An improved data-free surrogate model for solving partial differential equations using deep neural networks

Abstract Partial differential equations (PDEs) are ubiquitous in natural science and engineering problems. Traditional discrete methods for solving PDEs are usually time-consuming and labor-intensive due to the need for tedious mesh generation and numerical iterations. Recently, deep neural networks...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Xinhai Chen, Rongliang Chen, Qian Wan, Rui Xu, Jie Liu
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/ee9c6c1fc44c4cd888099bf81d409da1
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:ee9c6c1fc44c4cd888099bf81d409da1
record_format	dspace
spelling	oai:doaj.org-article:ee9c6c1fc44c4cd888099bf81d409da12021-12-02T17:18:22ZAn improved data-free surrogate model for solving partial differential equations using deep neural networks10.1038/s41598-021-99037-x2045-2322https://doaj.org/article/ee9c6c1fc44c4cd888099bf81d409da12021-09-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-99037-xhttps://doaj.org/toc/2045-2322Abstract Partial differential equations (PDEs) are ubiquitous in natural science and engineering problems. Traditional discrete methods for solving PDEs are usually time-consuming and labor-intensive due to the need for tedious mesh generation and numerical iterations. Recently, deep neural networks have shown new promise in cost-effective surrogate modeling because of their universal function approximation abilities. In this paper, we borrow the idea from physics-informed neural networks (PINNs) and propose an improved data-free surrogate model, DFS-Net. Specifically, we devise an attention-based neural structure containing a weighting mechanism to alleviate the problem of unstable or inaccurate predictions by PINNs. The proposed DFS-Net takes expanded spatial and temporal coordinates as the input and directly outputs the observables (quantities of interest). It approximates the PDE solution by minimizing the weighted residuals of the governing equations and data-fit terms, where no simulation or measured data are needed. The experimental results demonstrate that DFS-Net offers a good trade-off between accuracy and efficiency. It outperforms the widely used surrogate models in terms of prediction performance on different numerical benchmarks, including the Helmholtz, Klein–Gordon, and Navier–Stokes equations.Xinhai ChenRongliang ChenQian WanRui XuJie LiuNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-17 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Xinhai Chen Rongliang Chen Qian Wan Rui Xu Jie Liu An improved data-free surrogate model for solving partial differential equations using deep neural networks
description	Abstract Partial differential equations (PDEs) are ubiquitous in natural science and engineering problems. Traditional discrete methods for solving PDEs are usually time-consuming and labor-intensive due to the need for tedious mesh generation and numerical iterations. Recently, deep neural networks have shown new promise in cost-effective surrogate modeling because of their universal function approximation abilities. In this paper, we borrow the idea from physics-informed neural networks (PINNs) and propose an improved data-free surrogate model, DFS-Net. Specifically, we devise an attention-based neural structure containing a weighting mechanism to alleviate the problem of unstable or inaccurate predictions by PINNs. The proposed DFS-Net takes expanded spatial and temporal coordinates as the input and directly outputs the observables (quantities of interest). It approximates the PDE solution by minimizing the weighted residuals of the governing equations and data-fit terms, where no simulation or measured data are needed. The experimental results demonstrate that DFS-Net offers a good trade-off between accuracy and efficiency. It outperforms the widely used surrogate models in terms of prediction performance on different numerical benchmarks, including the Helmholtz, Klein–Gordon, and Navier–Stokes equations.
format	article
author	Xinhai Chen Rongliang Chen Qian Wan Rui Xu Jie Liu
author_facet	Xinhai Chen Rongliang Chen Qian Wan Rui Xu Jie Liu
author_sort	Xinhai Chen
title	An improved data-free surrogate model for solving partial differential equations using deep neural networks
title_short	An improved data-free surrogate model for solving partial differential equations using deep neural networks
title_full	An improved data-free surrogate model for solving partial differential equations using deep neural networks
title_fullStr	An improved data-free surrogate model for solving partial differential equations using deep neural networks
title_full_unstemmed	An improved data-free surrogate model for solving partial differential equations using deep neural networks
title_sort	improved data-free surrogate model for solving partial differential equations using deep neural networks
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/ee9c6c1fc44c4cd888099bf81d409da1
work_keys_str_mv	AT xinhaichen animproveddatafreesurrogatemodelforsolvingpartialdifferentialequationsusingdeepneuralnetworks AT rongliangchen animproveddatafreesurrogatemodelforsolvingpartialdifferentialequationsusingdeepneuralnetworks AT qianwan animproveddatafreesurrogatemodelforsolvingpartialdifferentialequationsusingdeepneuralnetworks AT ruixu animproveddatafreesurrogatemodelforsolvingpartialdifferentialequationsusingdeepneuralnetworks AT jieliu animproveddatafreesurrogatemodelforsolvingpartialdifferentialequationsusingdeepneuralnetworks AT xinhaichen improveddatafreesurrogatemodelforsolvingpartialdifferentialequationsusingdeepneuralnetworks AT rongliangchen improveddatafreesurrogatemodelforsolvingpartialdifferentialequationsusingdeepneuralnetworks AT qianwan improveddatafreesurrogatemodelforsolvingpartialdifferentialequationsusingdeepneuralnetworks AT ruixu improveddatafreesurrogatemodelforsolvingpartialdifferentialequationsusingdeepneuralnetworks AT jieliu improveddatafreesurrogatemodelforsolvingpartialdifferentialequationsusingdeepneuralnetworks
_version_	1718381118290395136

An improved data-free surrogate model for solving partial differential equations using deep neural networks

Ejemplares similares