CSE Distinguished Seminar | Kui Ren

Abstract

The task of simultaneously reconstructing multiple physical coefficients in PDEs from observed data is ubiquitous in applications. We propose an integrated data-driven and model-based iterative reconstruction framework for such joint inversion problems where additional data on the unknown coefficients are supplemented for better reconstructions. Our method couples the supplementary data with the PDE model to make the data-driven modeling process consistent with the model-based reconstruction procedure. This coupling strategy allows us to characterize the impact of learning uncertainty on the joint inversion results for two typical inverse problems. Numerical evidence is provided to demonstrate the feasibility of using data-driven models to improve the joint inversion of multiple coefficients in PDEs.

Bio

Kui Ren is a professor of applied mathematics at Columbia University. His research interest centers around computational and mathematical analysis of inverse and imaging problems related to partial differential equations. Ren received his Ph.D. from Columbia University. Following his Ph.D., he moved to the University of Chicago in 2007 where he worked as an L. E. Dickson instructor in mathematics and computer science. In Fall  2008, Ren joined the University of Texas at Austin as an assistant professor in the Department of Mathematics and the Oden Institute for Computational Sciences, Engineering and Mathematics, and was promoted to Associate Professor in 2014, and Full Professor in 2018 when he moved back to Columbia.