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.
Lecturer
Date
2nd April ~ 18th June, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 13:30 - 16:55 | A3-1-301 | ZOOM 06 | 537 192 5549 | BIMSA |
Prerequisite
Knowledges on partial differential equations, deep learning, and the Python language.
Syllabus
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
Reference
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.
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
No
Notes Public
No
Language
Chinese
Lecturer Intro
Fansheng Xiong (熊繁升) is currently an Assistant Researcher Fellow of BIMSA. Before that, he got a bachelor's degree from China University of Geosciences (Beijing), and a doctoral degree from Tsinghua University. He was a visiting student at Yale University for one year. His research interest mainly focuses on solving PDE-related forward/inverse problems based on machine learning algorithms (DNN, PINN, DeepONet, etc.), and their applications in geophysical wave propagation problems and turbulence modeling of fluid mechanics. The relevant efforts have been published in journals such as JGR Solid Earth, GJI, Geophysics, etc.