  We put forth a long short-term memory (LSTM) nudging framework for the
enhancement of reduced order models (ROMs) of fluid flows utilizing noisy
measurements for air traffic improvements. Toward emerging applications of
digital twins in aviation, the proposed approach allows for constructing a
realtime predictive tool for wake-vortex transport and decay systems. We build
on the fact that in realistic application, there are uncertainties in initial
and boundary conditions, model parameters, as well as measurements. Moreover,
conventional nonlinear ROMs based on Galerkin projection (GROMs) suffer from
imperfection and solution instabilities, especially for advection-dominated
flows with slow decay in the Kolmogorov width. In the presented LSTM nudging
(LSTM-N) approach, we fuse forecasts from a combination of imperfect GROM and
uncertain state estimates, with sparse Eulerian sensor measurements to provide
more reliable predictions in a dynamical data assimilation framework. We
illustrate our concept by solving a two-dimensional vorticity transport
equation. We investigate the effects of measurements noise and state estimate
uncertainty on the performance of the LSTM-N behavior. We also demonstrate that
it can sufficiently handle different levels of temporal and spatial measurement
sparsity, and offer a huge potential in developing next-generation digital twin
technologies.
