广州数学大讲坛第三期

第二十一讲——东南大学刘继军教授学术报告

题目：Large Variational Data Assimilation for Initial Potential Vorticity in a Two-Layer Quasi-Geostrophic Model

时间：2026年3月29日（星期日）下午15:30-16:30

地点：理学实验楼312

报告人：刘继军 教授

摘要：We study a variational data assimilation approach for recovering the initial potential vorticity arising in a two-layer quasi-geostrophic model from partial and noisy observations of the stream functions specified in an internal submain. Based on the well-posedness of the forward problem and the unique continuation property of the solution, the unique recovery of the initial state is established based on the Carlemann estimate. By reformulating this inverse problem as a PDE-constrained optimization problem, with a misfit functional defined on the observation subdomain and time window, a two-point gradient iteration with a discrepancy principle stopping rule is employed for stable numerical reconstruction. Numerical experiments with manufactured solutions demonstrate that our proposed method is robust under noisy data and that the reconstruction accuracy improves significantly as the size of the spatial observation domain increases.

报告人简介：

刘继军，东南大学二级教授，博士生导师，享受国务院政府特殊津贴专家。现任南京应用数学中心副主任，全国大学生数学建模竞赛组委会委员，中国工业与应用数学学会数学建模竞赛专业委员会委员，江苏省计算数学学会副理事长。国家精品资源共享课《数学建模与数学实验》主持人。长期从事数学物理反问题、大规模科学计算和介质成像的数学理论和方法的研究。主持完成国家自然科学基金重大研究计划培育项目、面上项目、国际合作项目等项目。已在SIAM J. Appl. Math， IP等刊物发表学术论文140余篇，在科学出版社出版学术专著2本。2012-2017年任Inverse Problems in Sciences and Engineering编委，2018年起任J. Inverse and Ill-posed Problems编委。作为主持人获江苏省教学成果一等奖、江苏省自然科学三等奖、教育部自然科学二等奖。