Topological Data Assimilation using Wasserstein Distance


Jianwei Ma, Harbin Institute of Technology


2018.11.27 15:00-16:00


601 Pao Yue-Kong Library


This work combines a level-set approach and the optimal transport-based Wasserstein distance in a data assimilation framework. The primary motivation of this work is to reduce assimilation artifacts resulted from the position and observation error in the tracking and forecast of pollutants present on the surface of oceans or lakes. Both errors lead to spurious effect on the forecast that need to be corrected. In general, the geometric contour of such pollution can be retrieved from observation while more detailed characteristics such as concentration remain unknown. Herein, level sets are tools of choice to model such contours and the dynamical evolution of their topology structures. They are compared with contours extracted from observation using the Wasserstein distance. This allows to better capture position mismatches between both sources compared with the more classical Euclidean distance. Finally, the viability of this approach is demonstrated through academic test cases and its numerical performance is discussed.


Jianwei Ma received the Ph.D. degree in engineering from Tsinghua University, Beijing, in 2002. He was an Assistant Professor and an Associate Professor with the School of Aerospace, Tsinghua University, from 2006 to 2010. He was a Scientist with Florida State University, from 2010 to 2011. He has been a Post-Doctoral Researcher and has visiting experiences with the University of Cambridge, the University of Grenoble, the Ecole des Mines de Paris, The University of Texas at Austin, and University of California at Los Angeles, since 2002. He is currently the Professor of the Department of Mathematics, the Director of the Center of Geophysics and the Vice Dean of the Artificial Intelligence Laboratory, Harbin Institute of Technology, China. His research interests include sparse transforms, geophysical data processing, compressed sensing, inverse problems, and deep learning. Dr. Ma received the NFSC Distinguished Young Scholarship in 2016. He is a Principal Investigator for the National Key Research and Development Program of China.