A competitive baseline for deep learning enhanced data assimilation using conditional Gaussian ensemble Kalman filtering

IF 6.9 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Zachariah Malik , Romit Maulik
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引用次数: 0

Abstract

Ensemble Kalman Filtering (EnKF) is a popular technique for data assimilation, with far ranging applications. However, the vanilla EnKF framework is not well-defined when perturbations are nonlinear. We study two non-linear extensions of the vanilla EnKF – dubbed the conditional-Gaussian EnKF (CG-EnKF) and the normal score EnKF (NS-EnKF) – which sidestep assumptions of linearity by constructing the Kalman gain matrix with the ‘conditional Gaussian’ update formula in place of the traditional one. We then compare these models against a state-of-the-art deep learning based particle filter called the score filter (SF). This model uses an expensive score diffusion model for estimating densities and also requires a strong assumption on the perturbation operator for validity. In our comparison, we find that CG-EnKF and NS-EnKF dramatically outperform SF for two canonical systems in data assimilation: the Lorenz-96 system and a double well potential system. Our analysis also demonstrates that the CG-EnKF and NS-EnKF can handle highly non-Gaussian additive noise perturbations, with the latter typically outperforming the former.
基于条件高斯集合卡尔曼滤波的深度学习竞争基线增强数据同化
集成卡尔曼滤波(EnKF)是一种流行的数据同化技术,有着广泛的应用。然而,当扰动是非线性的时候,普通的EnKF框架不是很好定义的。我们研究了普通EnKF的两种非线性扩展——条件高斯EnKF (CG-EnKF)和正态分数EnKF (NS-EnKF)——它们通过用“条件高斯”更新公式代替传统公式构建卡尔曼增益矩阵来回避线性假设。然后,我们将这些模型与最先进的基于深度学习的粒子过滤器(称为分数过滤器(SF))进行比较。该模型使用昂贵的分数扩散模型来估计密度,并且还需要对扰动算子进行强假设以保证有效性。在我们的比较中,我们发现CG-EnKF和NS-EnKF在两个典型系统(Lorenz-96系统和双阱势系统)的数据同化中显著优于SF。我们的分析还表明,CG-EnKF和NS-EnKF可以处理高度非高斯加性噪声扰动,后者通常优于前者。
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来源期刊
CiteScore
12.70
自引率
15.30%
发文量
719
审稿时长
44 days
期刊介绍: Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.
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