Beijing Institute of Mathematical Sciences and Applications

Shing Toung Yau

Xiao Pei Jiao

Wednesday, February 5, 2025 9:00 PM - 10:00 PM

Online

In this talk, we shall mainly investigate novel deep learning based filter algorithm named DGLG. The optimal filtering problem for nonlinear state-observation systems involves solving the Duncan-Mortensen-Zakai (DMZ) equation. This paper proposes a new filtering algorithm combining a physics-informed neural network for the Kolmogorov equation and a probability density approximator based on generalized Legendre polynomials. By using deep learning and Galerkin approximation, the algorithm maintains accuracy while reducing computational load. The method's convergence is proven, and experiments show that the deep generalized Legendre-Galerkin (DGLG) algorithm outperforms methods like the extended Kalman filter and particle filter in both accuracy and efficiency.

Xiaopei Jiao received his bachelor's degree from the Zhiyuan College of Shanghai Jiao Tong University and his Ph.D. from the Department of Mathematical Sciences at Tsinghua University. He subsequently worked as a postdoctoral researcher at the Beijing Institute of Mathematical Sciences and Applications (BIMSA) and at the University of Twente in the Netherlands. His current research interests include finite-dimensional filtering theory, Yau-Yau filtering methods, physics-informed neural networks, and bioinformatics. His research focuses primarily on: (1) using geometric tools such as Lie algebras for solving partial differential equations and classifying nonlinear systems; (2) designing novel numerical algorithms based on physics-informed neural networks.