  The characterization of an exoplanet's interior is an inverse problem, which
requires statistical methods such as Bayesian inference in order to be solved.
Current methods employ Markov Chain Monte Carlo (MCMC) sampling to infer the
posterior probability of planetary structure parameters for a given exoplanet.
These methods are time consuming since they require the calculation of a large
number of planetary structure models. To speed up the inference process when
characterizing an exoplanet, we propose to use conditional invertible neural
networks (cINNs) to calculate the posterior probability of the internal
structure parameters. cINNs are a special type of neural network which excel in
solving inverse problems. We constructed a cINN using FrEIA, which was then
trained on a database of $5.6\cdot 10^6$ internal structure models to recover
the inverse mapping between internal structure parameters and observable
features (i.e., planetary mass, planetary radius and composition of the host
star). The cINN method was compared to a Metropolis-Hastings MCMC. For that 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 of
the internal structure parameters from both methods are very similar, with the
biggest differences seen in the exoplanet's water content. Thus cINNs are a
possible alternative to the standard time-consuming sampling methods. Indeed,
using cINNs allows for orders of magnitude faster inference of an exoplanet's
composition than what is possible using an MCMC method, however, it still
requires the computation of a large database of internal structures to train
the cINN. Since this database is only computed once, we found that using a cINN
is more efficient than an MCMC, when more than 10 exoplanets are characterized
using the same cINN.
