  We compute the initial energy densities produced in ultrarelativistic
heavy-ion collisions from NLO perturbative QCD using a saturation conjecture to
control soft particle production, and describe the subsequent space-time
evolution of the system with hydrodynamics, event by event. The resulting
centrality dependence of the low-$p_T$ observables from this pQCD + saturation
+ hydro ("EKRT") framework are then compared simultaneously to the LHC and RHIC
measurements. With such an analysis we can test the initial state calculation,
and constrain the temperature dependence of the shear viscosity-to-entropy
ratio $\eta/s$ of QCD matter. Using these constraints from the current RHIC and
LHC measurements we then predict the charged hadron multiplicities and flow
coefficients for the 5.023 TeV Pb+Pb collisions.
