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 = r_cmb/r_surf), 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.

中文翻译：

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建立行星地幔热状态的统一模型：平均场深度学习的估计

陆地行星的冷却取决于将热量从内部传递到地面并随后散发到太空的机制。表面边界条件，几何形状，内部过程和瑞利数是影响冷却速率的最重要的控制参数。在这项研究中，我们采用机器学习算法来训练学习模型，这些模型根据其曲率（f =  r _cmb / r _surf）估算行星的热状态。），瑞利数和两个端部成员行星的内部加热-刚性和自由滑面行星。三维球形控制量模型用于生成训练样本。使用回归学习算法，我们证明了有监督的机器学习（SML）技术可以成功地预测简化模型行星的热状态（预测结果与计算结果），并且有可能将该方法扩展到将复杂度合并到实际行星中的实际行星。模型。预测模型可用于估算表面热通量和行星的平均温度。我们发现，与从具有多项式特征的简单机器学习模型获得的结果相比，深度学习模型提供的预测准确性更高。在深度学习模型中，对于未知数据的预测准确度接近平均地幔温度和平均表面热通量的99％。这样，深度学习技术可以用于更复杂的地幔问题中，其中存在更复杂且高度依赖压力和温度的过程。