ExoMDN: Rapid characterization of exoplanets interiors with machine learning

Characterizing the interior structure of exoplanets, that is, the size and mass of their main compositional reservoirs, is an essential part in understanding the diversity of observed exoplanets and the processes that govern their formation and evolution. However, the interior of an exoplanet is inaccessible to observations, and can only be investigated via numerical structure models. This poses an inverse problem, where the structure models need to conform to observed parameters. Unlike the planets in the Solar System, for which a wealth of observational data is available, mass and radius often remain the only parameters which can be determined for an exoplanet. Since the relative proportions of iron, silicates, water ice, and volatile elements inside the planet are not known, this poses a highly non-unique problem, where even with accurate radius and mass measurements many different solutions for the internal structure can be found.

Probabilistic inference methods, such as Markov chain Monte Carlo sampling, are a common tool to solve this inverse problem and obtain a comprehensive picture of possible planetary interiors, while also taking into account observational uncertainties. However, these typically require the calculation of hundreds of thousands of interior structures per investigated planet, which makes the characterization of exoplanets a computationally expensive and time-consuming process.

We explore an alternative approach to interior characterization utilizing machine learning. The application of machine learning methods has seen an extensive growth in the geodynamics and planetary science community in recent years, primarily driven by the need to address increasingly complex and computationally and data intensive problems that traditional methods of modeling and analysis struggle to solve. In particular, machine learning offers the opportunity to speed up time-consuming numerical simulations.

We present here ExoMDN, a stand-alone machine-learning model based on mixture density networks (MDNs) that is capable of providing a full probabilistic inference of exoplanet interiors in under a second, without the need for extensive modeling of each exoplanet's interior or even a dedicated interior model. ExoMDN is trained on a large database of 5.6 million precomputed, synthetic interior structures of low mass exoplanets.

The fast prediction times allow investigations into planetary interiors which were not feasible before. We demonstrate how ExoMDN can be leveraged to perform large-scale interior characterizations across the entire population of low-mass exoplanets. We can show how ExoMDN can be used to comprehensively quantify the effect of measurement uncertainties on the ability to constrain the interior of a planet, and to which accuracy these parameters need to be measured to well characterize a planet’s interior.

Training the model on different (potentially) observable parameters allows us to search for parameters which can better constrain the interior. Among these, the inclusion of the fluid Love number k₂ helps to significantly reduce the degeneracy of interior structures.

ExoMDN is freely accessible on GitHub at https://github.com/philippbaumeister/ExoMDN