Physics-informed neural network (PINN) modeling of charged particle multiplicity using the two-component framework in heavy-ion collisions: A comparison with data-driven neural networks

In this study, we employ a conventional deep neural network (NN) framework integrated with physics-based constraints to predict charged hadron multiplicity ($N_{\text{ch}}$) in heavy-ion collisions. The goal is to assess the performance of a purely data-driven deep neural network in comparison to a physics-informed neural network (PINN). To accomplish this, we have taken data generated from the HYDJET++ model for testing and training purposes. We train our neural network frameworks using the data of one million individual $^{96}_{40}\text{Zr}+^{96}_{40}\text{Zr}$ collision events. Our PINN model successfully extracts the hard-scattering fraction ($x$) by learning its underlying relation from the event data. For further testing and comparison with the conventional NN, we take data of $^{96}_{44}\text{Ru}+^{96}_{44}\text{Ru}$ (isobar of Zr) and $^{197}_{79}\text{Au}+^{197}_{79}\text{Au}$ collisions using the same simulation model. We found that the NN model needs more time to train with physics. However, once trained, the PINN model is capable of accurately predicting data that it has not encountered during training, such as Au+Au collision results. Especially in a region of sparse data corresponding to high $N_{\text{ch}}$ in our study, PINN has a clear advantage over a simple NN.