  Physics-informed neural networks (PINNs) can be used to solve partial
differential equations (PDEs) and identify hidden variables by incorporating
the governing equations into neural network training. In this study, we apply
PINNs to the assimilation of turbulent mean flow data and investigate the
method's ability to identify inaccessible variables and closure terms from
sparse data. Using high-fidelity large-eddy simulation (LES) data and particle
image velocimetry (PIV) measured mean fields, we show that PINNs are suitable
for simultaneously identifying multiple missing quantities in turbulent flows
and providing continuous and differentiable mean fields consistent with the
provided PDEs. In this way, consistent and complete mean states can be
provided, which are essential for linearized mean field methods. The presented
method does not require a grid or discretization scheme, is easy to implement,
and can be used for a wide range of applications, making it a very promising
tool for mean field-based methods in fluid mechanics.
