求解微分方程的机器学习方法 II
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，例如物理内嵌神经网络（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
2022年09月15日 至 2023年01月05日
网站
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
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.
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.
参考资料
20+ publications, will be distributed before each class
听众
Undergraduate
视频公开
不公开
笔记公开
不公开
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。