AI4Science: Learning and solving PDE
AI for Science is promoting the transformation of scientific research paradigm, which has a great impact on the research of forward and inverse problems related to partial differential equation models describing various natural and social phenomenon. The main content of this course is to explain the literature related to "machine learning and differential equations" in recent years, including machine learning-based methods for solving PDE forward and inverse problems and dynamical system modeling, numerical examples, and code. Meanwhile, audiences studying on ML&XDE are encouraged to share your research work.
Lecturer
Date
10th October ~ 26th December, 2023
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 13:30 - 16:55 | A3-1-301 | ZOOM 06 | 537 192 5549 | BIMSA |
Syllabus
1. Course description, Introduction to “Machine Learning and PDE”, Nature literatures
2. Solving PDE with PINN(a): Causal sweeping, Adaptive local viscosity, A case study
3. Solving PDE with PINN(b): DaPINN, PIRBN
4. Solving PDE with Extreme Learning Machine (ELM)
5. Solving inverse problem with PINN: Subsurface flow, Turbulence (RANS), Full Waveform Inversion (FWI)
6. Data-driven discovery of PDE(a): SINDy/PDE-FIND, Black-box PINN, PINN-SR, PDE Net, PeRCNN
7. Data-driven discovery of PDE(b): Gray-box learning (Symbolic regression coupled with XPINN), Reduced-order modelling (ROM)
8. Learning PDE with Operator Learning(a): DeepONet, Reliable extrapolation
9. Learning PDE with Operator Learning(b): DeepONet for learning non-autonomous ODE, closure modeling of PROM
10. Learning PDE with Operator Learning(c): A operator regression framework, Koopman operator
11. Learning thermodynamically stable PDEs
12. Course review, Communication and interaction
2. Solving PDE with PINN(a): Causal sweeping, Adaptive local viscosity, A case study
3. Solving PDE with PINN(b): DaPINN, PIRBN
4. Solving PDE with Extreme Learning Machine (ELM)
5. Solving inverse problem with PINN: Subsurface flow, Turbulence (RANS), Full Waveform Inversion (FWI)
6. Data-driven discovery of PDE(a): SINDy/PDE-FIND, Black-box PINN, PINN-SR, PDE Net, PeRCNN
7. Data-driven discovery of PDE(b): Gray-box learning (Symbolic regression coupled with XPINN), Reduced-order modelling (ROM)
8. Learning PDE with Operator Learning(a): DeepONet, Reliable extrapolation
9. Learning PDE with Operator Learning(b): DeepONet for learning non-autonomous ODE, closure modeling of PROM
10. Learning PDE with Operator Learning(c): A operator regression framework, Koopman operator
11. Learning thermodynamically stable PDEs
12. Course review, Communication and interaction
Reference
Published literatures related to machine learning and differential equations, and the recommended reading list will be provided before each class.
Audience
Undergraduate
, Graduate
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.