  This paper presents a machine learning methodology to improve the predictions
of traditional RANS turbulence models in channel flows subject to strong
variations in their thermophysical properties. The developed formulation
contains several improvements over the existing Field Inversion Machine
Learning (FIML) frameworks described in the literature, as well as the
derivation of a new modelling technique. We first showcase the use of efficient
optimization routines to automatize the process of field inversion in the
context of CFD, combined with the use of symbolic algebra solvers to generate
sparse-efficient algebraic formulas to comply with the discrete adjoint method.
The proposed neural network architecture is characterized by the use of an
initial layer of logarithmic neurons followed by hyperbolic tangent neurons,
which proves numerically stable. The machine learning predictions are then
corrected using a novel weighted relaxation factor methodology, that recovers
valuable information from otherwise spurious predictions. The study uses the
K-fold cross-validation technique, which is beneficial for small datasets. The
results show that the machine learning model acts as an excellent non-linear
interpolator for DNS cases well-represented in the training set, and that
moderate improvement margins are obtained for sparser DNS cases. It is
concluded that the developed machine learning methodology corresponds to a
valid alternative to improve RANS turbulence models in flows with strong
variations in their thermophysical properties without introducing prior
modeling assumptions into the system.
