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 Professor of BIMSA. Before that, he received his doctoral degree in 2020 from Tsinghua University, and he was a visiting research assistant at Yale University during 2018-2019. His research interest mainly focuses on solving forward/inverse problems of PDEs based on machine learning method, and the application of PINN, DeepONet, Reduced Order Model in exploration geophysics, especially seismic rock physics. He is PI for grant from National Natural Science Foundation of China, and he has published papers in journals like Journal of Geophysical Research-Solid Earth, Geophysical Journal International, and Geophysics.