Computing the internal structure of transiting planets is intrinsically a strongly degenerate problem, as there are many planetary compositions that can match a given observed density. The interpretation is traditionally done using a Bayesian analysis, to derive the posterior distribution of planetary main internal structure parameters (e.g. core mass, amount of water). Such Bayesian analysis frequently relies on Markov-Chain-Monte-Carlo or similar methods, which are numerically demanding and sometimes fail to provide the whole posterior distribution (in particular when it has multiple local maxima).
In this study, in collaboration with colleagues from the University of Heidelberg, we applied for the first time the Invertible Neural Network technique to the analysis of transiting planets observations. INN a type of neural network architecture that is able to provide the posterior distribution of planetary structure parameters for any given choice of observed parameters. cINN are INN conditioned on observed parameters which learn how to map the posterior distribution of planetary internal parameters to a gaussian distribution, conditional on planetary observed parameters.
In this paper we demonstrate how INN and cINN compare to traditional MCMC method on test data and for the planet K2-111b.
A cINN learns to encode all information about the physical parameters x in the latent variables z (while enforcing that these follow a Gaussian distribution) that is not contained in the observations y. At prediction time, conditioned on the new observation y, the cINN transforms the known prior distribution p(z) to x-space to retrieve the posterior distribution p(x|y).
Adapted from Haldemann et al., (2023), Astronomy & Astrophysics; A&A 672, A180. doi:10.1051/0004-6361/202243230.
Comparison of the cINN and an MCMC method for a toy model. The data in the lower triangle of each subfigure (black points) was generated with the cINN method, while the data in the upper triangle (blue points) was generated with the MCMC sampler. Adapted from Haldemann et al., (2023), Astronomy & Astrophysics; A&A 672, A180.
doi:10.1051/0004-6361/202243230.