  We investigate the application of artificial neural networks to stabilize
proper orthogonal decomposition based reduced order models for quasi-stationary
geophysical turbulent flows. An extreme learning machine concept is introduced
for computing an eddy-viscosity closure dynamically to incorporate the effects
of the truncated modes. We consider a four-gyre wind-driven ocean circulation
problem as our prototype setting to assess the performance of the proposed
data-driven approach. Our framework provides a significant reduction in
computational time and effectively retains the dynamics of the full-order model
during the forward simulation period beyond the training data set. Furthermore,
we show that the method is robust for larger choices of time steps and can be
used as an efficient and reliable tool for long time integration of general
circulation models.
