  Transverse momentum spectra of identified particles produced in heavy-ion
collisions at the Large Hadron Collider are described with relativistic fluid
dynamics. We perform a systematic comparison of experimental data for pions,
kaons and protons up to a transverse momentum of 3 GeV$/c$ with calculations
using the FluiduM code package to solve the evolution equations of fluid
dynamics, the TrENTo model to describe the initial state and the FastReso code
to take resonance decays into account. Using data in five centrality classes at
the center-of-mass collision energy per nucleon pair
$\sqrt{s_\text{NN}}=2.76\,\text{TeV}$, we determine systematically the most
likely parameters of our theoretical model including the shear and bulk
viscosity to entropy ratios, the initialization time, initial density and
freeze-out temperature through a global search and quantify their posterior
probability. This is facilitated by the very efficient numerical implementation
of FluiduM and FastReso. Based on the most likely model parameters we present
predictions for the transverse momentum spectra of multi-strange hadrons as
well as identified particle spectra from Pb-Pb collisions at
$\sqrt{s_\text{NN}}=5.02\,\text{TeV}$.
