Multi-scale Deep Neural Networks for Solving High Dimensional PDEs

25 October 2019

Papers citing "Multi-scale Deep Neural Networks for Solving High Dimensional PDEs"

17 / 17 papers shown

Title
Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systems Siavash Khodakarami Vivek Oommen Aniruddha Bora George Karniadakis AI4CE 65 2 0 17 Mar 2025
Addressing Spectral Bias of Deep Neural Networks by Multi-Grade Deep Learning Ronglong Fang Yuesheng Xu 29 3 0 21 Oct 2024
Transfer Learning on Multi-Dimensional Data: A Novel Approach to Neural Network-Based Surrogate Modeling Adrienne M. Propp Daniel M. Tartakovsky AI4CE 33 2 0 16 Oct 2024
On the expressiveness and spectral bias of KANs Yixuan Wang Jonathan W. Siegel Ziming Liu Thomas Y. Hou 37 10 0 02 Oct 2024
Dilated convolution neural operator for multiscale partial differential equations Bo Xu Xinliang Liu Lei Zhang AI4CE 34 3 0 16 Jul 2024
Approximation of Solution Operators for High-dimensional PDEs Nathan Gaby Xiaojing Ye 30 0 0 18 Jan 2024
Neural Control of Parametric Solutions for High-dimensional Evolution PDEs Nathan Gaby X. Ye Haomin Zhou 19 6 0 31 Jan 2023
Computing non-equilibrium trajectories by a deep learning approach E. Simonnet AI4CE 27 6 0 08 Oct 2022
On the Activation Function Dependence of the Spectral Bias of Neural Networks Q. Hong Jonathan W. Siegel Qinyan Tan Jinchao Xu 34 23 0 09 Aug 2022
A Neural Network Approach for Homogenization of Multiscale Problems Jihun Han Yoonsang Lee 35 13 0 04 Jun 2022
BI-GreenNet: Learning Green's functions by boundary integral network Guochang Lin Fu-jun Chen Pipi Hu Xiang Chen Junqing Chen Jun Wang Zuoqiang Shi 34 20 0 28 Apr 2022
Overview frequency principle/spectral bias in deep learning Z. Xu Yaoyu Zhang Tao Luo FaML 33 66 0 19 Jan 2022
Hierarchical Learning to Solve Partial Differential Equations Using Physics-Informed Neural Networks Jihun Han Yoonsang Lee AI4CE 24 10 0 02 Dec 2021
An Upper Limit of Decaying Rate with Respect to Frequency in Deep Neural Network Tao Luo Zheng Ma Zhiwei Wang Z. Xu Yaoyu Zhang 4 4 0 25 May 2021
Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning Fan Chen J. Huang Chunmei Wang Haizhao Yang 28 30 0 15 Dec 2020
Wide-band butterfly network: stable and efficient inversion via multi-frequency neural networks Matthew T.C. Li L. Demanet Leonardo Zepeda-Núnez 35 8 0 24 Nov 2020
A priori generalization error for two-layer ReLU neural network through minimum norm solution Zhi-Qin John Xu Jiwei Zhang Yaoyu Zhang Chengchao Zhao MLT 8 1 0 06 Dec 2019