  Particle image velocimetry (PIV) is an effective tool in experimental fluid
mechanics to extract flow fields from images. Recently, convolutional neural
networks (CNNs) have been used to perform PIV analysis with accuracy on par
with classical methods. Here we extend the use of CNNs to analyze PIV data
while providing simultaneous uncertainty quantification on the inferred flow
field. The method we apply in this paper is a Bayesian convolutional neural
network (BCNN) which learns distributions of the CNN weights through
variational Bayes. We compare the performance of three different BCNN models.
The first network estimates flow velocity from image interrogation regions
only. Our second model learns to infer velocity from both the image
interrogation regions and interrogation region cross-correlation maps. Finally,
our best performing network derives velocities from interrogation region
cross-correlation maps only. We find that BCNNs using interrogation region
cross-correlation maps as inputs perform better than those using interrogation
windows only as inputs and discuss reasons why this may be the case.
Additionally, we test the best performing BCNN on a full test image pair,
showing that 100% of true particle displacements can be captured within its 95%
confidence interval. Finally, we show that BCNNs can be generalized to be used
with multi-pass PIV algorithms with a moderate loss in accuracy, which may be
overcome by future work on finetuning and training schemes. To our knowledge,
this is the first effort to use Bayesian neural networks to perform particle
image velocimetry.
