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. For this study, we specifically examined the coupling between chemistry and radiation in GCMs and compared different methods for the mixing of 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 evaluated the DS method alongside other published methods such as adaptive equivalent extinction (AEE) and random overlap with rebinning and resorting (RORR). We integrated these mixing methods into our GCM (expeRT/MITgcm) and assessed 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 observed that the accuracy of AEE depends on its specific implementation and may introduce numerical issues in achieving radiative transfer solution convergence. We then applied the DS mixing method in a simplified chemical disequilibrium situation, where we modeled the rainout of TiO and VO, and confirmed 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：为了理解系外行星和褐矮星的高精度观测，我们需要包含流体动力学、化学和辐射过程的详尽而复杂的通用环流模型（GCM）。在本研究中，我们重点考察了GCM中化学与辐射的耦合机制，并比较了在无法假设化学平衡时，相关-k方法框架下不同化学物种不透明度混合方法的差异。我们提出了一种基于深度集合（DeepSets, DS）的快速机器学习方法，该方法能有效组合独立的相关系数不透明度（k表格）。我们评估了DS方法及其他已发表方法（如自适应等效消光AEE和重采样重排序随机重叠RORR），并将这些混合方法集成到我们的GCM（expeRT/MITgcm）中，以热木星HD~209458 b为例分析其精度与性能。结果表明：DS方法兼具高精度与高效率，适用于GCM，而RORR方法计算速度过慢。此外，我们发现AEE方法的精度依赖于具体实现方式，并可能在辐射传输解收敛过程中引入数值问题。我们在简化的化学非平衡场景中应用DS混合方法，模拟了TiO和VO的雨除效应，证实其会阻碍平流层的形成。为进一步推进GCM中非平衡化学自洽计算的开发，我们提供了耦合DS方法与相关-k辐射传输求解器的文档和代码。DS方法经过充分测试，其精度足以满足GCM需求；但加速大气反演可能需要其他方法。