Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems

Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been successfully employed to solve diverse forward and inverse...

Full description

Saved in:
Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 393; no. C; p. 114823
Main Authors: Yu, Jeremy, Lu, Lu, Meng, Xuhui, Karniadakis, George Em
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.04.2022
Elsevier BV
Elsevier
Subjects:
Deep learning
ENGINEERING
Gradient-enhanced
MATHEMATICS AND COMPUTING
Neural networks
Partial differential equations
Physics
Physics-informed neural networks
Residual-based adaptive refinement
Training
Deep learning
Partial differential equations
Residual-based adaptive refinement
Gradient-enhanced
Physics-informed neural networks
ISSN:0045-7825, 1879-2138
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been successfully employed to solve diverse forward and inverse PDE problems. However, one disadvantage of the first generation of PINNs is that they usually have limited accuracy even with many training points. Here, we propose a new method, gradient-enhanced physics-informed neural networks (gPINNs), for improving the accuracy of PINNs. gPINNs leverage gradient information of the PDE residual and embed the gradient into the loss function. We tested gPINNs extensively and demonstrated the effectiveness of gPINNs in both forward and inverse PDE problems. Our numerical results show that gPINN performs better than PINN with fewer training points. Furthermore, we combined gPINN with the method of residual-based adaptive refinement (RAR), a method for improving the distribution of training points adaptively during training, to further improve the performance of gPINN, especially in PDEs with solutions that have steep gradients. •We propose a new method, gradient-enhanced physics-informed neural networks (gPINNs).•gPINNs leverage gradient information of the PDE residual and embed it into the loss.•We demonstrate the effectiveness of gPINNs in both forward and inverse PDE problems.•We combine gPINN with the residual-based adaptive refinement for further improvement.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
SC0019453; FA9550-20-1-0358
USDOE Office of Science (SC)
US Air Force Office of Scientific Research (AFOSR)
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2022.114823