Deep Data Assimilation: Integrating Deep Learning with Data Assimilation
Deep Data Assimilation: Integrating Deep Learning with Data Assimilation
复制标题
深度数据同化：深度学习与数据同化的结合
DOI：
10.3390/app11031114
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Yike Guo
中科院分区：
文献类型：
--
作者：
Rossella Arcucci;Jiangcheng Zhu;Shuang Hu;Yike Guo
在本文中，我们提出了深度数据同化（DDA），这是数据同化（DA）与机器学习（ML）的集成。DA是将时间分布观测与动态模型以最优方式相结合，对某一物理系统在给定时间的真实状态的贝叶斯近似。我们使用ML模型来学习同化过程。特别地，一个循环神经网络，训练与动力系统的状态和数据处理的结果，用于此目的。在每次迭代中，我们学习一个函数，该函数累积预测模型结果与数据分析结果之间的不拟合。随后，我们将该函数与动态模型组合在一起。由此产生的组合是一个动态模型，它包含了数据分析过程的特征，可以用于未来预测，而不需要数据分析。事实上，我们证明了DDA方法意味着模型误差的减小，在每次迭代中减小；这是由于在训练过程中使用了数据处理。在某些时间步长无法获得观测值且不能应用DA来减小模型误差的情况下，DDA非常有用。通过算例和灵敏度研究验证了该方法的有效性。本文将DDA技术应用于两种不同的应用：二重积分质量点系统和洛伦兹系统。然而，在这项工作中提出的算法和数值方法可以应用于涉及其他方程和/或状态变量的其他物理问题。
In this paper, we propose Deep Data Assimilation (DDA), an integration of Data Assimilation (DA) with Machine Learning (ML). DA is the Bayesian approximation of the true state of some physical system at a given time by combining time-distributed observations with a dynamic model in an optimal way. We use a ML model in order to learn the assimilation process. In particular, a recurrent neural network, trained with the state of the dynamical system and the results of the DA process, is applied for this purpose. At each iteration, we learn a function that accumulates the misfit between the results of the forecasting model and the results of the DA. Subsequently, we compose this function with the dynamic model. This resulting composition is a dynamic model that includes the features of the DA process and that can be used for future prediction without the necessity of the DA. In fact, we prove that the DDA approach implies a reduction of the model error, which decreases at each iteration; this is achieved thanks to the use of DA in the training process. DDA is very useful in that cases when observations are not available for some time steps and DA cannot be applied to reduce the model error. The effectiveness of this method is validated by examples and a sensitivity study. In this paper, the DDA technology is applied to two different applications: the Double integral mass dot system and the Lorenz system. However, the algorithm and numerical methods that are proposed in this work can be applied to other physics problems that involve other equations and/or state variables.