Nonlinear filter and deep learning
As an important branch of control theory, nonlinear filtering refers to the estimation or filtering out of noise from a system where the underlying system dynamics are nonlinear. These problems arise in various fields, such as signal processing, robotics, and economics. The nonlinear property originating from the system makes it difficult to apply traditional linear filtering techniques such as the Kalman filter and its variants, particle filter, etc.
This course will focus on the mathematical foundation and algorithms to handle nonlinear filtering. In the 1983 International Congress of Mathematics, Brockett proposed the classification problem for finite-dimensional filters. We shall first introduce the so-called Brockett-Mitter program by applying geometric methods, e.g., Lie algebra. Later, we shall concentrate on the well-known Yau-Yau filter to introduce the theory and the corresponding developed numerical algorithms. Finally, combined with recent popular deep learning techniques, some novel filtering algorithms to deal with infinite-dimensional filters will be introduced.
After completing the course, participants will be familiar with important mathematical tools and their applications in nonlinear filtering. This course will also contain many cutting-edge academic results from the lecturer himself.
This course will focus on the mathematical foundation and algorithms to handle nonlinear filtering. In the 1983 International Congress of Mathematics, Brockett proposed the classification problem for finite-dimensional filters. We shall first introduce the so-called Brockett-Mitter program by applying geometric methods, e.g., Lie algebra. Later, we shall concentrate on the well-known Yau-Yau filter to introduce the theory and the corresponding developed numerical algorithms. Finally, combined with recent popular deep learning techniques, some novel filtering algorithms to deal with infinite-dimensional filters will be introduced.
After completing the course, participants will be familiar with important mathematical tools and their applications in nonlinear filtering. This course will also contain many cutting-edge academic results from the lecturer himself.
讲师
日期
2025年03月19日 至 07月02日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周三 | 14:20 - 16:55 | A3-1-101 | ZOOM 2 | 638 227 8222 | BIMSA |
修课要求
Basic knowledge of Calculus, linear algebra and differential equation.
课程大纲
1. Introduction to nonlinear filter problem, mathematical formulation, and popular filtering algorithms
Brockett-Mitter program of classification
2. Basic knowledge of Lie group and Lie algebra
3. Finite dimensional filter(I)
4. Finite dimensional filter(II)
5. Finite dimensional filter(III)
6. Finite dimensional filter(IV)
Optimal nonlinear filter
7. Basic knowledge of Partial differential equation
8. Yau-Yau filter (I)
9. Yau-Yau filter (II)
10. Yau-Yau filter (III)
11. Yau-Yau filter (IV)
Deep learning filter
12. Basic introduction to scientific machine learning
13. Deep learning-inspired filter algorithms (I)
14. Deep learning-inspired filter algorithms (II)
15. Deep learning-inspired filter algorithms (III)
16. Deep learning-inspired filter algorithms (IV)
Brockett-Mitter program of classification
2. Basic knowledge of Lie group and Lie algebra
3. Finite dimensional filter(I)
4. Finite dimensional filter(II)
5. Finite dimensional filter(III)
6. Finite dimensional filter(IV)
Optimal nonlinear filter
7. Basic knowledge of Partial differential equation
8. Yau-Yau filter (I)
9. Yau-Yau filter (II)
10. Yau-Yau filter (III)
11. Yau-Yau filter (IV)
Deep learning filter
12. Basic introduction to scientific machine learning
13. Deep learning-inspired filter algorithms (I)
14. Deep learning-inspired filter algorithms (II)
15. Deep learning-inspired filter algorithms (III)
16. Deep learning-inspired filter algorithms (IV)
参考资料
Latest papers of the lecturer and the related literature.
听众
Undergraduate
, Graduate
, Researcher
视频公开
公开
笔记公开
公开
语言
中文
, 英文
讲师介绍
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。