15 citations · 15 across the 4 of their papers we have counts for
4 papers
From Frequency Bias to Spectral Balance: Operator-Aware Preconditioners for PINNs
Roy Y. He, Ying Liang, Hongkai Zhao +1
When neural networks (NNs) are used as a type of nonlinear parametric representation to solve partial differential equations (PDEs), they often display frequency-dependent learning…
What Can One Expect When Solving PDEs Using Shallow Neural Networks?
Roy Y. He, Ying Liang, Hongkai Zhao +1
We use elliptic partial differential equations (PDEs) as examples to show various properties and behaviors when shallow neural networks (SNNs) are used to represent the solutions.…
Deep Network Approximation: Beyond ReLU to Diverse Activation Functions
Shijun Zhang, Jianfeng Lu, Hongkai Zhao
This paper explores the expressive power of deep neural networks for a diverse range of activation functions. An activation function set is defined to encompass the m…
On Enhancing Expressive Power via Compositions of Single Fixed-Size ReLU Network
Shijun Zhang, Jianfeng Lu, Hongkai Zhao
This paper explores the expressive power of deep neural networks through the framework of function compositions. We demonstrate that the repeated compositions of a single fixed-siz…