Physics-constrained bayesian neural network for fluid flow reconstruction with sparse and noisy data
By Luning Sun, Jian-Xun Wang. 2020
212 citations recorded by the source corpus.
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.
Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mechanics
- G. Em Karniadakis
- Zhiping Mao
- Jian-Xun Wang
- Shengze Cai
- Han Gao
- Zhicheng Wang
- Paris Perdikaris
- Sifan Wang
In Computer Vision and Pattern Recognition
- Jian-Xun Wang
- Sifan Wang
- G. Em Karniadakis
- Zhiping Mao
- Han Gao
- Paris Perdikaris
- Shengze Cai
- Wei Peng
In Statistical and Nonlinear Physics
- G. Em Karniadakis
- Shengze Cai
- Zhiping Mao
- Jian-Xun Wang
- Zhicheng Wang
- Han Gao
- Paris Perdikaris
- Sifan Wang
Citations in the corpus
- Self-adaptive loss balanced Physics-informed neural networks (2021, methodology): “Variational inference [29] was used to estimate the posterior distributions of the reconstructed flow [30].”
- When and why PINNs fail to train: A neural tangent kernel perspective (2020, background): “Thanks to the approximation capabilities of neural networks, physics-informed neural networks (PINNs) have already led to a series of remarkable results across a range of problems in computational science and engineering, including fluids mechanics [1, 2, 4, 5], bio-engineering [6, 7], meta-material”
- Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems (2021, background): “Also, the GCN can be formulated as a Bayesian network via variational inference to deal with data noise and quantify the uncertainty [55].”
- Physics-informed neural networks (PINNs) for fluid mechanics: a review (2021, background): “Another important extension is the uncertainty quantification for the PDE solutions inferred by neural networks [29,30,31,32,33].”