Physics-constrained bayesian neural network for fluid flow reconstruction with sparse and noisy data

摘要

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 equationbased 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 physicsconstrained Bayesian learning.Several test cases on idealized vascular flows with synthetic measurement data are studied to demonstrate the merit of the proposed method.