8 papers
A Novel Fourier Feature Network for Solving Partial Differential Equations
Qihong Yang, Zhijie Su, Yangtao Deng +1
Building on the foundation of single-hidden-layer neural networks, Fourier Feature Networks (FENs) are proposed, which incorporate Fourier features using , , or a combi…
Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEs
Qihong Yang, Qiaolin He
Solving high-frequency partial differential equations (PDEs) with neural networks is notoriously difficult due to the spectral bias of conventional architectures. We propose the Mu…
Adaptive feature capture method for solving partial differential equations with near singular solutions
Yangtao Deng, Qiaolin He, Xiaoping Wang
Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh gene…
A Novel Tensor Product-Based Neural Network for Solving Partial Differential Equations
Qihong Yang, Yangtao Deng, Qiaolin He +1
This paper presents the Tensor Product Network (TPNet), a novel neural architecture for efficient and accurate function approximation and PDE solving. The core of the proposal invo…
A Multi-Level Deep Framework for Deep Solvers of Partial Differential Equations
Yu Yang, Qiaolin He
In this paper, inspired by the multigrid method, we propose a multi-level deep framework for deep solvers. Overall, it divides the entire training process into different levels of…
A novel number-theoretic sampling method for neural network solutions of partial differential equations
Yu Yang, Pingan He, Xiaoling Peng +1
Traditional Monte Carlo integration using uniform random sampling exhibits degraded efficiency in low-regularity or high-dimensional problems. We propose a novel deep learning fram…