Computational Fluid Dynamics has been widely used to model flows for engineering applications. The challenge has been to model or resolve turbulent flows accurately and there exist different approaches such as Direct Numerical Simulations (DNS), Large Eddy Simulations (LES) and Reynolds Averaged Navier Stokes (RANS). With limitations on the available computational power and time, RANS is the favorable choice to model such flows despite significant modeling errors.
With recent advancements in machine learning (ML) algorithms and availability of high-fidelity (accurate) data, the turbulence community has been actively working to improve RANS modeling by informing it from the reference data and developing corrections. This is also known as data driven turbulence modeling. There exist several algorithms that have improved RANS modeling but their computational cost and lack of physical interpretability remains an issue to gain an understanding of flow physics and the relation between different flow quantities.

The present study implements two data driven methods to provide corrections ad improve RANS modeling, focusing on Turbulent Kinetic Energy and the Reynolds Stress Tensor. However, the goal is
to also obtain symbolic models and physically interpretable corrections, while ensuring computational cost remains minimum.

A priori analysis, where only the reference data is used to develop corrections, shows significant re- ductions in the computational cost (function calls to the CFD solver) while converging to acceptable
correlations as well. The superior of the two methods is selected for a posteriori study where it is
coupled with a CFD solver. The correction is now formulated by differentiating the CFD code. This
information is given to the ML algorithm which adjusts its parameters accordingly to optimize the objective function and improve turbulence modeling. Results show that, with regularization, a generalized symbolic formula can be obtained which when tested on different geometries improves the prediction of flow quantities and turbulence modeling, as a whole.