  Measurements of inclusive, differential cross-sections for the production of
events with missing transverse momentum in association with jets in
proton-proton collisions at $\sqrt{s}=13$~TeV are presented. The measurements
are made with the ATLAS detector using an integrated luminosity of
140~fb$^{-1}$ and include measurements of dijet distributions in a region in
which vector-boson fusion processes are enhanced. They are unfolded to correct
for detector resolution and efficiency within the fiducial acceptance, and are
designed to allow robust comparisons with a wide range of theoretical
predictions. A measurement of differential cross sections for the $Z~\to
\nu\nu$ process is made. The measurements are generally well-described by
Standard Model predictions except for the dijet invariant mass distribution.
Auxiliary measurements of the hadronic system recoiling against isolated
leptons, and photons, are also made in the same phase space. Ratios between the
measured distributions are then derived, to take advantage of cancellations in
modelling effects and some of the major systematic uncertainties. These
measurements are sensitive to new phenomena, and provide a mechanism to easily
set constraints on phenomenological models. To illustrate the robustness of the
approach, these ratios are compared with two common Dark Matter models, where
the constraints derived from the measurement are comparable to those set by
dedicated detector-level searches.
