Speaker: Prof. Ming-Chih Lai（赖明治教授）
Time: 15:30-16:30, 11 October 2023 (Wednesday) (Beijing time)
Venue: 华信书院，CC126
Tencent Meeting ID: 989-480-985
Abstract
In this talk, we shall introduce a series of neural network methodologies for solving elliptic interface problems and Stokes interface problems. There are several novel features in the present neural network approach; namely, (i) it is a single network architecture regardless of the number of existed interfaces; (ii) the solution and derivative jump discontinuities are accurately captured by simply augmenting an extra interface feature input, (iii) the network can be completely shallow (one-hidden-layer) if the solutions are not complex, (iv) it is completely mesh-free so the problems in irregular domains with irregular interfaces can be handled easily. Numerical results show better efficiency in terms of the number of trainable parameters used, and better accuracy than the traditional finite difference method such as the immersed interface method.
About Prof. Lai
Prof. Ming-Chih Lai received his Ph.D. degree in Mathematics from Courant Institute of Mathematical Sciences, New York University (NYU) in 1998. His major research interests are mainly on Numerical Methods for PDEs and Computational Fluid Dynamics, especially in developing mathematical models and numerical methods for incompressible fluids with interfaces. Very recently, he has extended his research area to Scientific Machine Learning (SciML). Prof. Lai is a leading expert on numerical methods on interfacial flows and has published over than 80 high quality papers in JCP, SISC, JFM etc. He has got numerous prestigious awards in Taiwan. In addition to his outstanding research performance, he has served the President of SIAM East Asia Section (EASIAM) in the year of 2013-2014, the President of Mathematical Society of Taiwan in the year of 2016-2017, and the President of Taiwan Society of Industrial and Applied Mathematics (TWSIAM) in the year of 2018-2020. Currently, he is a Chair Professor and the Dean of College of Science of Yang Ming Chiao Tung University in Taiwan.
