Unsupervised Legendre-Galerkin Neural Network for Singularly Perturbed Partial Differential Equations

21 July 2022

Papers citing "Unsupervised Legendre-Galerkin Neural Network for Singularly Perturbed Partial Differential Equations"

28 / 28 papers shown

Title
A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks Chen-Chun Wu Min Zhu Qinyan Tan Yadhu Kartha Lu Lu 63 371 0 21 Jul 2022
Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport Lu Lu R. Pestourie Steven G. Johnson Giuseppe Romano AI4CE 47 107 0 14 Apr 2022
Respecting causality is all you need for training physics-informed neural networks Sizhuang He Shyam Sankaran P. Perdikaris PINN CML AI4CE 131 200 0 14 Mar 2022
MIONet: Learning multiple-input operators via tensor product Pengzhan Jin Shuai Meng Lu Lu 50 169 0 12 Feb 2022
Hierarchical Learning to Solve Partial Differential Equations Using Physics-Informed Neural Networks Jihun Han Yoonsang Lee AI4CE 39 10 0 02 Dec 2021
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 91 406 0 06 Nov 2021
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems Jeremy Yu Lu Lu Xuhui Meng George Karniadakis PINN AI4CE 61 462 0 01 Nov 2021
Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations Benjamin Moseley Andrew Markham T. Nissen‐Meyer PINN 71 221 0 16 Jul 2021
Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space Zhen Chen V. Churchill Kailiang Wu D. Xiu AI4CE 40 47 0 07 Jun 2021
Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control M. Ainsworth Justin Dong 23 37 0 28 May 2021
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets Sizhuang He Hanwen Wang P. Perdikaris AI4CE 75 695 0 19 Mar 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 161 455 0 18 Dec 2020
Deep neural network for solving differential equations motivated by Legendre-Galerkin approximation Bryce Chudomelka Youngjoon Hong Hyunwoo J. Kim Jinyoung Park 46 7 0 24 Oct 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 453 2,384 0 18 Oct 2020
Weak Form Theory-guided Neural Network (TgNN-wf) for Deep Learning of Subsurface Single and Two-phase Flow R. Xu Dongxiao Zhang Miao Rong Nanzhe Wang AI4CE 45 49 0 08 Sep 2020
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 119 903 0 28 Jul 2020
Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks K. Shukla P. C. D. Leoni J. Blackshire D. Sparkman George Karniadakis PINN AI4CE 64 232 0 07 May 2020
B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data Liu Yang Xuhui Meng George Karniadakis PINN 228 779 0 13 Mar 2020
On generalized residue network for deep learning of unknown dynamical systems Zhen Chen D. Xiu AI4CE 41 46 0 23 Jan 2020
Variational Physics-Informed Neural Networks For Solving Partial Differential Equations E. Kharazmi Z. Zhang George Karniadakis 58 242 0 27 Nov 2019
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators Lu Lu Pengzhan Jin George Karniadakis 198 2,108 0 08 Oct 2019
PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs Xuhui Meng Zhen Li Dongkun Zhang George Karniadakis PINN AI4CE 54 450 0 23 Sep 2019
DeepXDE: A deep learning library for solving differential equations Lu Lu Xuhui Meng Zhiping Mao George Karniadakis PINN AI4CE 95 1,521 0 10 Jul 2019
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems Dongkun Zhang Lu Lu Ling Guo George Karniadakis UQCV 100 407 0 21 Sep 2018
On the Spectral Bias of Neural Networks Nasim Rahaman A. Baratin Devansh Arpit Felix Dräxler Min Lin Fred Hamprecht Yoshua Bengio Aaron Courville 120 1,432 0 22 Jun 2018
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 113 1,380 0 30 Sep 2017
DGM: A deep learning algorithm for solving partial differential equations Justin A. Sirignano K. Spiliopoulos AI4CE 84 2,057 0 24 Aug 2017
Multi-Scale Convolutional Neural Networks for Time Series Classification Zhicheng Cui Wenlin Chen Yixin Chen 35 565 0 22 Mar 2016