  In relativistic heavy-ion collisions, the production of heavy quarks at large
transverse momenta is strongly suppressed compared to proton-proton collisions.
In addition an unexpectedly large azimuthal anisotropy was observed for the
emission of charmed hadrons in non-central collisions. Both observations pose
challenges to the theoretical understanding of the coupling between heavy
quarks and the quark-gluon plasma produced in these collisions. Transport
models for the evolution of heavy quarks in a QCD medium offer the opportunity
to study these effects - two of the most successful approaches are based on the
linearized Boltzmann transport equation and the Langevin equation. In this
work, we develop a hybrid transport model that combines the strengths of both
of these approaches: heavy quarks scatter with medium partons using
matrix-elements calculated in perturbative QCD, while between these discrete
hard scatterings they evolve using a Langevin equation with empirical transport
coefficients to capture the non-perturbative soft part of the interaction. With
the hybrid transport model coupled to a state-of-the-art event-by-event bulk
evolution model based on 2+1D relativistic viscous fluid dynamics, we study the
azimuthal anisotropy and nuclear modification factor of heavy quarks in Pb+Pb
collisions at $\sqrt{s} = 5.02$ TeV. The parameters of our model are calibrated
using a Bayesian analysis comparing to available $D$-meson and $B$-meson data
at the LHC. Using the calibrated model, we study the implications on
heavy-flavor transport properties and predict novel observables.
