Machine learning techniques in studies of the interior structure of rocky exoplanets

Abstract

Context. Earth-sized exoplanets have been discovered and characterized thanks to new developments in observational techniques, particularly those planets that may have a rocky composition that is comparable to terrestrial planets of the Solar System. Characterizing the interiors of rocky exoplanets is one of the main objectives in investigations of their habitability. Theoretical mass-radius relations are often used as a tool to constrain the internal structure of rocky exoplanets. But one mass-radius curve only represents a single interior structure and a great deal of computation time is required to obtain all possible interior structures that comply with the given mass and radius of a planet. Aims. We apply a machine-learning approach based on mixture density networks (MDNs) to investigate the interiors of rocky exoplanets. We aim to provide a well-trained MDN model to quickly and efficiently predict the interior structure of rocky exoplanets. Methods. We presented a training data set of rocky exoplanets with masses between 0.1 and 10 Earth masses based on three-layer interior models by assuming Earth-like compositions. This data set was then used to train the MDN model to predict the layer thicknesses and core properties of rocky exoplanets, where planetary mass, radius, and water content are inputs to the MDN. The performance of the trained MDN model was investigated in order to discern its predictive ability. Results. The MDN model is found to show good performance in predicting the layer thicknesses and core properties of rocky exoplanets through a comparison with the real solutions obtained by solving the interior models. We also applied the MDN model to the Earth and the super-Earth exoplanet LHS 1140b. The MDN predictions are in good agreement with the interior model solutions within the uncertainties of planetary mass and radius. More importantly, the MDN model takes a much shorter computational time compared to the cost of the interior model calculations, offering a convenient and powerful tool for quickly obtaining information on planetary interiors.