求解偏微分方程的数据驱动机器学习方法
本课程将回顾近年来关于使用机器学习方法求解偏微分方程的论文,例如物理支持神经网络(PINN)。 本课程将涵盖正向法,逆向法,降阶建模,以及观测数据与科学原理的融合等内容。
讲师
日期
2023年03月02日 至 06月29日
位置
Weekday | Time | Venue | Online | ID | Password |
---|---|---|---|---|---|
周四 | 09:50 - 12:15 | Online | ZOOM 07 | 559 700 6085 | BIMSA |
修课要求
求解偏微分方程的数值方法以及机器学习方法的基本知识
课程大纲
- 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.
参考资料
20+ publications, will be distributed before each class
听众
Undergraduate
, Graduate
视频公开
不公开
笔记公开
公开
语言
中文
讲师介绍
张晓明博士先后在浙江大学、北京大学、麻省理工学院获得学士、硕士和博士学位。现任北京雁栖湖应用数学研究院研究员,人工智能和机器学习团队PI。他目前的研究兴趣是对开发由数据和领域知识驱动的机器学习算法,并将其应用于各种物理、生物和社会现象的解释和量化。