深度神经网络在四维变分同化中的应用  

The Application of Deep Neural Networks in Four-Dimensional Variational Assimilation

作　　者：李景诗 LI Jing-shi(Department of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044

出　　处：《数学的实践与认识》2024年第11期246-256,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金青年基金(12201310);江苏省自然科学基金(BK20190766)。

摘　　要：四维变分同化是修正初值或模式误差的有力工具,研究如何高效求解四维变分同化中的最优控制问题对数值天气预报有着重要的意义.文章针对两类最优控制问题分别构造了模型驱动的损失函数,并采用深度神经网络方法学习得到最优控制.该方法不仅消除了数据导向的神经网络方法需要大量训练数据的弊端,且相比于经典方法,如差分法结合共轭梯度法等,文章方法易于实现,且无需求解伴随问题。数值实验部分以Burgers方程为例展示了算法的计算效果.Four-dimensional variational assimilation is a powerful tool for correcting initial values or model errors,and studying efficient solutions to the optimal control problems in four-dimensional variational assimilation is of significant importance for numerical weather forecasting.In this paper,a novel deep neural network is designed to learn the optimal control variables in four-dimensional variational assimilation for two types of optimal control problems.Our approach not only eliminates the drawback of existing neural network methods requiring extensive training data,but also compared to classical methods such as differential methods combined with conjugate gradient methods,is easy to implement and does not require solving adjoint problems.The numerical experiments,using the Burgers equation as an example,demonstrate the computational effectiveness of the algorithm.

关 键 词：四维变分同化 最优控制问题 深度神经网络 模式驱动 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程] O232[自动化与计算机技术—控制科学与工程]