  Model extrapolation to unseen flow is one of the biggest challenges facing
data-driven turbulence modeling, especially for models with high dimensional
inputs that involve many flow features. In this study we review previous
efforts on data-driven Reynolds-Averaged Naiver Stokes (RANS) turbulence
modeling and model extrapolation, with main focus on the popular methods being
used in the field of transfer learning. Several potential metrics to measure
the dissimilarity between training flows and testing flows are examined.
Different Machine Learning (ML) models are compared to understand how the
capacity or complexity of the model affects its behavior in the face of dataset
shift. Data preprocessing schemes which are robust to covariate shift, like
normalization, transformation, and importance re-weighted likelihood, are
studied to understand whether it is possible to find projections of the data
that attenuate the differences in the training and test distributions while
preserving predictability. Three metrics are proposed to assess the
dissimilarity between training/testing dataset. To attenuate the dissimilarity,
a distribution matching framework is used to align the statistics of the
distributions. These modifications also allow the regression tasks to have
better accuracy in forecasting under-represented extreme values of the target
variable. These findings are useful for future ML based turbulence models to
evaluate their model predictability and provide guidance to systematically
generate diversified high-fidelity simulation database.
