Neural network enhanced Bayesian global analysis of relativistic heavy ion collisions

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+1 D second-order viscous hydrodynamics with a dynamical freeze-out, and with perturbative 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 $\sqrt{s_{NN}}=200$ GeV Au+Au collisions at RHIC and $2.76$ TeV Pb+Pb, $5.02$ TeV Pb+Pb, and $5.44$ TeV Xe+Xe collisions at the LHC. 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 $v_4$ 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 $\eta /s$ with a minimum-value plateau at temperatures $150\lesssim T\lesssim 230$ MeV, with $0.12\lesssim (\eta /s{)}_{\min }\lesssim 0.18$. The bulk viscous coefficient $\zeta /s$ is non-zero at $200\lesssim T\lesssim 300$ 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.

29 pages, 17 figures. Published in Phys. Rev. C. The code for neural network training is available at Zenodo, DOI: 10.5281/zenodo.20499598

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