【講題】Neural networks for interface problems and evolutionary PDEs

【演講時間】5月15日(星期五)下午1點30分  

【演講地點】清華大學校本部第二綜合大樓B側8樓A813室

【摘要】

In this talk, I introduce neural network methods for solving partial differential equations (PDEs), with emphasis on problems involving non-smooth solutions, sharp spatial gradients, and rapid temporal variations. The main focus is on specialized architectures designed to resolve interface-induced irregularities, including the discontinuity-capturing shallow neural network (DCSNN), the cusp-capturing neural network (CuspNN), and categorical embedding-based physics-informed neural networks (CE-PINNs). These approaches incorporate problem-specific features, such as indicator functions and level set representations, to accurately capture jumps and derivative singularities. Their effectiveness and computational efficiency are demonstrated through representative numerical experiments. If time permits, I will give a brief discussion of extensions to evolutionary PDEs using time-dependent neural network formulations and present numerical comparisons to benchmark solutions.