The Method of Manufactured Universes for validating uncertainty quantification methods

Abstract

The Method of Manufactured Universes is presented as a validation framework for uncertainty quantification (UQ) methodologies and as a tool for exploring the effects of statistical and modeling assumptions embedded in these methods. The framework calls for a manufactured reality from which “experimental” data are created (possibly with experimental error), an imperfect model (with uncertain inputs) from which simulation results are created (possibly with numerical error), the application of a system for quantifying uncertainties in model predictions, and an assessment of how accurately those uncertainties are quantified. The application presented in this paper manufactures a particle-transport “universe”, models it using diffusion theory with uncertain material parameters, and applies both Gaussian process and Bayesian MARS algorithms to make quantitative predictions about new “experiments” within the manufactured reality. The results of this preliminary study indicate that, even in a simple problem, the improper application of a specific UQ method or unrealized effects of a modeling assumption may produce inaccurate predictions. We conclude that the validation framework presented in this paper is a powerful and flexible tool for the investigation and understanding of UQ methodologies.