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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...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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American Association for the Advancement of Science
2021
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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. |
format | Online Article Text |
id | pubmed-8480920 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | American Association for the Advancement of Science |
record_format | MEDLINE/PubMed |
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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