Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partials Differential Equations Article Swipe
Wenrui Hao
,
Xinliang Liu
,
Yahong Yang
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2405.14096
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2405.14096
Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology, and engineering. However, classical neural network methods for solving nonlinear PDEs, such as Physics-Informed Neural Networks (PINN), Deep Ritz methods, and DeepONet, often encounter challenges when confronted with the presence of multiple solutions inherent in the nonlinear problem. These methods may encounter ill-posedness issues. In this paper, we propose a novel approach called the Newton Informed Neural Operator, which builds upon existing neural network techniques to tackle nonlinearities. Our method combines classical Newton methods, addressing well-posed problems, and efficiently learns multiple solutions in a single learning process while requiring fewer supervised data points compared to existing neural network methods.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2405.14096
- https://arxiv.org/pdf/2405.14096
- OA Status
- green
- Cited By
- 2
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4398796519
All OpenAlex metadata
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https://openalex.org/W4398796519Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2405.14096Digital Object Identifier
- Title
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Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partials Differential EquationsWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-05-23Full publication date if available
- Authors
-
Wenrui Hao, Xinliang Liu, Yahong YangList of authors in order
- Landing page
-
https://arxiv.org/abs/2405.14096Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2405.14096Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2405.14096Direct OA link when available
- Concepts
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Operator (biology), Nonlinear system, Applied mathematics, Mathematics, Computer science, Artificial neural network, Differential operator, Mathematical analysis, Artificial intelligence, Physics, Gene, Chemistry, Quantum mechanics, Repressor, Transcription factor, BiochemistryTop concepts (fields/topics) attached by OpenAlex
- Cited by
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2Total citation count in OpenAlex
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2025: 1, 2024: 1Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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