Basic knowledge on numerical methods for partial differential equations and 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.
20+ publications, will be distributed before each class
1. 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.
2. 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.
3. Reveal hidden dynamics and discover governing equations from data
4. Study various applications in transportation, electrical systems, infectious models, reservoir and seismology problems, and optimal control problems.
Dr. Zhang Xiaoming, a native of Zhejiang province, is a national specially-appointed expert. He received his bachelor's, master's, and doctor's degrees from Zhejiang University, Peking University, and Massachusetts Institute of technology. At present, he is an industrial and application researcher of Beijing Institute of Mathematical Sciences and Applications and the head of the artificial intelligence and big data team. Before returning to China, Dr. Zhang served as a technology executive of several well-known American enterprises. After returning to China, he served as director of the Textile Industry Big Data Center of Zhejiang China Light Textile City Group Co., Ltd., researcher of Data Science Research Institute of Tsinghua University, visiting professor of East China Normal University, and part-time professor of Zhejiang University of Technology.
As a Principal Investigator, he has won and presided over 20 research projects funded and awarded by the governments and major corporations. He has published more than 30 papers in international professional journals, of which two have been published in Nature subsidiary journals. He led his group won the first place in the Micro Array Quality Control (MAQC) competition hosted by the US Food and Drug Administration, twice the first places in the Alibaba Qianlima Industrial Big Data Competition, the second place and the third place in the First and Second China Industrial Internet Competitions respectively. Dr. Zhang led the development of the digital and intelligent service platform "Printing and Dyeing Brain", and is known as the "Godfather of intelligent printing and dyeing" in the industry.
Dr. Zhang has been engaged in the research, development and application of artificial intelligence methods to the prediction and resource optimization and allocation for a long time. At present, his work focuses on the research and development of digital twins and process twins in the industrial field, which are used to optimize the process flow, help enterprises improve the yield and production efficiency, reduce energy consumption and pollution, improve product grade and increase their core competitiveness.
Lecturer Email: firstname.lastname@example.org
TA: Dr. Liangze Yang, email@example.com