Diffeomorphism neural operator for various domains and parameters of partial differential equations
Abstract Solving partial differential equations (PDEs) across varying geometric domains and parameters represents a significant challenge in fields such as materials science, engineering, design and medical imaging, primarily due to the high computing cost associated with recomputing the solution fo...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-01-01
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| Series: | Communications Physics |
| Online Access: | https://doi.org/10.1038/s42005-024-01911-3 |
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| _version_ | 1841544574548312064 |
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| author | Zhiwei Zhao Changqing Liu Yingguang Li Zhibin Chen Xu Liu |
| author_facet | Zhiwei Zhao Changqing Liu Yingguang Li Zhibin Chen Xu Liu |
| author_sort | Zhiwei Zhao |
| collection | DOAJ |
| description | Abstract Solving partial differential equations (PDEs) across varying geometric domains and parameters represents a significant challenge in fields such as materials science, engineering, design and medical imaging, primarily due to the high computing cost associated with recomputing the solution for every change in geometry or parameters. This paper presents a neural operator learning framework for solving PDEs with various domains and parameters, named diffeomorphism neural operator (DNO). The framework transforms the problem of operator learning on varying domains into learning on a generic domain through a diffeomorphic mapping. The efficiency and effectiveness of DNO are validated in experiments that rapidly provide solutions to various PDEs across different domains and parameters. Our method obtains solutions multiple orders of magnitude faster when adapted to changes in shape and size. DNO offers advangates for a broad spectrum of scientific and engineering applications that require dynamic domain and parameter handling. |
| format | Article |
| id | doaj-art-32950c3f0d094e65b3be5f9efd6d790b |
| institution | Kabale University |
| issn | 2399-3650 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Communications Physics |
| spelling | doaj-art-32950c3f0d094e65b3be5f9efd6d790b2025-01-12T12:26:43ZengNature PortfolioCommunications Physics2399-36502025-01-018111110.1038/s42005-024-01911-3Diffeomorphism neural operator for various domains and parameters of partial differential equationsZhiwei Zhao0Changqing Liu1Yingguang Li2Zhibin Chen3Xu Liu4College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and AstronauticsCollege of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and AstronauticsCollege of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and AstronauticsCollege of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and AstronauticsSchool of Mechanical and Power Engineering, Nanjing Tech UniversityAbstract Solving partial differential equations (PDEs) across varying geometric domains and parameters represents a significant challenge in fields such as materials science, engineering, design and medical imaging, primarily due to the high computing cost associated with recomputing the solution for every change in geometry or parameters. This paper presents a neural operator learning framework for solving PDEs with various domains and parameters, named diffeomorphism neural operator (DNO). The framework transforms the problem of operator learning on varying domains into learning on a generic domain through a diffeomorphic mapping. The efficiency and effectiveness of DNO are validated in experiments that rapidly provide solutions to various PDEs across different domains and parameters. Our method obtains solutions multiple orders of magnitude faster when adapted to changes in shape and size. DNO offers advangates for a broad spectrum of scientific and engineering applications that require dynamic domain and parameter handling.https://doi.org/10.1038/s42005-024-01911-3 |
| spellingShingle | Zhiwei Zhao Changqing Liu Yingguang Li Zhibin Chen Xu Liu Diffeomorphism neural operator for various domains and parameters of partial differential equations Communications Physics |
| title | Diffeomorphism neural operator for various domains and parameters of partial differential equations |
| title_full | Diffeomorphism neural operator for various domains and parameters of partial differential equations |
| title_fullStr | Diffeomorphism neural operator for various domains and parameters of partial differential equations |
| title_full_unstemmed | Diffeomorphism neural operator for various domains and parameters of partial differential equations |
| title_short | Diffeomorphism neural operator for various domains and parameters of partial differential equations |
| title_sort | diffeomorphism neural operator for various domains and parameters of partial differential equations |
| url | https://doi.org/10.1038/s42005-024-01911-3 |
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