Parameter Estimation for Subgrid-Scale Models Using Markov Chain Monte Carlo Approximate Bayesian Computation
Abstract
We use approximate Bayesian computation (ABC) combined with an “improved” Markov chain Monte Carlo (IMCMC) method to estimate posterior distributions of model parameters in subgrid-scale (SGS) closures for large eddy simulations (LES) of turbulent flows. The ABC-IMCMC approach avoids the need to directly compute a likelihood function during the parameter estimation, enabling a substantial speed-up and greater flexibility as compared to full Bayesian approaches. The method also naturally provides uncertainties in parameter estimates, avoiding the artificial certainty implied by many optimization methods for determining model parameters. In this study, we outline details of the present ABC-IMCMC approach, including the use of an adaptive proposal and a calibration step to accelerate the parameter estimation process. We demonstrate the approach by estimating parameters in two nonlinear SGS closures using reference data from direct numerical simulations of homogeneous isotropic turbulence. We show that the resulting parameter values give excellent agreement with reference probability density functions of the SGS stress and kinetic energy production rate in a priori tests, while also providing stable solutions in forward LES (i.e., a posteriori tests) for homogeneous isotropic turbulence. The ABC-IMCMC method is thus shown to be an effective and efficient approach for estimating unknown parameters, including their uncertainties, in SGS closure models for LES of turbulent flows.
Olga Doronina
Postdoctoral Researcher
Working on data-driven turbulence modeling using an Approximate Bayesian Computation (ABC) approach.
Colin Towery
Postdoctoral Research Associate
Colin is a former research associate in the Paul M. Rady Department of Mechanical Engineering at the University of Colorado Boulder and also a former student in the Turbulence and Energy Systems Laboratory, earned his PhD in May 2018.
Peter Hamlington
Associate Professor
Peter is an associate professor in the Paul M. Rady Department of Mechanical Engineering at the University of Colorado Boulder and the principal investigator of the Turbulence and Energy Systems Laboratory.