  In computational fluid dynamics, there is an inevitable trade off between
accuracy and computational cost. In this work, a novel multi-fidelity deep
generative model is introduced for the surrogate modeling of high-fidelity
turbulent flow fields given the solution of a computationally inexpensive but
inaccurate low-fidelity solver. The resulting surrogate is able to generate
physically accurate turbulent realizations at a computational cost magnitudes
lower than that of a high-fidelity simulation. The deep generative model
developed is a conditional invertible neural network, built with normalizing
flows, with recurrent LSTM connections that allow for stable training of
transient systems with high predictive accuracy. The model is trained with a
variational loss that combines both data-driven and physics-constrained
learning. This deep generative model is applied to non-trivial high Reynolds
number flows governed by the Navier-Stokes equations including turbulent flow
over a backwards facing step at different Reynolds numbers and turbulent wake
behind an array of bluff bodies. For both of these examples, the model is able
to generate unique yet physically accurate turbulent fluid flows conditioned on
an inexpensive low-fidelity solution.
