Data assimilation is a central problem in many geophysical applications, such as weather forecasting. It aims to estimate the state of a potentially large system, such as the atmosphere, from sparse observations, supplemented by prior physical knowledge. The size of the systems involved and the complexity of the underlying physical equations make it a challenging task from a computational point of view. Neural networks represent a promising method of emulating the physics at low cost, and therefore have the potential to considerably improve and accelerate data assimilation. In this work, we introduce a deep learning approach where the physical system is modeled as a sequence of coarse-to-fine Gaussian prior distributions parametrized by a neural network. This allows us to define an assimilation operator, which is trained in an end-to-end fashion to minimize the reconstruction error on a dataset with different observation processes. We illustrate our approach on chaotic dynamical physical systems with sparse observations, and compare it to traditional variational data assimilation methods.

翻译：数据同化是许多地球物理应用（如天气预报）中的核心问题，其目标是通过稀疏观测数据并结合先验物理知识，估计潜在大型系统（如大气）的状态。所涉及系统的规模以及底层物理方程的复杂性，从计算角度来看使其成为一项具有挑战性的任务。神经网络代表了一种有前景的低成本物理模拟方法，因此具有显著改进和加速数据同化的潜力。在本工作中，我们提出了一种深度学习方法，其中物理系统被建模为由神经网络参数化的一系列从粗到细的高斯先验分布序列。这使得我们能够定义一个同化算子，并以端到端的方式对其进行训练，以最小化在不同观测过程数据集上的重构误差。我们在具有稀疏观测的混沌动力物理系统上验证了所提方法，并将其与传统变分数据同化方法进行了比较。