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 welllogging
1980s--present
• There are more 10 research groups working on Theoretical Analysis
and Numerical Algorithm for Inverse Problems with Applications.
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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
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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
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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！