DWNN: Deep Wavelet Neural Network for Solving Partial Differential Equations

In this paper, we propose a deep wavelet neural network (DWNN) model to approximate the natural phenomena that are described by some classical PDEs. Concretely, introduce wavelets architecture obtain fine feature description and extraction. That is, constructs expansion layer based on family of vanishing momentum wavelets. Second, Gaussian error function is considered as activation owing its fast convergence rate zero-centered output. Third, design cost considering residual governing equation, initial/boundary conditions an adjustable term observations. The last added deal with shock wave problems interface problems, which conducive rectify model. Finally, variety numerical experiments carried out demonstrate effectiveness proposed approach. results validate our method more accurate than state-of-the-art