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，负责人工智能与大数据研究团队。张博士长期从事人工智能技术在大数据预测和资源优化配置问题上的研究、开发和应用。主持研发的数字智能服务平台“印染大脑”，得到业界的认可。目前，他的工作重点是工业领域数字孪生构建中的数学问题。