北京雁栖湖应用数学研究院

高瑞泽 , 韩立岩 , 李振 , 龙飞 , 史冬波 , 汤珂 , 张琦

焦小沛

2025年10月10日 15:00 至 16:00

A3-2-303

Zoom 435 529 7909 (BIMSA)

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 1981 International Congress of Mathematician, the well known Brockett-Mitter program was proposed classify finite dimensional filter by using Wei-Norman approach. One of the most important tool is estimation algebra. Since 1990, through about 2 decades, Yau and his collaborator have made significant progress in classifying maximal rank filter. In this talk we shall review the most recent progress made by speaker about the complicated extension to classification on non-maximal rank filters. Followed by this theoretical results, speaker shall then talk about numerical approximation on the FDF by utilizing powerful deep learning technique and Yau-Yau filter.

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。