AI for Solving Forward and Inverse PDE Problems
AI for Science is currently a research hotspot. This series of courses continues to introduce machine learning (ML) methods for solving forward and inverse problems of partial differential equations. Compared to previous courses, this semester's course places more emphasis on using lecture notes summarized and written by the instructor. Meanwhile, for each knowledge point of ML in modelling and scientific computing, the latest published literatures will be supplemented for explanation, including methods, numerical examples, and codes. Audiences studying on the relevant topics are encouraged to present your research and interact more.
讲师
日期
2024年10月08日 至 12月24日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二 | 13:30 - 16:55 | A3-1-301 | ZOOM 06 | 537 192 5549 | BIMSA |
修课要求
Basic knowledges on deep neural networks, partial differential equations, and the Python language.
课程大纲
1. Introduction to important knowledge points related to Machine Learning and Differential Equations, Some review literatures
ML Methods for Solving Forward Problems:
2. Physics-Informed Neural Networks (a)
3. Physics-Informed Neural Networks (b)
4. Physics-Informed Neural Networks (c)
ML Methods for Solving Inverse Problems:
5. Neural Network Surrogate Modeling Method
6. Discovery of ODE/PDE from Data (a)
7. Discovery of ODE/PDE from Data (b)
Operator Learning & Reduced Order Modeling:
8. Deep Neural Operator (a)
9. Deep Neural Operator (b)
10. Reduced Order Modeling (a)
11. Reduced Order Modeling (b)
12. Course review, Communication, and Interaction
ML Methods for Solving Forward Problems:
2. Physics-Informed Neural Networks (a)
3. Physics-Informed Neural Networks (b)
4. Physics-Informed Neural Networks (c)
ML Methods for Solving Inverse Problems:
5. Neural Network Surrogate Modeling Method
6. Discovery of ODE/PDE from Data (a)
7. Discovery of ODE/PDE from Data (b)
Operator Learning & Reduced Order Modeling:
8. Deep Neural Operator (a)
9. Deep Neural Operator (b)
10. Reduced Order Modeling (a)
11. Reduced Order Modeling (b)
12. Course review, Communication, and Interaction
参考资料
1. The lecture notes written by the instructor.
2. Latest published literatures related to machine learning and differential equations, which will be recommended before each class.
2. Latest published literatures related to machine learning and differential equations, which will be recommended before each class.
听众
Undergraduate
, Advanced Undergraduate
, 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。