Beijing Institute of Mathematical Sciences and Applications

Zhen Li , Xin Liang , Zhiting Ma , Hamid Mofidi , Li Wang , Fansheng Xiong , Shuo Yang , Wuyue Yang

Xiaopei Jiao

Thursday, March 6, 2025 3:00 PM - 4:00 PM

A3-4-312

Zoom 787 662 9899 (BIMSA)

Abstract: The nonlinear filtering problem, which dates back to the 1600s, aims to infer reliable state estimates from stochastic measurements. The introduction of the Kalman filter in the 1960s revolutionized fields such as aerospace engineering and navigation. Nevertheless, achieving optimal state estimation hinges on computing the conditional density, governed by the Duncan-Mortensen-Zakai (DMZ) equation introduced in the 1970s. In the 21st century, the Yau-Yau filter, was innovatively proposed to emerge as a groundbreaking tool for nonlinear filtering. The Yau-Yau filter remains a uniquely powerful method for effectively handling complex nonlinear systems, such as those involving cubic sensors. Building on the Yau-Yau framework, we introduced the Extended Direct Method (EDM) to address more general infinite-dimensional systems compared to the traditional Direct Method. EDM is supported by rigorous existence and uniqueness analyses, and numerical results demonstrate that this explicit algorithm can achieve near-optimal accuracy comparable to spectral methods. Additionally, we developed the Deep Generalized Galerkin Method based on Physics-Informed Neural Networks (PINNs), which accelerates the offline computations of the Yau-Yau filter while preserving its high accuracy. Numerical simulations validate the efficiency and precision of these advancements, highlighting their potential for broader applications in nonlinear filtering.

Jiao Xiaopei graduated with a bachelor's degree from the Zhi Yuan College of Shanghai Jiao Tong University (Physics Department) in 2017 and obtained his PhD from the Department of Mathematical Sciences at Tsinghua University in 2022, under the guidance of Professor Stephen Shing-Toung Yau (IEEE Fellow, former tenured professor at the University of Illinois at Chicago). He has conducted postdoctoral research at the Beijing Institute of Mathematica Science and Application and at the University of Twente in the Netherlands (under the guidance of Professor Johannes Schmidt-Hieber, Fellow of the Institute of Mathematical Statistics). His current research interests include control theory, numerical partial differential equations, and bioinformatics.