To understand high precision observations of exoplanets and brown dwarfs, we need detailed and complex general circulation models (GCMs) that incorporate hydrodynamics, chemistry, and radiation. In this study, we specifically examine the coupling between chemistry and radiation in GCMs and compare different methods for mixing opacities of different chemical species in the correlated-k assumption, when equilibrium chemistry cannot be assumed. We propose a fast machine learning method based on DeepSets (DS), which effectively combines individual correlated-k opacities (k-tables). We evaluate the DS method alongside other published methods like adaptive equivalent extinction (AEE) and random overlap with rebinning and resorting (RORR). We integrate these mixing methods into our GCM (expeRT/MITgcm) and assess their accuracy and performance for the example of the hot Jupiter HD~209458 b. Our findings indicate that the DS method is both accurate and efficient for GCM usage, whereas RORR is too slow. Additionally, we observe that the accuracy of AEE depends on its specific implementation and may introduce numerical issues in achieving radiative transfer solution convergence. We then apply the DS mixing method in a simplified chemical disequilibrium situation, where we model the rainout of TiO and VO, and confirm that the rainout of TiO and VO would hinder the formation of a stratosphere. To further expedite the development of consistent disequilibrium chemistry calculations in GCMs, we provide documentation and code for coupling the DS mixing method with correlated-k radiative transfer solvers. The DS method has been extensively tested to be accurate enough for GCMs, however, other methods might be needed for accelerating atmospheric retrievals.

翻译：为理解系外行星和褐矮星的高精度观测结果，我们需要包含流体动力学、化学和辐射过程的详细且复杂的全球环流模型（GCMs）。本研究重点关注GCMs中化学与辐射的耦合过程，并比较了在无法假定平衡化学时，利用相关k假设混合不同化学物种不透明度的方法。我们提出了一种基于DeepSets（DS）的快速机器学习方法，该方法能有效组合单个相关k不透明度（k表）。我们将DS方法与已发表的其他方法（如自适应等效消光（AEE）和重分箱降序随机重叠（RORR））进行了比较。通过将这些混合方法集成到我们的GCM模型（expeRT/MITgcm）中，并以热木星HD 209458 b为例评估其精度与性能。结果表明，DS方法兼具准确性与高效性，适用于GCMs，而RORR方法过于缓慢。此外，我们发现AEE方法的精度依赖于其具体实现方式，并可能在辐射传输解收敛过程中引入数值问题。随后，我们在简化的化学非平衡情景中应用DS混合方法，模拟了TiO和VO的雨出效应，证实TiO和VO的雨出会抑制平流层的形成。为进一步加速GCMs中非平衡化学计算的一致性发展，我们提供了DS混合方法与相关k辐射传输求解器耦合的文档与代码。DS方法经过广泛测试，其精度足以满足GCMs需求，但加速大气反演可能需要其他方法。