Seminar| Institute of Mathematical Sciences
Time: Monday, December 11th , 2024 , 11:00-12:00
Speaker: Zhiping Mao, Xiamen University
Abstract: In the talk, I shall present some numerical results for the forward and inverse problems of PDEs with sharp solutions by using deep neural network-based methods. In particular, we developed a deep operator learning enhanced PINN for PDEs with sharp solutions, which can be asymptotically approached by using problems with smooth solutions. Firstly, we solve the smooth problems by using deep operator learning, and we adopt the framework of DeepONet. Then we combine the pre-trained DeepONet and PINN to solve the sharp problem. We demonstrate the effectiveness of the present method by testing several equations, including viscous Burger equation, Cavity flow as well Navier-stokes equation. Furthermore, we solve the ill-posed problems that with insufficient boundary conditions by using the present method.