Beijing Institute of Mathematical Sciences and Applications

Stephen S-T. Yau

Jiayi Kang

Monday, May 1, 2023 3:00 PM - 3:30 PM

Online

This paper presents a unified framework for particle data fusion using optimal transportation. We address prediction, filtering, and smoothing problems by representing particle methods as paths on the Wasserstein space. We use optimal transportation to develop robust and stable algorithms for prediction and filtering, known as optimal transportation particle prediction and optimal transportation particle filtering. We derive optimal transportation particle smoothing using Mayne-Fraser's two-filter formula. We derive equations for empirical mean and covariance, equivalent to the explicit solution of filtering and smoothing. We provide detailed convergence results for our proposed algorithms. Finally, we test our algorithms on missing observation processes, requiring a hybrid data fusion approach.

Jiayi Kang received his Ph.D. in Mathematics from Tsinghua University in 2024. He joined the Beijing Institute of Mathematical Sciences and Applications (BIMSA) as an Assistant Researcher in July 2024, and became an Assistant Professor at the Hetao Institute for Mathematical and Interdisciplinary Sciences (HIMIS) in November 2025. His research focuses on the intersection of deep learning, nonlinear filtering, and computational biology. His main research interests include: neural network-based filtering algorithms and their mathematical foundations, sampling methods in Wasserstein geometry, nonlinear filtering theory (including the Yau-Yau method) and its applications in climate science and other fields, as well as computational genomics and evolutionary system modeling. He is committed to solving complex problems in science and engineering using mathematical and machine learning methods.