Inverse Problems Activities in China

Jin Cheng (程晋 )Fudan University

1950s—1980s

• Prof. Feng Kang, Academician, (Academy of Science, China), 1920--1993– 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！