ExoMDN: Rapid characterization of exoplanet interior structures with Mixture Density Networks

Abstract

Characterizing the interior structure of exoplanets is essential for understanding their diversity, formation, and evolution. As the interior of exoplanets is inaccessible to observations, an inverse problem must be solved, where numerical structure models need to conform to observable parameters such as mass and radius. This is a highly degenerate problem whose solution often relies on computationally-expensive and time-consuming inference methods such as Markov Chain Monte Carlo. We present ExoMDN, a machine-learning model for the interior characterization of exoplanets based on Mixture Density Networks (MDN). The model is trained on a large dataset of more than 5.6 million synthetic planets below 25 Earth masses consisting of an iron core, a silicate mantle, a water and high-pressure ice layer, and a H/He atmosphere. We employ log-ratio transformations to convert the interior structure data into a form that the MDN can easily handle. Given mass, radius, and equilibrium temperature, we show that ExoMDN can deliver a full posterior distribution of mass fractions and thicknesses of each planetary layer in under a second on a standard Intel i5 CPU. Observational uncertainties can be easily accounted for through repeated predictions from within the uncertainties. We use ExoMDN to characterize the interior of 22 confirmed exoplanets with mass and radius uncertainties below 10% and 5% respectively, including the well studied GJ 1214 b, GJ 486 b, and the TRAPPIST-1 planets. We discuss the inclusion of the fluid Love number $k_2$ as an additional (potential) observable, showing how it can significantly reduce the degeneracy of interior structures. Utilizing the fast predictions of ExoMDN, we show that measuring $k_2$ with an accuracy of 10% can constrain the thickness of core and mantle of an Earth analog to $\approx 13\%$ of the true values.

15 pages, 15 figures, accepted for publication in Astronomy & Astrophysics. The ExoMDN model is freely accessible at https://github.com/philippbaumeister/ExoMDN

References in corpus (20)

• Mass-Radius Relationships for Solid Exoplanets
• Growth Model Interpretation of Planet Size Distribution
• On the radiative equilibrium of irradiated planetary atmospheres
• Can we constrain interior structure of rocky exoplanets from mass and radius measurements?
• Detailed Models of super-Earths: How well can we infer bulk properties?
• A generalized bayesian inference method for constraining the interiors of super Earths and sub-Neptunes
• Constraints on Super-Earths Interiors from Stellar Abundances
• Bayesian analysis of interiors of HD 219134b, Kepler-10b, Kepler-93b, CoRoT-7b, 55 Cnc e, and HD 97658b using stellar abundance proxies
• ExoMiner: A Highly Accurate and Explainable Deep Learning Classifier that Validates 301 New Exoplanets
• The Compositional Diversity of Low-Mass Exoplanets
• Characterisation of the hydrospheres of TRAPPIST-1 planets
• Machine learning inference of the interior structure of low-mass exoplanets
• An estimate of the $k_2$ Love number of WASP-18Ab from its radial velocity measurements
• Realistic On-the-fly Outcomes of Planetary Collisions II: Bringing Machine Learning to N-body Simulations
• Detectability of shape deformation in short-period exoplanets
• Retrieval of the fluid Love number $k_2$ in exoplanetary transit curves
• MAGRATHEA: an open-source spherical symmetric planet interior structure code
• Empirical Structure Models of Uranus and Neptune
• Using Deep Neural Networks to compute the mass of forming planets
• Deep learning for surrogate modelling of 2D mantle convection

Cited by in corpus (18)

• GASTLI: An open-source coupled interior-atmosphere model to unveil gas giant composition
• Three super-Earths and a possible water world from TESS and ESPRESSO
• H${}_2$-H${}_2$O demixing in Uranus and Neptune: Adiabatic structure models
• NeuralCMS: A deep learning approach to study Jupiter's interior
• Flow Matching for Atmospheric Retrieval of Exoplanets: Where Reliability meets Adaptive Noise Levels
• Searching for Hot Water World Candidates with CHEOPS: Refining the radii and analysing the internal structures and atmospheric lifetimes of TOI-238 b and TOI-1685 b
• Retrieving interior properties of hot Jupiters with Love numbers and atmospheric measurements
• Exo-Geoscience Perspectives Beyond Habitability
• Tidally Heated Sub-Neptunes, Refined Planetary Compositions, and Confirmation of a Third Planet in the TOI-1266 System
• TOI-2458 b: A mini-Neptune consistent with in situ hot Jupiter formation
• TOI-2322: two transiting rocky planets close to the stellar rotation period and its first harmonic
• No Robust Statistical Evidence for a Population of Water Worlds in a 2025 Sample of Planets Orbiting M Stars
• The atmospheres of rocky exoplanets III. Using atmospheric spectra to constrain surface rock composition
• Exploring the habitability and interior composition of exoplanets lying within the extended habitable zone
• A transiting rocky super-Earth and a non-transiting sub-Neptune orbiting the M dwarf TOI-771
• Discovery of a transiting hot water-world candidate orbiting Ross 176 with TESS and CARMENES
• Sibling Sub-Neptunes Around Sibling M Dwarfs: TOI-521 and TOI-912
• Improved characterization of the TOI-2141 system: a dense sub-Neptune with non-transiting inner and outer companions