Inverse Problems Activities in China Jin Cheng ( 程晋 ) Fudan University

1950s—1980s Prof. Feng Kang, Academician, (Academy of Science, China), – Prof. Zhang Guanquan, (Academy of Science, China) Inverse problems for hyperbolic equations with application in geophysics Prof. Li Tatsien, Academician, (Fudan University) – Prof. Tan Yongji Inverse problems for elliptic equations with application in well- logging

1980s--present There are more 10 research groups working on Theoretical Analysis and Numerical Algorithm for Inverse Problems with Applications. Fudan University, Shanghai (Prof. Jin Cheng) Southeast University, Nanjing (Prof. Jijun Liu) Lanzhou University, Lanzhou (Prof. Ting Wei & Prof. Chuli Fu) Academy of Science, Beijing (Prof. Bo Zhang & Prof. Yanfei Wang) Jilin University, Changchun (Prof. Fuming Ma) Harbin Institute of Technology, Harbin (Prof. Bo Han) Central South University, Changsha (Prof. Zhenhai Liu) Nanjing University, Nanjing (Prof. Sixun Huang & Dr. Zhi Qian) etc

Supports from Chinese Government Strong support from National Science Foundation of China (NSFC) – Key project (2005—2009), General Projects, – TianYuan projects (2009,2010) Supports from the Ministry of Science and Technology – 973 projects, etc Support from other sources – Key project (Shanghai Science Foundation) etc – Scientific Grants (Jiangsu Province)

Research group in Fudan University Members: – Jin Cheng – Wenbin Chen – Shuai Lu – Yanbo Wang (left to an Internet Game Company in 2007) – Yunxin Zhang – 2 post doc, 6 Ph D students, 3 master students etc

Research Fields (1) Inverse Problems for elliptic partial differential equations – Uniqueness, Conditional Stability, etc Inverse Problems for parabolic partial differential equations – Uniqueness, Conditional Stability, Stable Algorithms, etc

Research Fields (2) Numerical methods for inverse problems – Relations between the conditional stability and Tikhonov regularization Numerical methods for ill-posed problems – Regularization methods – Parameter identification and optimization – High performance computing

Joint research Prof. Masahiro Yamamoto, the University of Tokyo, Japan Prof. Gen Nakamura, Hokkaido University, Japan Prof. William Rundell, Texas A & M University, USA Prof. Victor Isakov, Wichita University, USA Prof. Mourad Choulli, University of Metz, France

Cooperation Institutes National Earthquake Institute of China, Beijing, China New Japan Steel Company, Tokyo, Japan

Research Group in Southeast University Members: – Jijun Liu – Tiejun Cui (Engineering Department) – Jiamu Zheng – Ping Guan – Hongwei Wu – 4 Ph D students, 10 master students

Research Fields Scattering and Inverse Scattering problems – Probe method, numerical realizations, etc Mathematical Problems for Magnetic Resonance Imaging (MRI) and MRE – Model analysis, efficient realizations, etc Numerical Methods for Ill-posed and Inverse Problems – Backward problems for Heat equations, etc – New schemes for choosing the regularizing parameters

Joint research Prof. G. Nakamura, Hokkaido University, Japan Prof. M.Yamamoto, University of Tokyo, Japan Prof. J.K. Seo, Yansei University, Korea Prof. E.J.Woo, Kyung University, Korea Dr. M.Sini (RICAM, Austria) Prof. R.Potthast (University of Reading, UK) Prof. H.Dietmar (WAIST, Germany)

Research Group in Lanzhou Members: – Ting Wei – Chuli Fu – Xiangtuan Xiong – 8 Ph D students, 8 master students etc

Research Fields Numerical Methods for Inverse Problems for Elliptic PDEs and Parabolic Equations Regularization Methods Boundary Identification Problems

Joint Research Prof. Y.C. Hon, City University of Hong Kong, China Prof. L Ling, Baptist University of Hong Kong Prof. M.Yamamoto, University of Tokyo, Japan

Research Group in Jilin University Members: – Prof. Muming Ma – Prof. Deyue Zhang – 5 Ph D students, 4 master students etc

Research Fields Scattering and Inverse Scattering problems for Helmholtz equations and Maxwell equations Numerical methods for Inverse Problems Numerical methods for partial differential equations

Joint Research Prof. Gang Bao, Michigan State University, USA Prof. Peijun Li, Purdue University, USA

Research Group in Academy of Science Members: – Prof. Bo Zhang – Prof. Wensheng Zhang – Prof. Yanfei Wang – 4 Ph D students etc

Research Fields Direct and Inverse Scattering Problems Numerical analysis and scientific computing Partial Differential Equations Machine Learning: Neural Networks and Support Vector machines

Joint Research School of Mathematical and Information Sciences, Coventry University, UK * Prof. Bo Zhang is also a Professor of Applied Mathematics in Coventry University

Thanks! 谢谢！