MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs

8 July 2021

Papers citing "MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs"

21 / 21 papers shown

Title
Orthogonal greedy algorithm for linear operator learning with shallow neural network Ye Lin Jiwei Jia Young Ju Lee Ran Zhang 42 1 0 06 Jan 2025
STAResNet: a Network in Spacetime Algebra to solve Maxwell's PDEs Alberto Pepe Sven Buchholz Joan Lasenby 33 0 0 24 Aug 2024
A Hybrid Kernel-Free Boundary Integral Method with Operator Learning for Solving Parametric Partial Differential Equations In Complex Domains Shuo Ling Liwei Tan Wenjun Ying 23 0 0 23 Apr 2024
FMint: Bridging Human Designed and Data Pretrained Models for Differential Equation Foundation Model Zezheng Song Jiaxin Yuan Haizhao Yang AI4CE 40 17 0 23 Apr 2024
Macroscopic auxiliary asymptotic preserving neural networks for the linear radiative transfer equations Hongyan Li Song Jiang Wenjun Sun Liwei Xu Guanyu Zhou 29 2 0 04 Mar 2024
Generating synthetic data for neural operators Erisa Hasani Rachel A. Ward AI4CE 47 8 0 04 Jan 2024
Energy stable neural network for gradient flow equations Gang-Han Fan Tianyu Jin Yuan Lan Yang Xiang Luchan Zhang 36 0 0 17 Sep 2023
Learning Specialized Activation Functions for Physics-informed Neural Networks Honghui Wang Lu Lu Shiji Song Gao Huang PINN AI4CE 16 11 0 08 Aug 2023
Learning Green's Function Efficiently Using Low-Rank Approximations Kishan Wimalawarne Taiji Suzuki S. Langer 19 1 0 01 Aug 2023
Capturing the Diffusive Behavior of the Multiscale Linear Transport Equations by Asymptotic-Preserving Convolutional DeepONets Keke Wu Xiongbin Yan Shi Jin Zheng Ma 28 6 0 28 Jun 2023
$Laplace-fPINNs: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion$ Laplace-fPINNs: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion Xiongbin Yan Zhi-Qin John Xu Zheng Ma 32 2 0 03 Apr 2023
A model-data asymptotic-preserving neural network method based on micro-macro decomposition for gray radiative transfer equations Haiyang Li Song Jiang Wenjun Sun Liwei Xu Guanyu Zhou 11 11 0 11 Dec 2022
Bayesian Inversion with Neural Operator (BINO) for Modeling Subdiffusion: Forward and Inverse Problems Xiongbin Yan Z. Xu Zheng Ma 14 2 0 22 Nov 2022
Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications Zhongkai Hao Songming Liu Yichi Zhang Chengyang Ying Yao Feng Hang Su Jun Zhu PINN AI4CE 35 89 0 15 Nov 2022
Approximation of Functionals by Neural Network without Curse of Dimensionality Yahong Yang Yang Xiang 29 6 0 28 May 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
Physics-Informed Neural Operator for Learning Partial Differential Equations Zong-Yi Li Hongkai Zheng Nikola B. Kovachki David Jin Haoxuan Chen Burigede Liu Kamyar Azizzadenesheli Anima Anandkumar AI4CE 62 384 0 06 Nov 2021
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks Sizhuang He Hanwen Wang P. Perdikaris 131 438 0 18 Dec 2020
Fourier Neural Operator for Parametric Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 226 2,287 0 18 Oct 2020
Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains Ziqi Liu Wei Cai Zhi-Qin John Xu AI4CE 223 122 0 22 Jul 2020