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

TL;DR

DBNets introduces an ensemble of convolutional neural networks to infer masses of gap-opening planets from dust continuum substructures in protoplanetary discs, with explicit uncertainty quantification that separates physics and model contributions. Trained on a large set of 2D hydrodynamical simulations and synthetic observations, the method delivers a high-quality mass proxy (lmse = 0.016, r^2 = 0.97) and robust uncertainty estimates (median ~0.14 dex) while providing a rejection criterion based on a 0.25 dex uncertainty threshold for out-of-distribution data. Applied to 33 discs with 48 gaps, DBNets yields predominantly sub-Jupiter masses and often aligns with literature within uncertainties, highlighting both the method’s efficiency and the importance of considering model limitations and missing physics. The work offers a practical, scalable tool for large surveys and population studies of young planets, with explicit guidance on applicability and caveats, and provides public access to the DBNets package for community use.

Abstract

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°, 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.

Figures (19)

• Figure 1: Pipeline adopted for the generation and preprocessing of the mock observations that we used to train and test our machine learning models. The $r_\text{max}$ denotes the outer radius of the simulated discs.
• Figure 2: Architecture of the trained CNNs. The disc image is fed to the convolutional part of the neural network made of three blocks. Each of them consists of two convolutional layers with filter size 3x3 (light orange) followed by a max pooling layer with filter size 2x2 (dark orange). The second part of the CNN consists of two fully connected layers. We omit in this image the dropout and normalization layers.
• Figure 3: Gallery of some mock observations in our dataset, before the beam convolution, organized to show how the morphology of the substructures varies with the disc’s and planet's physical parameters. The colour bar here refers to the disc brightness temperature, computed with Eq. (\ref{['eq:brightT']}) and then standardized by subtracting the mean of the image's pixels and dividing by the standard deviation.
• Figure 4: Planet mass distribution in the simulation dataset before (in blue) and after (in orange) removing images without azimuthally symmetric substructures.
• Figure 5: Scatter plot showing the correlation, in the results obtained on the test set, between the target planet mass and the estimate of the ensemble of CNNs (DBNets). The red line marks the ideal exact correlation that is targeted.