DBNets: A publicly available deep learning tool to measure the masses of young planets in dusty protoplanetary discs

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.