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Seminar on Control Theory and Nonlinear Filtering
Seminar on Control Theory and Nonlinear Filtering
The Hessian transport gradient flows and sampling methods
The Hessian transport gradient flows and sampling methods
Organizer
Stephen S-T. Yau
Speaker
Jiayi Kang
Time
Tuesday, September 20, 2022 4:30 PM - 5:00 PM
Venue
Online
Online
Tencent 735 7908 4302
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Abstract
It turns out that there are two geometric structures in the probability space related to the de Bruijn identity. One is Wasserstein geometry, which refers to the heat flows or Gaussian kernels. The other one is information geometry, which relates to the differential structures of the entropy. A natural question arises: What are natural families of geometries in the probability space that connect entropy/divergence functions, heat flows, and the de Bruijn identity?
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.