Hierarchical Learning to Solve Partial Differential Equations Using Physics-Informed Neural Networks

2 December 2021

Papers citing "Hierarchical Learning to Solve Partial Differential Equations Using Physics-Informed Neural Networks"

17 / 17 papers shown

Title
Dual Cone Gradient Descent for Training Physics-Informed Neural Networks Youngsik Hwang Dong-Young Lim AI4CE 86 3 0 27 Sep 2024
Physics-informed neural networks (PINNs) for fluid mechanics: A review Shengze Cai Zhiping Mao Zhicheng Wang Minglang Yin George Karniadakis PINN AI4CE 71 1,183 0 20 May 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 166 456 0 18 Dec 2020
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 128 908 0 28 Jul 2020
Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains Matthew Tancik Pratul P. Srinivasan B. Mildenhall Sara Fridovich-Keil N. Raghavan Utkarsh Singhal R. Ramamoorthi Jonathan T. Barron Ren Ng 116 2,414 0 18 Jun 2020
A Derivative-Free Method for Solving Elliptic Partial Differential Equations with Deep Neural Networks Jihun Han Mihai Nica A. Stinchcombe 54 50 0 17 Jan 2020
Multi-scale Deep Neural Networks for Solving High Dimensional PDEs Wei Cai Zhi-Qin John Xu AI4CE 84 39 0 25 Oct 2019
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks Zhi-Qin John Xu Yaoyu Zhang Yaoyu Zhang Yan Xiao Zheng Ma 121 513 0 19 Jan 2019
Data-driven discovery of PDEs in complex datasets Jens Berg K. Nystrom AI4CE PINN 46 141 0 31 Aug 2018
Training behavior of deep neural network in frequency domain Zhi-Qin John Xu Yaoyu Zhang Yan Xiao AI4CE 66 319 0 03 Jul 2018
On the Spectral Bias of Neural Networks Nasim Rahaman A. Baratin Devansh Arpit Felix Dräxler Min Lin Fred Hamprecht Yoshua Bengio Aaron Courville 131 1,436 0 22 Jun 2018
Neural Tangent Kernel: Convergence and Generalization in Neural Networks Arthur Jacot Franck Gabriel Clément Hongler 263 3,194 0 20 Jun 2018
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 117 1,384 0 30 Sep 2017
DGM: A deep learning algorithm for solving partial differential equations Justin A. Sirignano K. Spiliopoulos AI4CE 91 2,060 0 24 Aug 2017
A Closer Look at Memorization in Deep Networks Devansh Arpit Stanislaw Jastrzebski Nicolas Ballas David M. Krueger Emmanuel Bengio ... Tegan Maharaj Asja Fischer Aaron Courville Yoshua Bengio Simon Lacoste-Julien TDI 120 1,816 0 16 Jun 2017
Automatic differentiation in machine learning: a survey A. G. Baydin Barak A. Pearlmutter Alexey Radul J. Siskind PINN AI4CE ODL 156 2,800 0 20 Feb 2015
Adam: A Method for Stochastic Optimization Diederik P. Kingma Jimmy Ba ODL 1.7K 150,006 0 22 Dec 2014