  Turbulence remains a problem that is yet to be fully understood, with
experimental and numerical studies aiming to fully characterise the statistical
properties of turbulent flows. Such studies require huge amount of resources to
capture, simulate, store and analyse the data. In this work, we present
physics-informed neural network (PINN) based methods to predict flow quantities
and features of two-dimensional turbulence with the help of sparse data in a
rectangular domain with periodic boundaries. While the PINN model can reproduce
all the statistics at large scales, the small scale properties are not captured
properly. We introduce a new PINN model that can effectively capture the energy
distribution at small scales performing better than the standard PINN based
approach. It relies on the training of the low and high wavenumber behaviour
separately leading to a better estimate of the full turbulent flow. With 0.1 %
training data, we observe that the new PINN model captures the turbulent field
at inertial scales leading to a general agreement of the kinetic energy spectra
upto eight to nine decades as compared with the solutions from direct numerical
simulation (DNS). We further apply these techniques to successfully capture the
statistical behaviour of large scale modes in the turbulent flow. We believe
such methods to have significant applications in enhancing the retrieval of
existing turbulent data sets at even shorter time intervals.
