Determination of the impact parameter in high-energy heavy-ion collisions via deep learning

In this study, Au+Au collisions with an impact parameter of fm at GeV are simulated using the AMPT model to provide preliminary final-state information. After transforming this information into appropriate input data (the energy spectra of final-state charged hadrons), we construct a multi-layer perceptron (MLP) and convolutional neural network (CNN) to connect final-state observables with the impact parameters. The results show that both the MLP and CNN can reconstruct the impact parameters with a mean absolute error approximately fm, although the CNN behaves slightly better. Subsequently, we test the neural networks at different beam energies and pseudorapidity ranges in this task. These two models work well at both low and high energies. However, when conducting a test for a larger pseudorapidity window, the CNN exhibits a higher prediction accuracy than the MLP. Using the Grad-CAM method, we shed light on the 'attention' mechanism of the CNN model.