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，本科毕业于上海交通大学致远学院，博士毕业于清华大学数学科学系。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。现研究方向包括有限维滤波理论，丘-丘滤波方法，物理信息神经网络以及生物信息学。研究兴趣主要集中于（1）利用李代数等几何工具进行偏微分方程求解与有限维滤波系统的分类；（2）设计基于物理信息神经网络的新型数值算法。