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 k 2 . We create a dataset 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 k 2 bears constraints on the mass distribution in the planets' interior and will be measured for an increasing number of exoplanets in the future. Adding k 2 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.

Context. The mass and radius of a planet directly provide its bulk density, which can be interpreted in terms of its overall composition. Any measure of the radial mass distribution provides a first step in constraining the interior structure. The fluid Love number k 2 provides such a measure, and estimates of k 2 for extrasolar planets are expected to be available in the coming years thanks to improved observational facilities and the ever-extending temporal baseline of extrasolar planet observations. Aims. We derive a method for calculating the Love numbers k n of any object given its density profile, which is routinely calculated from interior structure codes. Methods. We used the matrix-propagator technique, a method frequently used in the geophysical community. Results. We detail the calculation and apply it to the case of GJ 436b, a classical example of the degeneracy of mass-radius relationships, to illustrate how measurements of k 2 can improve our understanding of the interior structure of extrasolar planets. We implemented the method in a code that is fast, freely available, and easy to combine with preexisting interior structure codes. While the linear approach presented here for the calculation of the Love numbers cannot treat the presence of nonlinear effects that may arise under certain dynamical conditions, it is applicable to close-in gaseous extrasolar planets like hot Jupiters, likely the first targets for which k 2 will be measured.

The evolution of Venus is still in many ways a mystery. Despite its similarity to Earth in terms of size and bulk composition (e.g., Lécuyer et al., 2000), the atmospheric 2 CO E mass of Venus is larger by more than five orders of magnitude (Donahue & Pollack, 1983). Whether Venus' atmosphere was 2 CO E -rich early in its evolution, or whether, and how, it diverged from Earth's atmosphere later in its evolution is a matter of debate (e.g.,