Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Neural network enhanced Bayesian global analysis of relativistic heavy ion collisions

Jussi Auvinen, Kari J. Eskola, Henry Hirvonen, Harri Niemi

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 $η/s$ with a minimum-value plateau at temperatures $150\lesssim T \lesssim 230$ MeV, with $0.12 \lesssim (η/s)_{\mathrm{min}} \lesssim 0.18$. The bulk viscous coefficient $ζ/s$ 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.

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 GeV Au+Au collisions at RHIC and TeV Pb+Pb, TeV Pb+Pb, and 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 and the normalized symmetric cumulant 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 with a minimum-value plateau at temperatures MeV, with . The bulk viscous coefficient is non-zero at MeV. The Knudsen number at the freeze-out is , while the ratio of the mean free path to the system size at freeze-out is in the range , implying that the freeze-out indeed happens at the expected limit of the applicability of hydrodynamics.

Paper Structure

This paper contains 23 sections, 28 equations, 17 figures, 15 tables.

Table of Contents

  1. Introduction
  2. Model description
  3. EbyE-EKRT initial state
  4. 2+1 D viscous hydrodynamics
  5. Dynamical freeze-out conditions
  6. Predicting hydrodynamic simulation output with neural networks
  7. Statistical analysis
  8. Input parameters
  9. Observables
  10. Principal component analysis
  11. Gaussian process emulators
  12. Likelihood function
  13. Results
  14. Posterior distribution
  15. Comparison to data
  16. ...and 8 more sections

Figures (17)

  • Figure 1: Validation of neural network predictions against full-simulation results for various observables in $\sqrt{s_{NN}}=5.02~\mathrm{TeV}$ Pb+Pb collisions. The predictions are compared with hydrodynamical simulation results for 10 parameter points across the centrality classes listed in Table III. The straight line is added as a reference to indicate where the two results match exactly. $\mathcal{E}$ is the root-mean-square (RMS) error of the observable, defined in Eq. \ref{['eq:rms_error']}.
  • Figure 2: Validation of the neural network prediction for normalized symmetric cumulants against hydrodynamic simulations with 50,000 simulated events. Note that only $NSC(4,2)$ is included in our Bayesian analysis.
  • Figure 3: The median and 90% credible interval for the specific shear viscosity $\eta/s$ with respect to temperature $T$.
  • Figure 4: The median and 90% credible interval for the bulk viscous coefficient $\zeta/s$ with respect to temperature $T$. Note that the lower limit of the prior is zero.
  • Figure 5: Posterior distribution based emulator predictions for the centrality dependence of charged particle multiplicity for all four collision systems (top panel) and average transverse momentum in Xe+Xe collisions at $\sqrt{s_{NN}}=5.44$ TeV (bottom panel). The violin plots reflect the distribution of emulator predictions, with more points concentrated on the broader parts of the violin. The horizontal line within the violin indicates the mean value of predictions. PHENIX data is from Ref. Adler:2004zn and ALICE data from Refs. Aamodt:2010cz (2.76 TeV), Adam:2015ptt (5.02 TeV), and ALICE:2018hza (5.44 TeV).
  • ...and 12 more figures