陆帅教授学术报告——Filter based methods for statistical linear inverse problems

作者:时间:2017-06-15浏览:509供图:审阅:来源:南京航空航天大学

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报告题目:Filter based methods for statistical linear inverse problems


报告人:陆帅,复旦大学教授

报告时间:2017年6月19日周一  11:00-12:00

报告地点:将军路校区理学院547报告厅


讲座内容:Ill-posed inverse problems are ubiquitous in applications. Understanding of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering methods have recently been used to solve inverse problems by introducing an artificial dynamical system. This opens up the possibility of using a range of other filtering methods, such as 3DVAR and Kalman based methods, to solve inverse problems, again by introducing an artificial dynamical system. The aim of this talk is to analyze such methods in the context of the ill-posed linear inverse problem.

    Statistical linear inverse problems are studied in the sense that the observational noise is assumed to be derived via realization of a Gaussian random variable. We investigate the asymptotic behavior of filter based methods for these statistical linear inverse problems. Rigorous convergence rates are established for 3DVAR and for the Kalman filters, including minimax rates in some instances. Blowup of 3DVAR and its variant form is also presented, and optimality of the Kalman filter is discussed. These analyses reveal close connection between (iterative) regularization schemes in deterministic inverse problems and filter based methods in data assimilation.  It is a joint work with Dr. M. A. Iglesias (U. of Nottingham, UK), Dr. K. Lin (Fudan U., China) and Prof. A. M. Stuart (Caltech, USA).  



报告人简介:陆帅,复旦大学数学科学学院教授。1997至2004就读于复旦大学数学系及数学研究所,获理学学士及硕士学位;2007年全优毕业于奥地利林茨大学,获数学博士学位。2007-2010年在奥地利科学院Radon计算及应用数学研究所从事博士后研究。2010年加入复旦大学数学科学学院,2015年晋升教授。主要研究方向为数学物理反问题,已合作出版英文专著一本,发表SCI论文30篇。其工作得到基金委优秀青年基金、德国洪堡基金以及上海市科委启明星计划等的资助,入选教育部青年长江及上海市教委曙光计划。