| Summary: | Abstract The cooling of terrestrial planets depends upon the mechanism whereby heat is transferred from the interior to the surface and thereafter is radiated to the space. The surface boundary condition, geometry, internal processes, and the Rayleigh number are the most important controlling parameter influencing the rate of cooling. In this study we employ machine learning algorithms to train learning models that estimate the thermal state of the planets based on their curvature (f = rcmb/rsurf), Rayleigh number, and internal heating for two end member planets—rigid and free‐slip surface planets. Three‐dimension‐spherical control volume models are used to generate training samples. Employing regression learning algorithms, we show that supervised machine learning (SML) techniques can successfully predict the thermal state of the simplified model planets (predicted results versus calculated) with the possibility of extending the method to the actual planets where the complexities are incorporated into the model. The predictive models can be used in estimation of the surface heat flux and the planets' mean temperature. We find that deep learned models provide higher prediction accuracies than those obtained from simple machine leaning models with polynomialized features. The prediction accuracies in deep learned models for the unseen data approached 99% for both mean mantle temperature and mean surface heat flux. As such, deep learning techniques can be employed in more complex mantle problems in which more complex and highly pressure and temperature dependent processes are present.
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