BIMSA >
BIMSA Computational Math Seminar
Yau-Yau filtering theory and novel algorithms based on deep learning
Yau-Yau filtering theory and novel algorithms based on deep learning
演讲者
时间
2025年03月06日 15:00 至 16:00
地点
A3-4-312
线上
Zoom 787 662 9899
(BIMSA)
摘要
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.
演讲者介绍
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。