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.
Lecturer
Date
8th April ~ 24th June, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 13:30 - 16:55 | A3-1-301 | ZOOM 08 | 787 662 9899 | BIMSA |
Prerequisite
Basic knowledge on deep learning, partial differential equations, and the Python language.
Syllabus
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
Reference
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.
Audience
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.