https://doi.org/10.1140/epjp/s13360-026-07716-3
Regular Article
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
1
Discipline of Natural Sciences, PDPM Indian Institute of Information Technology Design & Manufacturing, 482005, Jabalpur, India
2
Department of Physics, Institute of Science, Banaras Hindu University, 221005, Varanasi, India
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Received:
20
March
2026
Accepted:
17
April
2026
Published online:
6
May
2026
Abstract
In this study, we employ a conventional deep neural network (NN) framework integrated with physics-based constraints to predict charged hadron multiplicity (
) 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 
collision events. Our PINN 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 
(isobar of Zr) and 
collisions using the same simulation model. Once trained, the PINN demonstrates improved predictive performance on data not encountered during training, such as Au+Au collision results. Especially in regions of sparse data, corresponding to high in our study, the PINN shows a clear advantage over a purely data-driven neural network.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
