The use of machine learning based on neural networks for cloud microphysical parameterizations is investigated. As an example, we use the warm‐rain formation by collision‐coalescence, that is, the parameterization of autoconversion, accretion, and self‐collection of droplets in a two‐moment framework. Benchmark solutions of the kinetic collection equations are performed using a Monte Carlo superdroplet algorithm. The superdroplet method provides reliable but noisy estimates of the warm‐rain process rates. For each process rate, a neural network is trained using standard machine learning techniques. The resulting models make skillful predictions for the process rates when compared to the testing data. However, when solving the ordinary differential equations, the solutions are not as good as those of an established warm‐rain parameterization. This deficiency can be seen as a limitation of the machine learning methods that are applied, but at the same time, it points toward a fundamental ill‐posedness of the commonly used two‐moment warm‐rain schemes. More advanced machine learning methods that include a notion of time derivatives, therefore, have the potential to overcome these problems.

中文翻译：

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机器学习对暖雨云微物理过程建模的潜力和局限性

研究了基于神经网络的机器学习对云微物理参数化的使用。例如，我们使用通过碰撞聚结的温雨形成，即在两个矩的框架中对液滴的自动转换，吸积和自收集进行参数化。使用蒙特卡洛超液滴算法执行动力学收集方程的基准解。超级液滴法可提供可靠但嘈杂的暖雨过程速率估计。对于每个处理速率，都使用标准的机器学习技术来训练神经网络。与测试数据相比，生成的模型可以熟练地预测过程速率。但是，当求解常微分方程时，其解决方案不如已建立的暖雨参数化解决方案。这种缺陷可以看作是所应用的机器学习方法的局限性，但同时，它也指出了常用的两时温雨方案的基本不适。因此，包含时间导数概念的更高级的机器学习方法有可能克服这些问题。