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，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。