  Reynolds-averaged Navier-Stokes (RANS)-based transition modeling is widely
used in aerospace applications but suffers inaccuracies due to the Boussinesq
turbulent viscosity hypothesis. The eigenspace perturbation method can estimate
the accuracy of a RANS model by injecting perturbations to its predicted
Reynolds stresses. However, there lacks a reliable method for choosing the
strength of the injected perturbation, while existing machine learning models
are often complex and data craving. We examined two light-weighted machine
learning models to help select the strength of the injected perturbation for
estimating the RANS uncertainty of flows undergoing the transition to
turbulence over a Selig-Donovan 7003 airfoil. On the one hand, we examined
polynomial regression to construct a marker function augmented with eigenvalue
perturbations to estimate the uncertainty bound for the predicted skin friction
coefficient. On the other hand, we trained a convolutional neural network (CNN)
to predict high-fidelity turbulence kinetic energy. The trained CNN acts as a
marker function that can be integrated into the eigenspace perturbation method
to quantify the RANS uncertainty. Our findings suggest that the light-weighted
machine learning models are effective in constructing an appropriate marker
function that is promising to enrich the existing eigenspace perturbation
method to quantify the RANS uncertainty more precisely.
