  In this paper we propose a Bayesian method as a numerical way to correct and
stabilise projection-based reduced order models (ROM) in computational fluid
dynamics problems. The approach is of hybrid type, and consists of the
classical proper orthogonal decomposition driven Galerkin projection of the
laminar part of the governing equations, and Bayesian identification of the
correction term mimicking both the turbulence model and possible ROM-related
instabilities given the full order data. In this manner the classical ROM
approach is translated to the parameter identification problem on a set of
nonlinear ordinary differential equations. Computationally the inverse problem
is solved with the help of the Gauss-Markov-Kalman smoother in both ensemble
and square-root polynomial chaos expansion forms. To reduce the dimension of
the posterior space, a novel global variance based sensitivity analysis is
proposed.
