Analytical Modelling of Exoplanet Transit Specroscopy with Dimensional Analysis and Symbolic Regression

The physical characteristics and atmospheric chemical composition of newly discovered exoplanets are often inferred from their transit spectra which are obtained from complex numerical models of radiative transfer. Alternatively, simple analytical expressions provide insightful physical intuition into the relevant atmospheric processes. The deep learning revolution has opened the door for deriving such analytical results directly with a computer algorithm fitting to the data. As a proof of concept, we successfully demonstrate the use of symbolic regression on synthetic data for the transit radii of generic hot Jupiter exoplanets to derive a corresponding analytical formula. As a preprocessing step, we use dimensional analysis to identify the relevant dimensionless combinations of variables and reduce the number of independent inputs, which improves the performance of the symbolic regression. The dimensional analysis also allowed us to mathematically derive and properly parametrize the most general family of degeneracies among the input atmospheric parameters which affect the characterization of an exoplanet atmosphere through transit spectroscopy.