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 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.

A novel meta-learning initialization method for physics-informed neural networks

“…The problem of solving PDEs is transformed into an optimization problem of minimizing the loss function. Generally, training of a deep neural network model requires a vast number of labeled data, but the solutions of PDEs can be learned through a PINN model with less labeled data [47,61,57] or even without any labeled data [62,56]. Besides, compared to numerical methods, such as finite difference method [41], wavelets method [31,32,36] and laplace transform method [30], the PINN is a mesh-free approach by utilizing automatic differentiation [4] and avoids the curse of dimensionality [45,20].…”

Super-resolution and denoising of fluid flow using physics-informed convolutional neural networks without high-resolution labels

“…In a similar vein, Subramaniam et al [63] utilized the mass and momentum conservation law to constrain the training of a GAN for turbulence enrichment. Sun and Wang [64] developed a Bayesian physics-informed neural network using Navier-Stokes constrained Stein variational gradient descent to reconstruct fluid flows from limited noisy measurements. These studies have demonstrated the merits of introducing physics constraints.…”

Deploying deep learning in OpenFOAM with TensorFlow

“…In recent times, physics-informed machine learning algorithms have generated a lot of interest for computational fluid dynamics (CFD) applications. These algorithms have been applied for wide variety of tasks such as closure modeling [1][2][3][4][5][6][7][8][9][10][11][12][13], control [14][15][16][17][18], surrogate modeling [19][20][21][22][23][24][25][26][27][28][29][30][31][32], inverse problems [33][34][35][36][37], uncertainty quantification [38][39][40], data assimilation [35,[41][42][43] and super-resolution [44,45]. These studies have demonstrated that the ability of modern machine learning algorithms to learn complicated nonlinear relationships may be leveraged for improving accuracy of quantities of interest as well as significant reductions in computational ...…”