Beijing Institute of Mathematical Sciences and Applications

Liyan Han , Zhen Li , Fei Long , Ke Tang , Yu Wang

Jiayi Kang

Friday, February 28, 2025 3:00 PM - 4:00 PM

A3-2a-302

Zoom 637 734 0280 (BIMSA)

In practical estimation applications, observational data from physical models are invariably affected by various forms of noise. In the current data-driven era, extracting and recovering meaningful information has emerged as a critical challenge. Filtering theory, which combines time-series observational data with prior knowledge of physical models, provides a framework for addressing these estimation problems. This theory is widely applicable to sequential tasks in fields such as communications, finance, navigation, image processing, and geophysics. Traditional approaches to solving filtering problems generally rely on two methodological frameworks. The first involves formulating stochastic differential equations through the theory of stochastic partial differential equations, followed by applying analytical theories and numerical algorithms to derive closed-form solutions for specific cases or approximate solutions for broader scenarios. The second employs particle-based techniques, such as Monte Carlo methods, to reconstruct statistical properties of system states or approximate posterior density functions using particle ensembles. Recent advancements in artificial intelligence have enabled data-driven and AI-powered strategies to design more efficient filtering algorithms, opening new avenues for addressing complex industrial and financial challenges in real-world settings.

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.