Abstract. Machine learning represents a potential method to cope with the gray zone problem of representing motions in dynamical systems on scales comparable to the model resolution. Here we explore the possibility of using a neural network to directly learn the error caused by unresolved scales. We use a modified shallow water model which includes highly nonlinear processes mimicking atmospheric convection. To create the training dataset we run the model in a high and a low-resolution setup and compare the difference after one low resolution time step starting from the same initial conditions, thereby obtaining an exact target. The neural network is able to learn a large portion of the difference when evaluated offline on a validation set. When coupled to the low-resolution model, we find large forecast improvements up to one day on average. After this, the accumulated error due to the mass conservation violation of the neural network starts to dominate and deteriorates the forecast. This deterioration can effectively be delayed by adding a penalty term to the loss function used to train the ANN to conserve mass in a weak sense. This study reinforces the need to include physical constraints in neural network parameterizations.

中文翻译：

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使用神经网络改善灰色区域的仿真

摘要。机器学习是一种潜在的方法，可以解决在灰色系统中以与模型分辨率相当的比例来表示动态系统中的运动的问题。在这里，我们探索了使用神经网络直接学习由未解决尺度引起的误差的可能性。我们使用改良的浅水模型，其中包括模拟大气对流的高度非线性过程。为了创建训练数据集，我们以高分辨率和低分辨率设置运行模型，并比较从相同初始条件开始的一个低分辨率时间步长后的差异，从而获得精确的目标。当离线评估时，神经网络能够学习很大一部分差异在验证集上。当与低分辨率模型结合使用时，我们发现平均预报最多可以改善一天。此后，由于违反神经网络的质量守恒而引起的累积误差开始占主导地位，并使预测恶化。通过在损失函数上添加惩罚项以有效训练ANN以在较弱的意义上节省质量，可以有效地延迟这种恶化。这项研究强调了在神经网络参数化中包括物理约束的需求。