A nudged hybrid analysis and modeling approach for realtime wake-vortex transport and decay prediction

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