Exoplanet characterization using conditional invertible neural networks

¹ Department of Space Research & Planetary Sciences, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
e-mail: jonas.haldemann@unibe.ch
² Abteilung Physik, Gymnasium Lerbermatt, Kirchstrasse 64, 3098 Köniz, Switzerland
³ Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Straße 2, 69120 Heidelberg, Germany
e-mail: v.ksoll@uni-heidelberg.de
⁴ Universität Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
⁵ Computer Vision and Learning Lab (HCI, IWR), Universität Heidelberg Berliner Str. 43, 69120 Heidelberg, Germany

Received: 31 January 2022
Accepted: 20 February 2023

Abstract

Context. The characterization of the interior of an exoplanet is an inverse problem. The solution requires statistical methods such as Bayesian inference. Current methods employ Markov chain Monte Carlo (MCMC) sampling to infer the posterior probability of the planetary structure parameters for a given exoplanet. These methods are time-consuming because they require the evaluation of a planetary structure model ~10⁵ times.

Aims. To speed up the inference process when characterizing an exoplanet, we propose to use conditional invertible neural networks to calculate the posterior probability of the planetary structure parameters.

Methods. Conditional invertible neural networks (cINNs) are a special type of neural network that excels at solving inverse problems. We constructed a cINN following the framework for easily invertible architectures (FreIA). This neural network was then trained on a database of 5.6 × 10⁶ internal structure models to recover the inverse mapping between internal structure parameters and observable features (i.e., planetary mass, planetary radius, and elemental composition of the host star). We also show how observational uncertainties can be accounted for.

Results. The cINN method was compared to a commonly used Metropolis-Hastings MCMC. To do this, we repeated the characterization of the exoplanet K2-111 b, using both the MCMC method and the trained cINN. We show that the inferred posterior probability distributions of the internal structure parameters from both methods are very similar; the largest differences are seen in the exoplanet water content. Thus, cINNs are a possible alternative to the standard time-consuming sampling methods. cINNs allow infering the composition of an exoplanet that is orders of magnitude faster than what is possible using an MCMC method. The computation of a large database of internal structures to train the neural network is still required, however. Because this database is only computed once, we found that using an invertible neural network is more efficient than an MCMC when more than ten exoplanets are characterized using the same neural network.