Physics-constrained bayesian neural network for fluid flow reconstruction with sparse and noisy data
ABSTRACT: In many applications, flow measurements are usually sparse and possibly noisy. The reconstruction of a high-resolution flow field from limited and imperfect flow information is significant yet challenging. In this work, we propose an innovative physics-constrained Bayesian deep learning ap...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-03-01
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| Series: | Theoretical and Applied Mechanics Letters |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2095034920300295 |
| _version_ | 1819227121810145280 |
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| author | Luning Sun Jian-Xun Wang |
| author_facet | Luning Sun Jian-Xun Wang |
| author_sort | Luning Sun |
| collection | DOAJ |
| description | ABSTRACT: In many applications, flow measurements are usually sparse and possibly noisy. The reconstruction of a high-resolution flow field from limited and imperfect flow information is significant yet challenging. In this work, we propose an innovative physics-constrained Bayesian deep learning approach to reconstruct flow fields from sparse, noisy velocity data, where equation-based constraints are imposed through the likelihood function and uncertainty of the reconstructed flow can be estimated. Specifically, a Bayesian deep neural network is trained on sparse measurement data to capture the flow field. In the meantime, the violation of physical laws will be penalized on a large number of spatiotemporal points where measurements are not available. A non-parametric variational inference approach is applied to enable efficient physics-constrained Bayesian learning. Several test cases on idealized vascular flows with synthetic measurement data are studied to demonstrate the merit of the proposed method. |
| first_indexed | 2024-12-23T10:36:21Z |
| format | Article |
| id | doaj.art-177ce784b1aa4f80a8782aecc5d242b4 |
| institution | Directory Open Access Journal |
| issn | 2095-0349 |
| language | English |
| last_indexed | 2024-12-23T10:36:21Z |
| publishDate | 2020-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Theoretical and Applied Mechanics Letters |
| spelling | doaj.art-177ce784b1aa4f80a8782aecc5d242b42022-12-21T17:50:16ZengElsevierTheoretical and Applied Mechanics Letters2095-03492020-03-01103161169Physics-constrained bayesian neural network for fluid flow reconstruction with sparse and noisy dataLuning Sun0Jian-Xun Wang1Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN; Center for Informatics and Computational Science, University of Notre Dame, Notre Dame, INCorresponding author. (J.X. Wang).; Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN; Center for Informatics and Computational Science, University of Notre Dame, Notre Dame, INABSTRACT: In many applications, flow measurements are usually sparse and possibly noisy. The reconstruction of a high-resolution flow field from limited and imperfect flow information is significant yet challenging. In this work, we propose an innovative physics-constrained Bayesian deep learning approach to reconstruct flow fields from sparse, noisy velocity data, where equation-based constraints are imposed through the likelihood function and uncertainty of the reconstructed flow can be estimated. Specifically, a Bayesian deep neural network is trained on sparse measurement data to capture the flow field. In the meantime, the violation of physical laws will be penalized on a large number of spatiotemporal points where measurements are not available. A non-parametric variational inference approach is applied to enable efficient physics-constrained Bayesian learning. Several test cases on idealized vascular flows with synthetic measurement data are studied to demonstrate the merit of the proposed method.http://www.sciencedirect.com/science/article/pii/S2095034920300295SuperresolutionDenoisingPhysics-Informed Neural NetworksBayesian LearningNavier-Stokes |
| spellingShingle | Luning Sun Jian-Xun Wang Physics-constrained bayesian neural network for fluid flow reconstruction with sparse and noisy data Theoretical and Applied Mechanics Letters Superresolution Denoising Physics-Informed Neural Networks Bayesian Learning Navier-Stokes |
| title | Physics-constrained bayesian neural network for fluid flow reconstruction with sparse and noisy data |
| title_full | Physics-constrained bayesian neural network for fluid flow reconstruction with sparse and noisy data |
| title_fullStr | Physics-constrained bayesian neural network for fluid flow reconstruction with sparse and noisy data |
| title_full_unstemmed | Physics-constrained bayesian neural network for fluid flow reconstruction with sparse and noisy data |
| title_short | Physics-constrained bayesian neural network for fluid flow reconstruction with sparse and noisy data |
| title_sort | physics constrained bayesian neural network for fluid flow reconstruction with sparse and noisy data |
| topic | Superresolution Denoising Physics-Informed Neural Networks Bayesian Learning Navier-Stokes |
| url | http://www.sciencedirect.com/science/article/pii/S2095034920300295 |
| work_keys_str_mv | AT luningsun physicsconstrainedbayesianneuralnetworkforfluidflowreconstructionwithsparseandnoisydata AT jianxunwang physicsconstrainedbayesianneuralnetworkforfluidflowreconstructionwithsparseandnoisydata |