Direct Sampling Methods for Nonlinear Inverse Problems with Moving Inhomogeneous Inclusions

Abstract

In this talk, the speaker will review the current developments and some general principles and motivations of direct sampling type methods (DSMs) for solving general ill-posed inverse problems of Partial Differential Equations (PDEs). He will also discuss a basic framework for constructing direct sampling methods for nonlinear inverse problems with moving inhomogeneous inclusions. He shall illustrate the basic and important features of DSMs and explain why they are computationally cheap, highly parallel, robust against noise, and applicable to the physically important situations when very limited data is available.

These research projects were supported by the General Research Fund of the Research Grants Council of Hong Kong (Projects 14306921 and 14306719).

About the Speaker

Prof. ZOU Jun obtained his PhD from the Computing Center of the Chinese Academy of Sciences in 1989. He then worked in the Chinese Academy of Sciences as an Assistant Professor (1989-1991), in the Technical University of Munich as a Visiting Assistant Professor and an Alexander von Humboldt Research Fellow (1991-1993), and in the University of California, Los Angeles as a Post-doctoral Fellow and a CAM Assistant Professor (1993-1995). In 1995, he joined the Chinese University of Hong Kong (CUHK) as an Assistant Professor in Mathematics and was promoted to Associate Professor in 1997, to Full Professor in 2002, and to Chair Professor in 2012. He is currently Choh-Ming Li Chair Professor of Mathematics and Head of Department of Mathematics in CUHK.

Prof. Zou’s research interests include numerical methods and analyses of direct and inverse problems of partial differential equations. He has served as the Associate Editor of numerous international mathematics journals, including SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing and ESAIM: Mathematical Modelling and Numerical Analysis.

Prof. Zou was elected a Fellow of the Society for Industrial and Applied Mathematics in 2019 and of the American Mathematical Society in 2022. He is currently the President of Hong Kong Society for Industrial and Applied Mathematics, the Vice President of the Hong Kong Mathematical Society, and the President of the East Asia Section of the Inverse Problems International Association.

For Attendees' Attention

This talk will be held online via Zoom. To attend, please join the Zoom meeting at https://hkust.zoom.us/j/98673109334 (Meeting ID: 986 7310 9334 / Passcode: iasip2022).

About the Program

For more information, please refer to the program website at https://iasprogram.hkust.edu.hk/inverseproblems/.