| dc.description.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 for this research 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. To test further the responses of these UQ methods, we
conduct exercises with "experimental" replicates, "measurement" error, and choices
of physical inputs that reduce the accuracy of the diffusion model's approximation
of our manufactured laws.
Our first application of MMU was rich in areas for exploration and highly informative. In the case of the Gaussian process code, we found that the fundamental
statistical formulation was not appropriate for our functional data, but that the code
allows a knowledgable user to vary parameters within this formulation to tailor its
behavior for a specific problem. The Bayesian MARS formulation was a more natural emulator given our manufactured laws, and we used the MMU framework to develop
further a calibration method and to characterize the diffusion model discrepancy.
Overall, we conclude that an MMU exercise with a properly designed universe (that
is, one that is an adequate representation of some real-world problem) will provide
the modeler with an added understanding of the interaction between a given UQ
method and his/her more complex problem of interest. The modeler can then apply
this added understanding and make more informed predictive statements. | en |
