  High-resolution reconstruction of flow-field data from low-resolution and
noisy measurements is of interest due to the prevalence of such problems in
experimental fluid mechanics, where the measurement data are in general sparse,
incomplete and noisy. Deep-learning approaches have been shown suitable for
such super-resolution tasks. However, a high number of high-resolution examples
is needed, which may not be available for many cases. Moreover, the obtained
predictions may lack in complying with the physical principles, e.g. mass and
momentum conservation. Physics-informed deep learning provides frameworks for
integrating data and physical laws for learning. In this study, we apply
physics-informed neural networks (PINNs) for super-resolution of flow-field
data both in time and space from a limited set of noisy measurements without
having any high-resolution reference data. Our objective is to obtain a
continuous solution of the problem, providing a physically-consistent
prediction at any point in the solution domain. We demonstrate the
applicability of PINNs for the super-resolution of flow-field data in time and
space through three canonical cases: Burgers' equation, two-dimensional vortex
shedding behind a circular cylinder and the minimal turbulent channel flow. The
robustness of the models is also investigated by adding synthetic Gaussian
noise. Furthermore, we show the capabilities of PINNs to improve the resolution
and reduce the noise in a real experimental dataset consisting of
hot-wire-anemometry measurements. Our results show the adequate capabilities of
PINNs in the context of data augmentation for experiments in fluid mechanics.
