北京雁栖湖应用数学研究院

丘成栋

焦小沛

2025年02月05日 21:00 至 22:00

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.

焦小沛，于2017年本科毕业于上海交通大学致远学院（物理班），2022年博士毕业于清华大学数学科学系，师从丘成栋教授（IEEE fellow，前美国伊利诺伊大学芝加哥分校终身教授）。先后在北京雁栖湖应用数学研究院，荷兰特文特大学从事博士后工作（导师Johannes Schmidt-Hieber教授，国际数理统计学会会士）。现研究方向包括控制理论，数值偏微分方程，生物信息学。获得2025年国家青年科学基金[C类]资助。