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Seminar on Control Theory and Nonlinear Filtering
Seminar on Control Theory and Nonlinear Filtering
Nonexistence of finite-dimensional estimation algebras on a Riemannian manifold
Nonexistence of finite-dimensional estimation algebras on a Riemannian manifold
Organizer
Stephen S-T. Yau
Speaker
Jiayi Kang
Time
Wednesday, August 21, 2024 2:30 PM - 3:30 PM
Venue
Online
Abstract
In this report, I will present recent progress on the filtering problem for Riemannian manifolds. We have proven that the filtering problem on compact Riemannian manifolds does not admit a finite-dimensional estimation algebra, which implies that manifold-based filtering problems are inherently nonlinear. Furthermore, this conclusion suggests that the linearization approximations used in traditional algorithms may not be the optimal approach for addressing such problems!
Speaker Intro
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.