Two-stage initial-value iterative physics-informed neural networks for
simulating solitary waves of nonlinear wave equations

Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations

2 September 2024

Ming Zhong

George Karniadakis

Papers citing "Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations"

10 / 10 papers shown

Title
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 133 909 0 28 Jul 2020
B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data Liu Yang Xuhui Meng George Karniadakis PINN 231 785 0 13 Mar 2020
DeepXDE: A deep learning library for solving differential equations Lu Lu Xuhui Meng Zhiping Mao George Karniadakis PINN AI4CE 97 1,528 0 10 Jul 2019
A Review of automatic differentiation and its efficient implementation C. Margossian 52 315 0 12 Nov 2018
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems Dongkun Zhang Lu Lu Ling Guo George Karniadakis UQCV 105 408 0 21 Sep 2018
PDE-Net: Learning PDEs from Data Zichao Long Yiping Lu Xianzhong Ma Bin Dong DiffM AI4CE 43 755 0 26 Oct 2017
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 119 1,387 0 30 Sep 2017
Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review T. Poggio H. Mhaskar Lorenzo Rosasco Brando Miranda Q. Liao 97 576 0 02 Nov 2016
Automatic differentiation in machine learning: a survey A. G. Baydin Barak A. Pearlmutter Alexey Radul J. Siskind PINN AI4CE ODL 158 2,803 0 20 Feb 2015
Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification Kaiming He Xinming Zhang Shaoqing Ren Jian Sun VLM 323 18,613 0 06 Feb 2015