  Current methods to characterize embedded planets in protoplanetary disc
observations are severely limited either in their ability to fully account for
the observed complex physics or in their computational and time costs. To
address this shortcoming, we developed DBNets: a deep learning tool, based on
convolutional neural networks, that analyses substructures observed in the dust
continuum emission of protoplanetary discs to quickly infer the mass of
allegedly embedded planets. We focussed on developing a method to reliably
quantify not only the planet mass, but also the associated uncertainty
introduced by our modelling and adopted techniques. Our tests gave promising
results achieving an 87% reduction of the log Mp mean squared error with
respect to an analytical formula fitted on the same data (DBNets metrics: lmse
0.016, r2-score 97%). With the goal of providing the final user of DBNets with
all the tools needed to interpret their measurements and decide on their
significance, we extensively tested our tool on out-of-distribution data. We
found that DBNets can identify inputs strongly outside its training scope
returning an uncertainty above a specific threshold and we thus provided a
rejection criterion that helps determine the significance of the results
obtained. Additionally, we outlined some limitations of our tool: it can be
reliably applied only on discs observed with inclinations below approximately
60{\deg}, in the optically thin regime, with a resolution 8 times better than
the gap radial location and with a signal-to-noise ratio higher than
approximately ten. Finally, we applied DBNets to 33 actual observations of
protoplanetary discs measuring the mass of 48 proposed planets and comparing
our results with the available literature. We confirmed that most of the
observed gaps imply planets in the sub-Jupiter regime. DBNets is publicly
available at dbnets.fisica.unimi.it.
