Dust grains in the disk around a young star stick together, grow, and will eventually become planets. But to know how much planet-building material each disk holds, you need to measure its mass and size. You can't weigh a distant cloud directly: you have to infer it from the dust's radiation.

Astronomers trained a neural network on thousands of disk models computed with detailed computer code. The network learned to quickly output disk parameters from an image and spectrum. Then they coupled it with a Bayesian optimization algorithm that finds the best match between model and observations. This way, they processed 1.3 mm images and spectra of protoplanetary disks in the Ophiuchus molecular cloud.

It turned out that for Class II disks (more evolved), the model fits both the image and the spectrum well. For younger Class I objects and "flat" sources, the spectra fit worse — perhaps the dust is distributed differently or there is extra heating. The disk mass distribution came out broader and flatter than simple brightness-based estimates at 1.3 mm: there are more very light and very heavy disks.

The reason is that dust brightness depends not only on mass but also on temperature and optical depth. These effects are strongly tied to disk size and inclination, which are precisely what the images refine. It also emerged that as you go from young Class I objects to flat sources and Class II disks, the disk scale height and its "flaring" toward the edge decrease noticeably. Disks become thinner and flatter.