We propose a novel learning-based surrogate data assimilation (DA) model for efficient state estimation in a limited area. Our model employs a feedforward neural network for online computation, eliminating the need for integrating high-dimensional limited-area models. This approach offers significant computational advantages over traditional DA algorithms. Furthermore, our method avoids the requirement of lateral boundary conditions for the limited-area model in both online and offline computations. The design of our surrogate DA model is built upon a robust theoretical framework that leverages two fundamental concepts: observability and effective region. The concept of observability enables us to quantitatively determine the optimal amount of observation data necessary for accurate DA. Meanwhile, the concept of effective region substantially reduces the computational burden associated with computing observability and generating training data.

翻译：我们提出了一种基于学习的替代数据同化模型，用于实现有限区域内的高效状态估计。该模型采用前馈神经网络进行在线计算，无需对高维有限区域模型进行积分。与传统数据同化算法相比，本方法具有显著的计算优势。此外，在在线和离线计算中，本方法均回避了有限区域模型所需侧边界条件的约束。该替代数据同化模型的设计建立在稳健的理论框架之上，该框架利用了可观测性和有效区域这两个核心概念。可观测性概念使我们能够定量确定实现精准数据同化所需的最优观测数据量；同时，有效区域概念则显著降低了计算可观测性及生成训练数据时的计算负荷。