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Quantifying simulation uncertainties is a critical component of rigorouspredictive simulation. A key component of this is forward propagation ofuncertainties in simulation input data to output quantities of interest.Typical approaches involve repeated sampling of the simulation over theuncertain input data, and can require numerous samples when accuratelypropagating uncertainties from large numbers of sources. Often simulationprocesses from sample to sample are similar and much of the data generated fromeach sample evaluation could be reused. We explore a new method forimplementing sampling methods that simultaneously propagates groups of samplestogether in an embedded fashion, which we call embedded ensemble propagation.We show how this approach takes advantage of properties of modern computerarchitectures to improve performance by enabling reuse between samples,reducing memory bandwidth requirements, improving memory access patterns,improving opportunities for fine-grained parallelization, and reducingcommunication costs. We describe a software technique for implementing embeddedensemble propagation based on the use of C++ templates and describe itsintegration with various scientific computing libraries within Trilinos. Wedemonstrate improved performance, portability and scalability for the approachapplied to the simulation of partial differential equations on a variety ofCPU, GPU, and accelerator architectures, including up to 131,072 cores on aCray XK7 (Titan).

Embedded Ensemble Propagation for Improving Performance, Portability and  Scalability of Uncertainty Quantification on Emerging Computational  Architectures