数据与计算发展前沿 ›› 2026, Vol. 8 ›› Issue (5): 108-121.

CSTR: 32002.14.jfdc.CN10-1649/TP.2026.05.009

doi: 10.11871/jfdc.issn.2096-742X.2026.05.009

• 专刊：“东方”超级计算系统，助力青年科学家科技创新 • 上一篇    下一篇

基于对偶形式拟牛顿法的三维变分同化加速

张峰1,2(),姜金荣1,*(),刘娟娟3,李晨1,成巍4,迟学斌1,曹艺5,白成祖6,张硕6,汪子杰6   

  1. 1 中国科学院计算机网络信息中心， 北京 100083
    2 中国科学院大学， 北京 100049
    3 中国科学院大气物理研究所， 北京 100029
    4 北京应用气象研究所， 北京 100029
    5 天津工业大学， 天津 300387
    6 智能空间信息国家级重点实验室， 北京 100029
  • 收稿日期:2026-03-29 出版日期:2026-10-20 发布日期:2026-10-20
  • 通讯作者: *姜金荣（E-mail: jjr@sccas.cn）
  • 作者简介:张峰，中国科学院计算机网络信息中心，博士研究生，主要研究方向为GPU优化、数值天气预报和Krylov子空间方法。
    作者贡献：软件开发、架构设计、算法研究、可视化处理、论文撰写。
    ZHANG Feng is currently pursuing a Ph.D. at the Computer Network Information Center, Chinese Academy of Sciences. His research interests include GPU optimization, numerical weather forecasting, and Krylov subspace methods.
    In this paper, he is responsible for software development, architecture design, algorithm research, visualization, and paper writing. E-mail: zhangfeng@cnic.cn|姜金荣，中国科学院计算机网络信息中心，研究员，主要研究方向为高性能计算、并行算法及人工智能气候模型。
    作者贡献：论文审阅（把握项目整体研发方向）。
    JIANG Jinrong is a Professor at the Computer Network In-formation Center, Chinese Academy of Sciences. His research interests include high-performance computing, parallel algorithms, and AI climate models.
    In this paper, he is responsible for reviewing the paper and guiding the overall R&D direction of the project. E-mail: jjr@sccas.cn
  • 基金资助:
    国家重点研发计划(2022YFE0195900);北京市怀柔科学城成果落地项目(Z231100006623004);中国科学院计算机网络信息中心所青年基金(25YF07)

Accelerating 3D-Var Data Assimilation with a Dual-Form Quasi-Newton Method

ZHANG Feng1,2(),JIANG Jinrong1,*(),LIU Juanjuan3,LI Chen1,CHENG Wei4,CHI Xuebin1,CAO Yi5,BAI Chengzu6,ZHANG Shuo6,WANG Zijie6   

  1. 1 Computer Network Information Center, Chinese Academy of Sciences, Beijing 100083, China
    2 University of Chinese Academy of Sciences, Beijing 100049, China
    3 Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
    4 Beijing Institute of Applied Meteorology, Beijing 100029, China
    5 Tiangong University, Tianjin 300387, China
    6 National key laboratory of intelligent spatial information processing, Beijing 100029, China
  • Received:2026-03-29 Online:2026-10-20 Published:2026-10-20

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摘要：

【目的】 三维变分数据同化是数值天气预报中的关键技术。传统原始形式方法需要在高维控制空间中求解，计算开销较大；而对偶形式在观测空间中优化，理论上具有降维增效优势，但在现有 GSI 架构下的实际部署中，仍需处理遗留算子链的深度耦合、数值稳定性以及离散伴随一致性退化等工程问题。【方法】 本文提出一种基于统一控制变量变换的对偶形式拟牛顿框架，通过将优化变量转至观测空间显著降低求解维度，并以低侵入方式复用既有算子链实现工程部署。【结果与局限】在单个区域三维变分配置中的实验表明，本文对偶求解器在保持与原始形式拟牛顿求解器（lsqrt-qn）相近收敛行为的同时，实现了5.1倍整体加速，其中L-BFGS曲率历史递归模块加速达2,600倍。与当前业务配置下性能最优的求解器LS-PCG相比，该对偶求解器仍可实现约1.9倍加速，而代价函数降幅差异不足1%。不过，当前对偶形式拟牛顿求解器在更广泛算例和不同参数设置下的性能表现仍需进一步评估。【结论】 结果表明，对偶形式可以在保持分析质量的同时，以低侵入方式集成到业务 GSI 系统中并显著提升计算效率。这为现有业务系统中引入对偶降维求解提供了一条具有工程可行性的实现路径。

关键词: 三维变分同化, 格点统计插值系统, 对偶形式拟牛顿法, 统一控制变量变换, 低侵入式集成

Abstract:

[Objective] Three-dimensional variational data assimilation is a core technique in numerical weather prediction. Traditional primal-form methods optimize in a high-dimensional control space and are therefore computationally expensive. Although the dual-form reduces the optimization dimension by solving in observation space, deploying it within the current GSI architecture still requires handling deep coupling in the legacy operator chain, numerical stability issues, and degraded discrete adjoint consistency. [Methods] This paper proposes a dual-form quasi-Newton framework based on the Unified Control Variable Transform, which reduces the optimization dimension by solving in observation space and achieves engineering deployment by reusing existing operator chains in a low-intrusive manner. [Results and Limitations] In a single regional 3D-Var configuration, the proposed dual-form solver achieves convergence behavior comparable to that of the primal-form quasi-Newton solver (lsqrt-qn) while delivering an overall 5.1× speedup; the L-BFGS curvature-history recursion is accelerated by 2600×. Relative to LS-PCG, the best-performing solver in the current operational configuration, the proposed solver is about 1.9× faster, with less than a 1% difference in cost-function reduction. However, its performance across a broader range of cases and different parameter settings still requires further evaluation. [Conclusions] These results show that the dual reduced-dimensional solver can be introduced into existing operational systems in a low-intrusive manner while preserving analysis quality and improving computational efficiency. This provides an engineering-feasible implementation for introducing dual reduced-dimensional solvers into existing operational systems.

Key words: 3D-Var, GSI, dual-form quasi-Newton method, unified control variable transform, low-intrusive integration