Solving Parametric PDEs with Radial Basis Functions and Deep Neural Networks

no code implementations • 10 Apr 2024 • Guanhang Lei, Zhen Lei, Lei Shi, Chenyu Zeng

We propose the POD-DNN, a novel algorithm leveraging deep neural networks (DNNs) along with radial basis functions (RBFs) in the context of the proper orthogonal decomposition (POD) reduced basis method (RBM), aimed at approximating the parametric mapping of parametric partial differential equations on irregular domains.

Solving PDEs on Spheres with Physics-Informed Convolutional Neural Networks

no code implementations • 18 Aug 2023 • Guanhang Lei, Zhen Lei, Lei Shi, Chenyu Zeng, Ding-Xuan Zhou

In this paper, we establish rigorous analysis of the physics-informed convolutional neural network (PICNN) for solving PDEs on the sphere.

Solving parametric partial differential equations with deep rectified quadratic unit neural networks

no code implementations • 14 Mar 2022 • Zhen Lei, Lei Shi, Chenyu Zeng

In this study, we investigate the expressive power of deep rectified quadratic unit (ReQU) neural networks for approximating the solution maps of parametric PDEs.