Using Bayesian Deep Learning to Infer Planet Mass from Gaps in Protoplanetary Disks

Planet-induced substructures, like annular gaps, observed in dust emission from protoplanetary disks, provide a unique probe for characterizing unseen young planets. While deep-learning-based models have an edge in characterizing a planet's properties over traditional methods, such as customized simulations and empirical relations, they lacks the ability to quantify the uncertainties associated with their predictions. In this paper, we introduce a Bayesian deep-learning network, "DPNNet-Bayesian," which can predict planet mass from disk gaps and also provides the uncertainties associated with the prediction. A unique feature of our approach is that it is able to distinguish between the uncertainty associated with the deep-learning architecture and the uncertainty inherent in the input data due to measurement noise. The model is trained on a data set generated from disk-planet simulations using the fargo3d hydrodynamics code, with a newly implemented fixed grain size module and improved initial conditions. The Bayesian framework enables the estimation of a gauge/confidence interval over the validity of the prediction, when applied to unknown observations. As a proof of concept, we apply DPNNet-Bayesian to the dust gaps observed in HL Tau. The network predicts masses of 86.0 +/- 5.5 M (circle plus), 43.8 +/- 3.3 M (circle plus), and 92.2 +/- 5.1 M (circle plus), respectively, which are comparable to those from other studies based on specialized simulations.