Neural network enhanced Bayesian global analysis of relativistic heavy ion collisions

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 $0.12 \lesssim (\eta/s)_{\mathrm{min}} \lesssim 0.18$. 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.