  Our knowledge of the heating mechanisms that are at work in the chromosphere
of plage regions remains highly unconstrained from observational studies. The
purpose of our study is to estimate the chromospheric heating terms from a
plage dataset, characterize their spatio-temporal distribution and set
constraints on the heating processes that are at work. We make use of NLTE
inversions to infer a model of the photosphere and chromosphere of a plage
dataset acquired with the Swedish 1-m Solar Telescope. We use this model
atmosphere to calculate the chromospheric radiative losses from H i, Ca ii and
Mg ii atoms. We approximate the chromospheric heating terms by the net
radiative losses predicted by the inverted model. In order to make the analysis
of time-series over a large field-of-view computationally tractable, we make
use of a neural network. In the lower chromosphere, the contribution from the
Ca ii lines is dominant and located in the surroundings of the photospheric
footpoints. In the upper chromosphere, the H i contribution is dominant.
Radiative losses in the upper chromosphere form an homogeneous patch that
covers the plage region. The net radiative losses can be split in a periodic
component with an average amplitude of ampQ = 7.6 kW m^{-2} and a static (or
very slowly evolving) component with a mean value of -26.1 kW m^{-2}. Our
interpretation is that in the lower chromosphere, the radiative losses are
tracing the sharp lower edge of the hot magnetic canopy, where the electric
current is expected to be large. In the upper chromosphere, both the magnetic
field and the distribution of net radiative losses are room-filling, whereas
the amplitude of the periodic component is largest. Our results suggest that
acoustic wave heating may be responsible for one third of the energy deposition
in the upper chromosphere, whereas other heating mechanisms must be responsible
for the rest.
