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To understand high precision observations of exoplanets and brown dwarfs, weneed detailed and complex general circulation models (GCMs) that incorporatehydrodynamics, chemistry, and radiation. For this study, we specificallyexamined the coupling between chemistry and radiation in GCMs and compareddifferent methods for the mixing of opacities of different chemical species inthe correlated-k assumption, when equilibrium chemistry cannot be assumed. Wepropose a fast machine learning method based on DeepSets (DS), whicheffectively combines individual correlated-k opacities (k-tables). We evaluatedthe DS method alongside other published methods such as adaptive equivalentextinction (AEE) and random overlap with rebinning and resorting (RORR). Weintegrated these mixing methods into our GCM (expeRT/MITgcm) and assessed theiraccuracy and performance for the example of the hot Jupiter HD~209458 b. Ourfindings indicate that the DS method is both accurate and efficient for GCMusage, whereas RORR is too slow. Additionally, we observed that the accuracy ofAEE depends on its specific implementation and may introduce numerical issuesin achieving radiative transfer solution convergence. We then applied the DSmixing method in a simplified chemical disequilibrium situation, where wemodeled the rainout of TiO and VO, and confirmed that the rainout of TiO and VOwould hinder the formation of a stratosphere. To further expedite thedevelopment of consistent disequilibrium chemistry calculations in GCMs, weprovide documentation and code for coupling the DS mixing method withcorrelated-k radiative transfer solvers. The DS method has been extensivelytested to be accurate enough for GCMs; however, other methods might be neededfor accelerating atmospheric retrievals.

Harnessing machine learning for accurate treatment of overlapping opacity species in general circulation models