  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.
