Machine Learning in Modeling and Computing
AI for Science is currently an important topic. Machine learning (ML) have become remarkably successful, which has a great impact on the research of forward and inverse problems related to differential equation models describing various natural and social phenomenon. The main content of this course is to introduce knowledge about ML in modelling and scientific computing, including ML-based methods for solving differential equation-based forward and inverse problems, numerical examples, and codes. The latest published literatures related to machine learning and differential equations will also be introduced. Meanwhile, audiences studying on the relevant topics are encouraged to present your research.
讲师
日期
2024年04月02日 至 06月18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
Knowledges on partial differential equations, deep learning, and the Python language.
课程大纲
1. Introduction to “Machine Learning and Differential Equations”, Some review literatures
2. Numerical Method: Variational Principle, Spectral Method, Deep Neural Networks
3. Machine Learning Method for Solving Differential Equations
4. Physics-Informed Neural Networks (a)
5. Physics-Informed Neural Networks (b)
6. Discovering Differential Equations from Data (a)
7. Discovering Differential Equations from Data (b)
8. Deep Neural Operator (a)
9. Deep Neural Operator (b)
10. Multifidelity Technique
11. Reduced Order Modeling
12. Course review, Communication, and Interaction
2. Numerical Method: Variational Principle, Spectral Method, Deep Neural Networks
3. Machine Learning Method for Solving Differential Equations
4. Physics-Informed Neural Networks (a)
5. Physics-Informed Neural Networks (b)
6. Discovering Differential Equations from Data (a)
7. Discovering Differential Equations from Data (b)
8. Deep Neural Operator (a)
9. Deep Neural Operator (b)
10. Multifidelity Technique
11. Reduced Order Modeling
12. Course review, Communication, and Interaction
参考资料
1.《Machine Learning in Modeling and Simulation》
2. Published literatures related to machine learning and differential equations, and the recommended reading list will be provided before each class.
2. Published literatures related to machine learning and differential equations, and the recommended reading list will be provided 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。