2020ApJ...889...42B

We explore the application of machine-learning based on mixture density neural networks (MDNs) to the interior characterization of low-mass exoplanets up to 25 Earth masses constrained by mass, radius, and fluid Love number, k₂. We create a data set of 900,000 synthetic planets, consisting of an iron-rich core, a silicate mantle, a high-pressure ice shell, and a gaseous H/He envelope, to train a MDN using planetary mass and radius as inputs to the network. For this layered structure, we show that the MDN is able to infer the distribution of possible thicknesses of each planetary layer from mass and radius of the planet. This approach obviates the time-consuming task of calculating such distributions with a dedicated set of forward models for each individual planet. While gas-rich planets may be characterized by compositional gradients rather than distinct layers, the method presented here can be easily extended to any interior structure model. The fluid Love number k₂ bears constraints on the mass distribution in the planets' interiors and will be measured for an increasing number of exoplanets in the future. Adding k₂ as an input to the MDN significantly decreases the degeneracy of the possible interior structures. In an open repository, we provide the trained MDN to be used through a Python Notebook.