ExoMDN: Rapid characterization of exoplanet interior structures with mixture density networks

Abstract

Aims. 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. Methods. 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. Results. 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 used ExoMDN to characterize the interiors 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 k2 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 k2 with an accuracy of 10% can constrain the thickness of core and mantle of an Earth analog to ≈13% of the true values.

The PLATO Mission

“…Valencia et al 2007). Recent studies with more advanced interior models, allowing for additional phases and internal layers in the interior, confirmed these requirements on radius and mass precision when constraining the planets interior structure (Otegi et al, 2020;Dorn and Lichtenberg, 2021;Baumeister and Tosi, 2023).…”

“…The planetary bulk composition and evolving interior structure are also important for assessing the possible evolutionary pathways of such planets (especially for low-mass, rocky planets) and their surface processes. Studies focusing on Earth-like compositions have already shown that key processes such as plate tectonics, volcanic activity or magnetic field generation (all directly linked also to the atmospheric evolution) strongly depend on planetary mass, metallic core size and surface temperature (Wagner et al, 2011(Wagner et al, , 2012Valencia et al, 2007;Kite et al, 2009;Ortenzi et al, 2020;Dorn et al, 2018;Bonati et al, 2021;Kislyakova and Noack, 2020;Baumeister and Tosi, 2023). The atmospheric evolution is further influenced by the orbital distance of the planets, another observable of PLATO, leading to a bifurcation in atmospheric evolution (Hamano et al, 2013) and erosion efficiency (Godolt et al, 2019;Moore and Cowan, 2020), which can furthermore influence the measured planetary radius.…”

“…atmospheres as discussed already above. However, there are also additional observables from PLATO data alone, such as the fluid Love number for giant planets near the Roche limit (Correia, 2014;Kellermann et al, 2018;Padovan et al, 2018;Akinsanmi et al, 2019;Csizmadia et al, 2019;Hellard et al, 2019Hellard et al, , 2020Baumeister and Tosi, 2023), stellar parameters (e.g. heavy element content, activity), and especially age (e.g.…”

Comparison of Machine-learning and Bayesian Inferences for the Interior of Rocky Exoplanets with Large Compositional Diversity

“…We then feed each of them through the well-trained MDN model, yielding the predicted probability distributions of the output variables. Recently it has been suggested by Baumeister & Tosi (2023) that resampling from the predicted distributions and then merging these samples can reduce memory usage and improve computational efficiency. In this work, we experimented with this approach and found it to be markedly less demanding on memory and processing resources.…”

“…Based on this, Zhao & Ni (2021 expanded the MDN framework to simultaneously predict layer thicknesses and core properties for a wide range of planets, including Earth-like planets and gas giants. Baumeister & Tosi (2023) developed an ML model, ExoMDN, for predicting the thickness of various layers and mass distributions, based on observed parameters such as mass, radius, equilibrium temperature, and tidal Love number k 2 . The evolution of ML applications in planetary science highlights its potential to accelerate our understanding of the interiors of exoplanets.…”