  Nuclear masses play a fundamental role in understanding how the heaviest
elements in the Universe are created in the $r$-process. We predict $r$-process
nucleosynthesis yields using neutron capture and photodissociation rates that
are based on nuclear density functional theory. Using six Skyrme energy density
functionals based on different optimization protocols, we determine for the
first time systematic uncertainty bands -- related to mass modeling -- for
$r$-process abundances in realistic astrophysical scenarios. We find that
features of the underlying microphysics make an imprint on abundances
especially in the vicinity of neutron shell closures: abundance peaks and
troughs are reflected in trends of neutron separation energy. Further advances
in nuclear theory and experiments, when linked to observations, will help in
the understanding of astrophysical conditions in extreme $r$-process sites.
