Machine Learning Methods for Solving PDEs
AI for solving partial differential equations (PDEs) is an important content in the topic of AI for Science. This course focuses on using machine learning (ML) methods to solve forward and inverse problems of PDEs. We place more emphasis on using notes summarized and written by the lecturer, while for each knowledge point, previously and the latest published literatures will be introduced for explanation, including methods, numerical examples, and codes. There will be interactive time in every class and all attendees are welcome to ask questions and communicate with the lecturer.
讲师
日期
2025年04月08日 至 06月24日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二 | 13:30 - 16:55 | A3-1-301 | ZOOM 08 | 787 662 9899 | BIMSA |
修课要求
Basic knowledge on deep learning, partial differential equations, and the Python language.
课程大纲
1. Introduction to important knowledge points, possible skills of network training, some review literatures
ML Methods for Solving PDEs:
2. Physics-informed neural networks (PINNs) (a)
3. Physics-informed neural networks (PINNs) (b)
4. Physics-informed neural networks (PINNs) (c)
ML Methods for Solving Parameterized PDEs:
5. Deep neural operator (DeepONet) (a)
6. Deep neural operator (DeepONet) (b)
7. Reduced order modeling (ROM) (a)
8. Reduced order modeling (ROM) (b)
9. Other method: Fine designing of basis functions and coefficients
The Application of ML Methods in Some Problems:
10. Neural network surrogate modeling method
11. Discovery of ODE/PDE from data
12. Course review, communication, and interaction
ML Methods for Solving PDEs:
2. Physics-informed neural networks (PINNs) (a)
3. Physics-informed neural networks (PINNs) (b)
4. Physics-informed neural networks (PINNs) (c)
ML Methods for Solving Parameterized PDEs:
5. Deep neural operator (DeepONet) (a)
6. Deep neural operator (DeepONet) (b)
7. Reduced order modeling (ROM) (a)
8. Reduced order modeling (ROM) (b)
9. Other method: Fine designing of basis functions and coefficients
The Application of ML Methods in Some Problems:
10. Neural network surrogate modeling method
11. Discovery of ODE/PDE from data
12. Course review, communication, and interaction
参考资料
1. Knowledge points summarized by the lecturer.
2. Latest published literature related to machine learning and differential equations, which will be recommended before each class.
2. Latest published literature related to machine learning and differential equations, which will be recommended before each class.
听众
Graduate
, 博士后
, Researcher
视频公开
不公开
笔记公开
不公开
语言
中文
讲师介绍
熊繁升，现任北京雁栖湖应用数学研究院助理研究员，曾任北京应用物理与计算数学研究所所聘博士后。先后毕业于中国地质大学(北京)、清华大学，美国耶鲁大学联合培养博士。研究兴趣主要集中于基于机器学习算法(DNN、PINN、DeepONet等)求解微分方程模型正/反问题及其在地球物理波传播问题中的应用，相关成果发表在JGR Solid Earth、GJI、Geophysics等期刊上。