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Neural-network-enhanced Bayesian global analysis of relativistic heavy-ion collisions

Jussi Auvinen1,2,3,*, Kari J. Eskola2,3, Henry Hirvonen4,5, and Harri Niemi2,3

  • *Contact author: jussi.a.m.auvinen@jyu.fi
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Phys. Rev. C 114, 014904 – Published 10 July, 2026

DOI: https://doi.org/10.1103/13dy-4g64

Abstract

We introduce a novel deep convolutional neural-network-(NN) enhanced Bayesian global analysis of bulk observables in highest-energy heavy-ion collisions using relativistic 2+1D second-order viscous hydrodynamics with a dynamical freeze-out and with perturbative quantum chromodynamics (QCD) and saturation-based initial conditions from the event-by-event EKRT model. Our analysis has 13+2 free parameters for the QCD-matter properties + initial state, which are constrained by the experimental data from sNN=200 GeV Au+Au collisions at Relativistic Heavy Ion Collider and 2.76 TeV Pb+Pb, 5.02 TeV Pb+Pb, and 5.44 TeV Xe+Xe collisions at the Large Hadron Collider. We replace the computationally demanding hydrodynamical simulations by NNs, which predict bulk observables directly from the initial energy density profiles, event by event, and account for the QCD-matter properties. With the NN output, we train the Gaussian process emulators for obtaining centrality-class averaged observables and their uncertainties. The NNs reduce the computing time significantly, enabling us to include also statistics-hungry flow observables like v4 and the normalized symmetric cumulant NSC(4,2) in the analysis. In this paper, we demonstrate the feasibility of the NN-based Bayesian global analysis. We find the data favoring a specific shear viscosity η/s with a minimum-value plateau at temperatures 150≲T≲230 MeV, with 0.12≲(η/s)min≲0.18. The bulk viscous coefficient ζ/s is nonzero at 200≲T≲300 MeV. The Knudsen number at the freeze-out is 0.8–2.3, while the ratio of the mean free path to the system size at freeze-out is in the range 0.3–1.2, implying that the freeze-out indeed happens at the expected limit of the applicability of hydrodynamics.

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Phys. Rev. C 114, 014904– Published 10 July, 2026
  • Received 31 March 2026
  • Accepted 27 May 2026
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