報告題目：Filter based methods for statistical linear inverse problems

報告人：陸帥，復旦大學教授

報告時間：2017年6月19日周一  11：00-12：00

報告地點：將軍路校區理學院547報告廳

講座內容：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).  

報告人簡介：陸帥，復旦大學數學科學學院教授。1997至2004就讀于復旦大學數學系及數學研究所，獲理學學士及碩士學位；2007年全優畢業于奧地利林茨大學，獲數學博士學位。2007-2010年在奧地利科學院Radon計算及應用數學研究所從事博士后研究。2010年加入復旦大學數學科學學院，2015年晉升教授。主要研究方向為數學物理反問題，已合作出版英文專著一本，發表SCI論文30篇。其工作得到基金委優秀青年基金、德國洪堡基金以及上海市科委啟明星計劃等的資助，入選教育部青年長江及上海市教委曙光計劃。