Dust substructures observed in protoplanetary discs can be interpreted as signatures of embedded young planets, whose detection and characterisation would provide a better understanding of planet formation. Traditional techniques used to link the morphology of these substructures to the properties of putative embedded planets present several limitations, which the use of deep learning methods has partly overcome. In our previous work, we used these new techniques to develop DBNets, a tool that uses an ensemble of convolutional neural networks (CNNs) to estimate the mass of putative planets in disc dust substructures. This inference problem, however, is degenerate, as planets of different masses could produce the same rings and gaps if other physical disc properties differ. In this paper, we address this issue by improving our tool to estimate three other disc properties in addition to the planet mass: the disc α-viscosity, the disc scale height, and the dust Stokes number. For a given dust continuum observation, the full joint posterior for these four properties is inferred, exposing the existing degeneracies and enabling the integration of external constraints to improve the planet mass estimates. In addition to this new feature, we also addressed a few minor issues with our previous tool, which reduced its accuracy depending on the resolution of the observations, or in the case of peculiar disc morphologies. The new pipeline involves a CNN that summarises the input images into a set of summary statistics, followed by an ensemble of normalising flows that model the inferred posterior for the target properties. We tested our pipeline on a dedicated set of synthetic observations, using the TARP test and standard metrics to demonstrate that our estimates are good approximations of the actual posteriors. Additionally, we applied the results obtained on the test set to study the presence and shape of degeneracies between pairs of parameters. Finally, we applied the developed pipeline to a set of 49 gaps in 34 protoplanetary disc continuum observations. The results show typically low values of α-viscosity, disc scale heights, and planet masses, with 83% of them being lower than 1 MJ. These low masses are consistent with the non-detections of these putative planets in direct imaging surveys. Our tool is publicly available.
Ruzza et al. (Tue,) studied this question.