An approach for estimating the uncertainty in ParaDiS predictions.

This report outlines an approach for computing the uncertainties in the predictions of computationally expensive models. While general, we use ParaDiS , a dislocation dynamics simulator originating in Lawrence Livermore National Laboratory, as the target application. ParaDiS is a mesoscale model, and uses submodels constructed/upscaled from microscale (molecular statics and dynamics) simulations. ParaDiS outputs, in turn, are upscaled and used in continuum (macroscale) simulations, e.g., those performed by ALE3D. This report addresses how one may quantify the uncertainties introduced by upscaling (both from microscale to mesoscale, and mesoscale to continuum), and the dependence of uncertainties in ParaDiS predictions on those of the inputs. This dependence is established via sensitivity analysis, and we address how this may be performed with a minimum of ParaDiS runs, given its immense computational cost. This includes constructing a smaller version of the model, sparse sampling of the parameter space, and exploiting the asymptotic nature of the time-evolution of the model outputs. The report concludes with a discussion of the computational resources required to perform this uncertainty quantification study.