Beijing Institute of Mathematical Sciences and Applications

Stephen S-T. Yau

Jiayi Kang

Wednesday, September 11, 2024 2:30 PM - 3:00 PM

理科楼A-304

In this report, I will introduce the existence of estimation algebras in more general situations. In fact, for a class of noise-correlated filtering systems, finite dimensional estimation algebras can always exist. For a special class of filtering models, regardless of any assumptions added to the observation noise (general semimartingales) the estimation algebra is always finite-dimensional. For general noise-correlated models, the Wei-Norman method fails, and it becomes necessary to introduce the Lie symmetry theory for SPDEs (Stochastic Partial Differential Equations).

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.