- 控制理论和非线性滤波讨论班

Convergence and stability analysis of PDE-based filtering algorithm

组织者

丘成栋

演讲者

康家熠

时间

2022年11月15日 21:00 至 21:30

地点

Online

摘要

The direct method and the Yau-Yau method are two crucial filtering methods in nonlinear filtering problems. In this report, I demonstrated the explicit convergence rate of the spectral Galerkin method and provided an analysis of the global error for the Yau-Yau and direct methods in a path-wised point of view. Then, we analyzed the stability of spectral algorithm by using time discretization in a path-wised point of view.

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.