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Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Partial differential equations (PDEs) play a central role in the mathematical analysis and modeling of complex dynamic processes across all corners of science and engineering. Their solution often requires laborious analytical or computational tools, associated with a cost that is markedly amplified...

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Detalles Bibliográficos
Autores principales: Wang, Sifan, Wang, Hanwen, Perdikaris, Paris
Formato: Online Artículo Texto
Lenguaje:English
Publicado: American Association for the Advancement of Science 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8480920/
https://www.ncbi.nlm.nih.gov/pubmed/34586842
http://dx.doi.org/10.1126/sciadv.abi8605
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author Wang, Sifan
Wang, Hanwen
Perdikaris, Paris
author_facet Wang, Sifan
Wang, Hanwen
Perdikaris, Paris
author_sort Wang, Sifan
collection PubMed
description Partial differential equations (PDEs) play a central role in the mathematical analysis and modeling of complex dynamic processes across all corners of science and engineering. Their solution often requires laborious analytical or computational tools, associated with a cost that is markedly amplified when different scenarios need to be investigated, for example, corresponding to different initial or boundary conditions, different inputs, etc. In this work, we introduce physics-informed DeepONets, a deep learning framework for learning the solution operator of arbitrary PDEs, even in the absence of any paired input-output training data. We illustrate the effectiveness of the proposed framework in rapidly predicting the solution of various types of parametric PDEs up to three orders of magnitude faster compared to conventional PDE solvers, setting a previously unexplored paradigm for modeling and simulation of nonlinear and nonequilibrium processes in science and engineering.
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spelling pubmed-84809202021-10-08 Learning the solution operator of parametric partial differential equations with physics-informed DeepONets Wang, Sifan Wang, Hanwen Perdikaris, Paris Sci Adv Physical and Materials Sciences Partial differential equations (PDEs) play a central role in the mathematical analysis and modeling of complex dynamic processes across all corners of science and engineering. Their solution often requires laborious analytical or computational tools, associated with a cost that is markedly amplified when different scenarios need to be investigated, for example, corresponding to different initial or boundary conditions, different inputs, etc. In this work, we introduce physics-informed DeepONets, a deep learning framework for learning the solution operator of arbitrary PDEs, even in the absence of any paired input-output training data. We illustrate the effectiveness of the proposed framework in rapidly predicting the solution of various types of parametric PDEs up to three orders of magnitude faster compared to conventional PDE solvers, setting a previously unexplored paradigm for modeling and simulation of nonlinear and nonequilibrium processes in science and engineering. American Association for the Advancement of Science 2021-09-29 /pmc/articles/PMC8480920/ /pubmed/34586842 http://dx.doi.org/10.1126/sciadv.abi8605 Text en Copyright © 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY). https://creativecommons.org/licenses/by/4.0/This is an open-access article distributed under the terms of the Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Physical and Materials Sciences
Wang, Sifan
Wang, Hanwen
Perdikaris, Paris
Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
title Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
title_full Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
title_fullStr Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
title_full_unstemmed Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
title_short Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
title_sort learning the solution operator of parametric partial differential equations with physics-informed deeponets
topic Physical and Materials Sciences
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8480920/
https://www.ncbi.nlm.nih.gov/pubmed/34586842
http://dx.doi.org/10.1126/sciadv.abi8605
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