Beijing Institute of Mathematical Sciences and Applications

Stephen S-T. Yau

Jiayi Kang

Tuesday, June 20, 2023 2:30 PM - 3:00 PM

数学系理科楼A-203

In this talk, we present two of our on-going research projects. The first project is concerned with a generative model based on stochastic differential equations. More specifically, we design an approximate SDE bridging method that can draw samples from a target distribution by training a model with samples from a coupling of it. We show that this method is a state-of-the-art solution for image restoration problems (e.g., super-resolution or deblurring). The second project is concerned with a new class of convergent stochastic filters by using moment representations and a quadrature method. The key idea is to project the filtering distribution onto a sequence of moments, and use a moment quadrature method to propagate such a sequence in time. We show that this filter converges to the true distribution, and that the filter outperforms (in terms of convergence speed and computational cost) sequential Monte Carlo for low-dimensional models.

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.