Physics-Constrained Bayesian Neural Network for Fluid Flow Reconstruction with Sparse and Noisy Data
arXiv:2001.05542
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.
17 pages, 5 figures
References in corpus (16)
- Adam: A Method for Stochastic Optimization
- PyTorch: An Imperative Style, High-Performance Deep Learning Library
- Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising
- Weight Uncertainty in Neural Networks
- Surrogate Modeling for Fluid Flows Based on Physics-Constrained Deep Learning Without Simulation Data
- Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
- Searching for Activation Functions
- Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification
- Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
- Adversarial Uncertainty Quantification in Physics-Informed Neural Networks
- Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks
- Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors
- Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data
- Data-Driven CFD Modeling of Turbulent Flows Through Complex Structures
- Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning
- A particle filter to reconstruct a free-surface flow from a depth camera