  Data-driven approaches offer novel opportunities for improving the
performance of turbulent flow simulations, which are critical to wide-ranging
applications from wind farms and aerodynamic designs to weather and climate
forecasting. While conventional continuum Navier-Stokes solvers have been the
subject of a significant amount of work in this domain, there has hitherto been
very limited effort in the same direction for the more scalable and highly
performant lattice Boltzmann method (LBM), even though it has been successfully
applied to a variety of turbulent flow simulations using large-eddy simulation
(LES) techniques. In this work, we establish a data-driven framework for the
LES-based lattice Boltzmann simulation of near-wall turbulent flow fields. We
do this by training neural networks using improved delayed detached eddy
simulation data. Crucially, this is done in combination with physics-based
information that substantially constrains the data-driven predictions. Using
data from turbulent channel flow at a friction Reynolds number at $5200$, our
simulations accurately predict the behaviour of the wall model at arbitrary
friction Reynolds numbers up to $1.0 \times 10^6$. In contradistinction with
other models that use direct numerical simulation datasets, our
physics-informed model requires data from very limited regions within the
wall-bounded plane, reducing by three orders of magnitude the quantity of data
needed for training. We also demonstrate that our model can handle data
configurations when the near-wall grid is sparse. Our physics-informed neural
network approach opens up the possibility of employing LBM in combination with
highly specific and therefore much more limited quantities of macroscopic data,
substantially facilitating the investigation of a wide-range of turbulent flow
applications at very large scale.
