Workshop on Computation and Applications of PDEs Based on Machine Learning

A Summer Short Course on Numerical PDE and Machine Learning, which is sponsored by the Northeast Tianyuan Mathematics Center and undertaken by Jilin University officially, was held online from July 5 to July 9.

In the five-day short class, Professor Xu focused mainly on the combination of finite element method and machine learning. Professor Xu first introduced the basic theory of multigrid method and deep learning in detail, and then focused on MgNet^[1], a new network structure proposed by Professor Xu and his student Juncai He using multigrid method. MgNet has better performance in image classification problems than the mainstream network structure ResNet. Professor Xu also discussed the approximation property of deep neural work, including the widely used ReLU neural network.

Affected by the epidemic, the online teaching allows more teachers and students to participate in this course, and the average number of participants in each class is up to 500. The classroom atmosphere was not affected by the distance at all neither. Every student actively participated in the discussion, and the Q&A time for the last class was even more than one hour.

Reference:

[1] He, Juncai, and Jinchao Xu. "MgNet: A unified framework of multigrid and convolutional neural network." Science china mathematics 62, no. 7 (2019): 1331-1354.