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.
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.
no code implementations • 6 Apr 2023 • Guanhang Lei, Lei Shi
Regularized pairwise ranking with Gaussian kernels is one of the cutting-edge learning algorithms.
