  While many physics-based closure model forms have been posited for the
sub-filter scale (SFS) in large eddy simulation (LES), vast amounts of data
available from direct numerical simulation (DNS) create opportunities to
leverage data-driven modeling techniques. Albeit flexible, data-driven models
still depend on the dataset and the functional form of the model chosen.
Increased adoption of such models requires reliable uncertainty estimates both
in the data-informed and out-of-distribution regimes. In this work, we employ
Bayesian neural networks (BNNs) to capture both epistemic and aleatoric
uncertainties in a reacting flow model. In particular, we model the filtered
progress variable scalar dissipation rate which plays a key role in the
dynamics of turbulent premixed flames. We demonstrate that BNN models can
provide unique insights about the structure of uncertainty of the data-driven
closure models. We also propose a method for the incorporation of
out-of-distribution information in a BNN. The efficacy of the model is
demonstrated by a priori evaluation on a dataset consisting of a variety of
flame conditions and fuels.
