  Turbulent flows are of central importance across applications in science and
engineering problems. For design and analysis, scientists and engineers use
Computational Fluid Dynamics (CFD) simulations using turbulence models.
Turbulent models are limited approximations, introducing epistemic uncertainty
in CFD results. For reliable design and analysis, we require quantification of
these uncertainties. The Eigenspace Perturbation Method (EPM) is the preeminent
physics based approach for turbulence model UQ, but often leads to overly
conservative uncertainty bounds. In this study, we use Machine Learning (ML)
models to moderate the EPM perturbations and introduce our physics constrained
machine learning framework for turbulence model UQ. We test this framework in
multiple problems to show that it leads to improved calibration of the
uncertainty estimates.
