  This proposed work introduces a data-assimilation-assisted approach to train
neural networks, aimed at effectively reducing epistemic uncertainty in state
estimates of separated flows. This method, referred to as model-consistent
training, ensures that input features are derived directly from physics-based
models, such as Reynolds Averaged Navier Stokes (RANS) turbulence models, to
accurately represent the current state of the flow. Autoencoders have been
selected for this task due to their capability to capture essential information
from large datasets, making them particularly suitable for handling
high-dimensional data with numerous discretization points in both spatial and
temporal dimensions. This innovative approach integrates the ensemble Kalman
method to enhance the training process, providing a robust framework for
improving model accuracy and performance in turbulent flow predictions.
