Subgrid-Scale Model Development Using Approximate Bayesian Computation

The predictive power of large eddy simulations (LES) depends on the accuracy of closure models used to represent subgrid-scale (SGS) fluxes. Traditionally, model parameters have been determined through either direct inversion of model equations given some reference data or using optimization techniques. However, the former approach becomes complicated for models with many different parameters or when the model consists of partial differential equations, and the latter approach precludes the quantification of parameter uncertainty. In this talk, we use Approximate Bayesian Computation (ABC) and Markov Chain Monte Carlo (MCMC) methods to estimate parameter values, as well as their uncertainties, in SGS models. The MCMC-ABC approach avoids the need to directly compute a likelihood function during the parameter estimation, enabling a substantial speed-up as compared to full Bayesian analyses. The approach also naturally provides uncertainties in parameter estimates, avoiding the artificial certainty implied by optimization methods for parameter estimation. The MCMC-ABC approach is outlined, and both a priori and a posteriori test results for homogeneous isotropic turbulence are provided to demonstrate the accuracy and computational cost of the approach.