  Field inversion and machine learning are implemented in this study to
describe three-dimensional separation flow around an axisymmetric hill and
augment the Spart-Allmaras model. The discrete adjoint method is used to solve
the field inversion problem, and an artificial neural network is used as the
machine learning model. A validation process for field inversion is proposed to
adjust the hyperparameters and obtain a physically acceptable solution. The
field inversion result shows that the non-equilibrium turbulence effects in the
boundary layer upstream of the mean separation line and in the separating shear
layer dominate the flow structure in the 3-D separating flow, which agrees with
prior physical knowledge. However, the effect of turbulence anisotropy on the
mean flow appears to be limited. Two approaches are proposed and implemented in
the machine learning stage to overcome the problem of sample imbalance while
reducing the computational cost during training. The results are all
satisfactory, which proves the effectiveness of the proposed approaches.
