On April 17, Prof. Jinchao Xu was invited by Institute of Natural Sciences, Shanghai Jiao Tong University to give a distinguished lecture in natural sciences online. In the 60 minutes lecture, Prof. Xu discussed the topic “Numerical PDEs and Deep Learning”, which attracted more than 500 participants including both professors and students.

In the lecture, Prof. Xu first gave an elementary introduction to models and algorithms from two different fields: (1) machine learning, including logistic regression, support vector machine and deep neural networks, and (2) numerical PDEs, including finite element and multigrid methods. He then explored mathematical relationships between these models and algorithms and demonstrated how such relationships can be used to understand, study and improve the model structures, mathematical properties and relevant training algorithms for deep neural networks. In particular, He demonstrated how a new convolutional neural network (CNN), known as MgNet, can be derived by making very minor modifications of a classic geometric multigrid method for the Poisson equation and then discussed the theoretical and practical potentials of MgNet.