF) in RIKEN to investigate the nuclear equation of state. Reconstructing the impact parameter is one of the important tasks in the experiment as it relates to many observable. In this work, we employ three commonly used algorithms in machine learning, the artificial neural network (ANN), the convolutional neural network (CNN), and the light gradient boosting machine (LightGBM), to determine the impact parameter by analyzing either the charged particle spectra or several features simulated with events from the ultrarelativistic quantum molecular dynamics (UrQMD) model. To closely imitate experimental data and investigate the generalizability of the trained machine learning algorithms, incompressibility of nuclear equation of state and the in-medium nucleon-nucleon cross sections are varied in the UrQMD model to generate the training data. The mean absolute error Δb between the true and the predicted impact parameter is smaller than 0.45 fm if training and testing sets are sampled from the UrQMD model with the same parameter set. However, if training and testing sets are sampled with different parameter sets, Δb would increase to 0.8 fm. The generalizability of the trained machine learning algorithms suggests that these machine learning algorithms can be used reliably to reconstruct the impact parameter in experiment.