Tensor-Var: Efficient Four-Dimensional Variational Data Assimilation

• URL: http://arxiv.org/abs/2501.13312v3
• Date: Fri, 13 Jun 2025 00:46:38 GMT
• Title: Tensor-Var: Efficient Four-Dimensional Variational Data Assimilation
• Authors: Yiming Yang, Xiaoyuan Cheng, Daniel Giles, Sibo Cheng, Yi He, Xiao Xue, Boli Chen, Yukun Hu,
• Abstract summary: Four-dimensional variational assimilation (4D-Var) faces high computational costs in complex nonlinear systems and depends on imperfect state-observation mappings.<n>Deep learning (DL) offers more expressive approximators, while integrating DL models into 4D-Var is challenging due to their nonlinearities and lack of theoretical guarantees in assimilation results.<n>We propose a novel framework that integrates kernel conditional mean embedding (CME) with 4D-Var to linearize nonlinear dynamics, achieving convex optimization in a learned feature space.
• Score: 30.63086465547801
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Variational data assimilation estimates the dynamical system states by minimizing a cost function that fits the numerical models with the observational data. Although four-dimensional variational assimilation (4D-Var) is widely used, it faces high computational costs in complex nonlinear systems and depends on imperfect state-observation mappings. Deep learning (DL) offers more expressive approximators, while integrating DL models into 4D-Var is challenging due to their nonlinearities and lack of theoretical guarantees in assimilation results. In this paper, we propose Tensor-Var, a novel framework that integrates kernel conditional mean embedding (CME) with 4D-Var to linearize nonlinear dynamics, achieving convex optimization in a learned feature space. Moreover, our method provides a new perspective for solving 4D-Var in a linear way, offering theoretical guarantees of consistent assimilation results between the original and feature spaces. To handle large-scale problems, we propose a method to learn deep features using neural networks within the Tensor-Var framework. Experiments on chaotic systems and global weather prediction with real-time observations show that Tensor-Var outperforms conventional and DL hybrid 4D-Var baselines in accuracy while achieving a 10- to 20-fold speed improvement.

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