196 citations · 1.4k across the 75 of their papers we have counts for
9 papers · 1 filter
Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning
Fan Chen, Jianguo Huang, Chunmei Wang +1
This paper proposes Friedrichs learning as a novel deep learning methodology that can learn the weak solutions of PDEs via a minmax formulation, which transforms the PDE problem in…
Efficient Attention Network: Accelerate Attention by Searching Where to Plug
Zhongzhan Huang, Senwei Liang, Mingfu Liang +2
Recently, many plug-and-play self-attention modules are proposed to enhance the model generalization by exploiting the internal information of deep convolutional neural networks (C…
Neural Network Approximation: Three Hidden Layers Are Enough
Zuowei Shen, Haizhao Yang, Shijun Zhang
A three-hidden-layer neural network with super approximation power is introduced. This network is built with the floor function (), the exponential function ($2^x…
Structure Probing Neural Network Deflation
Yiqi Gu, Chunmei Wang, Haizhao Yang
Deep learning is a powerful tool for solving nonlinear differential equations, but usually, only the solution corresponding to the flattest local minimizer can be found due to the…
Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory
Tao Luo, Haizhao Yang
The problem of solving partial differential equations (PDEs) can be formulated into a least-squares minimization problem, where neural networks are used to parametrize PDE solution…
Deep Network with Approximation Error Being Reciprocal of Width to Power of Square Root of Depth
Zuowei Shen, Haizhao Yang, Shijun Zhang
A new network with super approximation power is introduced. This network is built with Floor () or ReLU () activation function in each neuron and hen…
Rapid Application of the Spherical Harmonic Transform via Interpolative Decomposition Butterfly Factorization
James Bremer, Ze Chen, Haizhao Yang
We describe an algorithm for the application of the forward and inverse spherical harmonic transforms. It is based on a new method for rapidly computing the forward and inverse ass…
SelectNet: Self-paced Learning for High-dimensional Partial Differential Equations
Yiqi Gu, Haizhao Yang, Chao Zhou
The least squares method with deep neural networks as function parametrization has been applied to solve certain high-dimensional partial differential equations (PDEs) successfully…
Deep Network Approximation for Smooth Functions
Jianfeng Lu, Zuowei Shen, Haizhao Yang +1
This paper establishes the (nearly) optimal approximation error characterization of deep rectified linear unit (ReLU) networks for smooth functions in terms of both width and depth…