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Background: $^{132}$Sn+$^{124}$Sn collisions at the beam energy of 270MeV$/$nucleon have been performed at the Radioactive Isotope Beam Factory(RIBF) in RIKEN to investigate the nuclear equation of state. Reconstructingimpact parameter is one of the important tasks in the experiment as it relatesto many observables. Purpose: In this work, we employ three commonly usedalgorithms in machine learning, the artificial neural network (ANN), theconvolutional neural network (CNN) and the light gradient boosting machine(LightGBM), to determine impact parameter by analyzing either the chargedparticles spectra or several features simulated with events from theultra-relativistic quantum molecular dynamics (UrQMD) model. Method: To closelyimitate experimental data and investigate the generalizability of the trainedmachine learning algorithms, incompressibility of nuclear equation of state andthe in-medium nucleon-nucleon cross sections are varied in the UrQMD model togenerate the training data. Results: The mean absolute error $\Delta b$ betweenthe true and the predicted impact parameter is smaller than 0.45 fm if trainingand testing sets are sampled from the UrQMD model with the same parameter set.However, if training and testing sets are sampled with different parametersets, $\Delta b$ would increase to 0.8 fm. Conclusion: The generalizability ofthe trained machine learning algorithms suggests that these machine learningalgorithms can be used reliably to reconstruct impact parameter in experiment.

Application of machine learning in the determination of impact parameter in the $^{132}$Sn+$^{124}$Sn system