Solving Partial Differential Equations with Data Driven Machine Learning Methods
This course reviews the publications of the recent years on using machine learning methods to solve partial differential equations, such as Physics Informed Neural Network (PINN). The course will cover the materials on forward method, inverse method, reduced order modeling, and the assimilation of observational data to the scientific principles.
Lecturer
Date
2nd March ~ 29th June, 2023
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Thursday | 09:50 - 12:15 | Online | ZOOM 07 | 559 700 6085 | BIMSA |
Prerequisite
Basic knowledge on numerical methods for partial differential equations and machine learning methods
Syllabus
- Review frequently used numerical methods for PDEs
- Introduce PINN framework, Fourier feature networks, Deep-O-Net, POD-ROM, DeLISA, bcPINN, CAN-PINN, PGNN, A-PINN, fPINN, SPINN, Meta-PINN, segmentation of computational domain, and the incorporation with various classical numerical methods and various neural network structures.
- Solve high-dimensional equations, high-order problems, strong nonlinear problems, free-boundary problems, stochastic equations, fractional-order differential equations, integral equations, Navier-Stokes equations, Maxwell equations, etc.
- Reveal hidden dynamics and discover governing equations from data
- Study various applications in transportation, electrical systems, infectious models, reservoir and seismology problems, and optimal control problems.
- Introduce PINN framework, Fourier feature networks, Deep-O-Net, POD-ROM, DeLISA, bcPINN, CAN-PINN, PGNN, A-PINN, fPINN, SPINN, Meta-PINN, segmentation of computational domain, and the incorporation with various classical numerical methods and various neural network structures.
- Solve high-dimensional equations, high-order problems, strong nonlinear problems, free-boundary problems, stochastic equations, fractional-order differential equations, integral equations, Navier-Stokes equations, Maxwell equations, etc.
- Reveal hidden dynamics and discover governing equations from data
- Study various applications in transportation, electrical systems, infectious models, reservoir and seismology problems, and optimal control problems.
Reference
20+ publications, will be distributed before each class
Audience
Undergraduate
, Graduate
Video Public
No
Notes Public
Yes
Language
Chinese
Lecturer Intro
Dr. Zhang Xiaoming received his bachelor's, master's, and doctor's degrees from Zhejiang University, Peking University, and Massachusetts Institute of Technology. He is currently a professor at the Beijing Institute of Mathematical Sciences and Applications, responsible for the artificial intelligence and big data research team. Dr. Zhang has long been engaged in the research, development, and application of artificial intelligence technologies to big data prediction and resource optimization and allocations problems. He presided over the development of digital intelligence service platform "printing and dyeing brain", which was well recognized in the industry. At present, his work focuses on the mathematical problems in developing industrial digital twins.