Aim & Scope:

For the past decade, deep learning has achieved great success in different scientific disciplines, including image recognition, natural language processing, and many other practical applications in our daily life. The main question for the Math community is how the AI can help to do our own research. In this special lecture, we shall give an example of using machine learning methods to solve partial differential equations, especially when PDEs become difficult to handle with traditional numerical methods (such as finite difference, finite element or spectral methods). As the speakers' interest, we start with our development of machine learning methodology by considering elliptic interface problems where the solutions are usually not smooth. We have successfully developed two different types of completely shallow neural network to solve above elliptic PDEs. To the best of our knowledge, this is the first work in literature that uses only one hidden layer with moderate number of neurons to solve the problems even in higher dimensions. In this lecture, we start by introducing some fundamental mathematical backgrounds for machine learning and the methodologies to solve PDEs. Then, we shall introduce our shallow neural network model to solve the elliptic interface problems in detail. Some remaining open questions and future directions can also be raised.

Invited Speakers:

Wei-Fan Hu (National Central University)

Ming-Chih Lai (National Yang Ming Chiao Tung University)

Te-Sheng Lin (National Yang Ming Chiao Tung University)

Online Information:

Time: 10:00 AM - 12:00 PM Thursday, Sep 2 2021 (UTC+08:00) Taipei

Meeting link: https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=m31e4ffdb4052093d21575e59649a9cb5

Agenda with Title & Abstract Download:(please click here)

Online Conference Video Link:

10:00-10:30 Professor Ming-Chih Lai:https://www.youtube.com/watch?v=TuOQd-X7SYY

10:30-11:00 Professor Wei-Fan Hu:https://www.youtube.com/watch?v=mTHEVu2Tnck

11:00-11:30 Professor Te-Sheng Lin:https://www.youtube.com/watch?v=a8Zxfcr69ZA