讲座主题：A novel spatial correlation regularized score filter for high-dimensional data assimilation under sparse observations

专家姓名：关晓飞

工作单位：同济大学

讲座时间：2026年10月21日 14:00-15:00

讲座地点：腾讯会议：507-223-666

主办单位：烟台大学数学与信息科学学院

内容摘要：

Data assimilation (DA) has become an essential tool for combining physical models with observational data to achieve accurate modeling and state estimation of complex dynamicalsystems. However, classical variational and Bayesian filtering methods often struggle with tackling high-dimensional and nonlinear assimilation problems. While the recently emerged ensemble score filter (EnSF) has demonstrated prominent potential to overcome these problems, its performance degrades significantly under sparse observation conditions, which are ubiquitous in many real-world DA scenarios. In the paper, we propose a novel spatial correlation regularized score filter (SC-RSF) for high-dimensional data assimilation under sparse observations, which incorporates an observation-informed regularization guidance to augment the posterior score function of EnSF model. By exploiting spatial correlations between observed and unobserved state components, this guidance enables effective information propagation from observational data to unobserved locations. Notably, SC-RSF achieves reliable global state estimation and efficient sampling from high-dimensional posterior distributions without requiring post-processing or outer-loop iterations. The accuracy and robustness of SC-RSF are validated across two high-dimensional benchmarks, including a Kolmogorov turbulent flow and a real-world ERA5 global atmospheric task.

主讲人介绍：

关晓飞，同济大学数学科学学院教授/博导，中国工业与应用数学学会不确定量化专委会常务委员，主要从事大数据和人工智能、多物理场多尺度建模与不确定性量化、优化决策和高性能并行计算等方面研究，主持和参于十多项国家级与省部级科研项目，并在SIAM J. Sci. Comput., J. Comput. Phy., J. Sci. Comput., Commun. Comput. Phy., Comput. Method Appl. M.等计算数学权威期刊及Mach. learn.: sci. technol, Eng. Appl. Artif. Intell.等人工智能权威期刊上发表50余篇SCI论文。