Background & Purpose

Nowadays, deep learning has achieved great success in various scientific disciplines, including image recognition, natural language processing, and many other practical applications in our daily life. When it comes to solving partial differential equations (PDEs), traditional numerical methods are well developed tools for finding solutions accurately, whereas sometimes tackling problems with complicated setup or in high dimensions using traditional methods can be extremely computational expensive or even infeasible. In this scenario deep learning techniques come to play an essential role to overcome those difficulties. In this lecture, we aim to introduce some traditional numerical methods for PDEs, then carry out mathematical model of neural networks and apply machine learning techniques to solve PDEs.