Topological Data Assimilation using Wasserstein Distance

Li Long Department of Mathematics and Center of Geophysics, Harbin Institute of Technology, 150001 Harbin, People’s Republic of China Vidard Arthur Université Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France Le Dimet Francois-Xavier Université Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France Ma Jianwei Department of Mathematics and Center of Geophysics, Harbin Institute of Technology, 150001 Harbin, People’s Republic of China

Optimization and Control mathscidoc:2103.27001

Inverse Problems, 35, (1), 015006, 2019.1
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 resulting 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.
Data assimilation, Wasserstein distance, level set, prediction of geophysical fluids, optimal transport approach, geophysical inverse problem.
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@inproceedings{li2019topological,
  title={Topological Data Assimilation using Wasserstein Distance},
  author={Li Long, Vidard Arthur, Le Dimet Francois-Xavier, and Ma Jianwei},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210323110357392913749},
  booktitle={Inverse Problems},
  volume={35},
  number={1},
  pages={015006},
  year={2019},
}
Li Long, Vidard Arthur, Le Dimet Francois-Xavier, and Ma Jianwei. Topological Data Assimilation using Wasserstein Distance. 2019. Vol. 35. In Inverse Problems. pp.015006. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210323110357392913749.
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