- 控制理论和非线性滤波讨论班

Estimation of the Linear system via Optimal Transportation and Its Application for Missing Data Observations

组织者

丘成栋

演讲者

康家熠

时间

2023年03月03日 21:30 至 22:00

地点

Online

摘要

In this report, we present a unified framework for particle data fusion based on optimal transportation. The sequence data fusion can be considered as three different types, prediction problems, filtering problem and smoothing problem. We summarise the different particle methods as the paths on the Wasserstein space. However, there are infinite-many flow models corresponding to the same path. Firstly, we design the tangent flow by using the optimal transportation so that this flow model is unique, deterministic and optimal in the sense of Wasserstein space. The tangent flow of PDE can be used to solve the prediction/sampling problem. The tangent flow of SPDE can be used to solve the filtering problem. Finally, we extend the filtering algorithm as smoothing algorithm by using the forward-backward duality of Mayne–Fraser two-filter formula.

演讲者介绍

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.