Physics-Informed Neural Networks with Complementary Soft and Hard Constraints for Solving Complex Boundary Navier-Stokes Equations Article Swipe
Chuyu Zhou
,
Tianyu Li
,
Chenxi Lan
,
Rui Du
,
Guoguo Xin
,
Pengyu Nan
,
Hangzhou Yang
,
Guoqing Wang
,
Xun Liu
,
Wei Li
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2411.08122
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2411.08122
Soft- and hard-constrained Physics Informed Neural Networks (PINNs) have achieved great success in solving partial differential equations (PDEs). However, these methods still face great challenges when solving the Navier-Stokes equations (NSEs) with complex boundary conditions. To address these challenges, this paper introduces a novel complementary scheme combining soft and hard constraint PINN methods. The soft-constrained part is thus formulated to obtain the preliminary results with a lighter training burden, upon which refined results are then achieved using a more sophisticated hard-constrained mechanism with a primary network and a distance metric network. Specifically, the soft-constrained part focuses on boundary points, while the primary network emphasizes inner domain points, primarily through PDE loss. Additionally, the novel distance metric network is proposed to predict the power function of the distance from a point to the boundaries, which serves as the weighting factor for the first two components. This approach ensures accurate predictions for both boundary and inner domain areas. The effectiveness of the proposed method on the NSEs problem with complex boundary conditions is demonstrated by solving a 2D cylinder wake problem and a 2D blocked cavity flow with a segmented inlet problem, achieving significantly higher accuracy compared to traditional soft- and hard-constrained PINN approaches. Given PINN's inherent advantages in solving the inverse and the large-scale problems, which are challenging for traditional computational fluid dynamics (CFD) methods, this approach holds promise for the inverse design of required flow fields by specifically-designed boundary conditions and the reconstruction of large-scale flow fields by adding a limited number of training input points. The code for our approach will be made publicly available.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2411.08122
- https://arxiv.org/pdf/2411.08122
- OA Status
- green
- Cited By
- 3
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4404406988
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W4404406988Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2411.08122Digital Object Identifier
- Title
-
Physics-Informed Neural Networks with Complementary Soft and Hard Constraints for Solving Complex Boundary Navier-Stokes EquationsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-11-12Full publication date if available
- Authors
-
Chuyu Zhou, Tianyu Li, Chenxi Lan, Rui Du, Guoguo Xin, Pengyu Nan, Hangzhou Yang, Guoqing Wang, Xun Liu, Wei LiList of authors in order
- Landing page
-
https://arxiv.org/abs/2411.08122Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2411.08122Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2411.08122Direct OA link when available
- Concepts
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Artificial neural network, Boundary (topology), Navier–Stokes equations, Physics, Computer science, Statistical physics, Applied mathematics, Classical mechanics, Mathematics, Mathematical analysis, Mechanics, Artificial intelligence, CompressibilityTop concepts (fields/topics) attached by OpenAlex
- Cited by
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3Total citation count in OpenAlex
- Citations by year (recent)
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2025: 3Per-year citation counts (last 5 years)
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.which | 70, 133, 214 |
| abstract_inverted_index.while | 99 |
| abstract_inverted_index.(NSEs) | 30 |
| abstract_inverted_index.Neural | 5 |
| abstract_inverted_index.PINN's | 203 |
| abstract_inverted_index.adding | 248 |
| abstract_inverted_index.areas. | 155 |
| abstract_inverted_index.cavity | 183 |
| abstract_inverted_index.design | 231 |
| abstract_inverted_index.domain | 105, 154 |
| abstract_inverted_index.factor | 138 |
| abstract_inverted_index.fields | 235, 246 |
| abstract_inverted_index.higher | 192 |
| abstract_inverted_index.method | 161 |
| abstract_inverted_index.metric | 89, 115 |
| abstract_inverted_index.number | 251 |
| abstract_inverted_index.obtain | 60 |
| abstract_inverted_index.scheme | 45 |
| abstract_inverted_index.serves | 134 |
| abstract_inverted_index.(PDEs). | 17 |
| abstract_inverted_index.(PINNs) | 7 |
| abstract_inverted_index.Physics | 3 |
| abstract_inverted_index.address | 36 |
| abstract_inverted_index.blocked | 182 |
| abstract_inverted_index.burden, | 68 |
| abstract_inverted_index.complex | 32, 167 |
| abstract_inverted_index.ensures | 146 |
| abstract_inverted_index.focuses | 95 |
| abstract_inverted_index.inverse | 209, 230 |
| abstract_inverted_index.lighter | 66 |
| abstract_inverted_index.limited | 250 |
| abstract_inverted_index.methods | 20 |
| abstract_inverted_index.network | 85, 102, 116 |
| abstract_inverted_index.partial | 14 |
| abstract_inverted_index.points, | 98, 106 |
| abstract_inverted_index.points. | 255 |
| abstract_inverted_index.predict | 120 |
| abstract_inverted_index.primary | 84, 101 |
| abstract_inverted_index.problem | 165, 178 |
| abstract_inverted_index.promise | 227 |
| abstract_inverted_index.refined | 71 |
| abstract_inverted_index.results | 63, 72 |
| abstract_inverted_index.solving | 13, 26, 173, 207 |
| abstract_inverted_index.success | 11 |
| abstract_inverted_index.through | 108 |
| abstract_inverted_index.However, | 18 |
| abstract_inverted_index.Informed | 4 |
| abstract_inverted_index.Networks | 6 |
| abstract_inverted_index.accuracy | 193 |
| abstract_inverted_index.accurate | 147 |
| abstract_inverted_index.achieved | 9, 75 |
| abstract_inverted_index.approach | 145, 225, 260 |
| abstract_inverted_index.boundary | 33, 97, 151, 168, 238 |
| abstract_inverted_index.compared | 194 |
| abstract_inverted_index.cylinder | 176 |
| abstract_inverted_index.distance | 88, 114, 126 |
| abstract_inverted_index.dynamics | 221 |
| abstract_inverted_index.function | 123 |
| abstract_inverted_index.inherent | 204 |
| abstract_inverted_index.methods, | 223 |
| abstract_inverted_index.methods. | 52 |
| abstract_inverted_index.network. | 90 |
| abstract_inverted_index.problem, | 189 |
| abstract_inverted_index.proposed | 118, 160 |
| abstract_inverted_index.publicly | 264 |
| abstract_inverted_index.required | 233 |
| abstract_inverted_index.training | 67, 253 |
| abstract_inverted_index.achieving | 190 |
| abstract_inverted_index.combining | 46 |
| abstract_inverted_index.equations | 16, 29 |
| abstract_inverted_index.mechanism | 81 |
| abstract_inverted_index.primarily | 107 |
| abstract_inverted_index.problems, | 213 |
| abstract_inverted_index.segmented | 187 |
| abstract_inverted_index.weighting | 137 |
| abstract_inverted_index.advantages | 205 |
| abstract_inverted_index.available. | 265 |
| abstract_inverted_index.challenges | 24 |
| abstract_inverted_index.conditions | 169, 239 |
| abstract_inverted_index.constraint | 50 |
| abstract_inverted_index.emphasizes | 103 |
| abstract_inverted_index.formulated | 58 |
| abstract_inverted_index.introduces | 41 |
| abstract_inverted_index.approaches. | 201 |
| abstract_inverted_index.boundaries, | 132 |
| abstract_inverted_index.challenges, | 38 |
| abstract_inverted_index.challenging | 216 |
| abstract_inverted_index.components. | 143 |
| abstract_inverted_index.conditions. | 34 |
| abstract_inverted_index.large-scale | 212, 244 |
| abstract_inverted_index.predictions | 148 |
| abstract_inverted_index.preliminary | 62 |
| abstract_inverted_index.traditional | 196, 218 |
| abstract_inverted_index.demonstrated | 171 |
| abstract_inverted_index.differential | 15 |
| abstract_inverted_index.Additionally, | 111 |
| abstract_inverted_index.Navier-Stokes | 28 |
| abstract_inverted_index.Specifically, | 91 |
| abstract_inverted_index.complementary | 44 |
| abstract_inverted_index.computational | 219 |
| abstract_inverted_index.effectiveness | 157 |
| abstract_inverted_index.significantly | 191 |
| abstract_inverted_index.sophisticated | 79 |
| abstract_inverted_index.reconstruction | 242 |
| abstract_inverted_index.hard-constrained | 2, 80, 199 |
| abstract_inverted_index.soft-constrained | 54, 93 |
| abstract_inverted_index.specifically-designed | 237 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 10 |
| citation_normalized_percentile |