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Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

SIAM/ASA Journal on Uncertainty Quantification

D'Elia, Marta; Phipps, Eric T.; Edwards, Harold C.; Hu, Jonathan J.; Rajamanickam, Sivasankaran

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble when applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.

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TYPE Journal Article YEAR 2018
DOIOSTI

ASC ATDM Level 2 Milestone #6015: Asynchronous Many-Task Software Stack Demonstration

Bennett, Janine C.; Bettencourt, Matthew T.; Clay, Robert L.; Edwards, Harold C.; Glass, Micheal W.; Hollman, David S.; Kolla, Hemanth; Lifflander, Jonathan J.; Littlewood, David J.; Markosyan, Aram; Moore, Stan G.; Olivier, Stephen L.; Phipps, Eric T.; Rizzi, Francesco; Slattengren, Nicole L.; Sunderland, Daniel; Wilke, Jeremiah

This report is an outcome of the ASC ATDM Level 2 Milestone 6015: Asynchronous Many-Task Software Stack Demonstration. It comprises a summary and in depth analysis of DARMA and a DARMA-compliant Asynchronous Many-Task (AMT) runtime software stack. Herein performance and productivity of the over- all approach are assessed on benchmarks and proxy applications representative of the Sandia ATDM applications. As part of the effort to assess the perceived strengths and weaknesses of AMT models compared to more traditional methods, experiments were performed on ATS-1 (Advanced Technology Systems) test bed machines and Trinity. In addition to productivity and performance assessments, this report includes findings on the generality of DARMAs backend API as well as findings on interoperability with node- level and network-level system libraries. Together, this information provides a clear understanding of the strengths and limitations of the DARMA approach in the context of Sandias ATDM codes, to guide our future research and development in this area.

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TYPE SAND Report YEAR 2017
DOIOSTI

Embedded ensemble propagation for improving performance, portability, and scalability of uncertainty quantification on emerging computational architectures

SIAM Journal on Scientific Computing

Phipps, Eric T.; Edwards, Harold C.; Hoemmen, Mark F.; Hu, Jonathan J.; Rajamanickam, Sivasankaran

In this study, quantifying simulation uncertainties is a critical component of rigorous predictive simulation. A key component of this is forward propagation of uncertainties in simulation input data to output quantities of interest. Typical approaches involve repeated sampling of the simulation over the uncertain input data, and can require numerous samples when accurately propagating uncertainties from large numbers of sources. Often simulation processes from sample to sample are similar and much of the data generated from each sample evaluation could be reused. We explore a new method for implementing sampling methods that simultaneously propagates groups of samples together in an embedded fashion, which we call embedded ensemble propagation. We show how this approach takes advantage of properties of modern computer architectures to improve performance by enabling reuse between samples, reducing memory bandwidth requirements, improving memory access patterns, improving opportunities for fine-grained parallelization, and reducing communication costs. We describe a software technique for implementing embedded ensemble propagation based on the use of C++ templates and describe its integration with various scientific computing libraries within Trilinos. We demonstrate improved performance, portability and scalability for the approach applied to the simulation of partial differential equations on a variety of CPU, GPU, and accelerator architectures, including up to 131,072 cores on a Cray XK7 (Titan).

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TYPE Journal Article YEAR 2017
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Algorithms and Abstractions for Assembly in PDE Codes: Workshop Report

Cyr, Eric C.; Phipps, Eric T.; Heroux, Michael A.; Brown, Jed; Coon, Ethan T.; Hoemmen, Mark F.; Kirby, Robert C.; Kolev, Tzanio V.; Sutherland, James C.; Trott, Christian R.

The emergence of high-concurrency architectures offering unprecedented performance has brought many high-performance partial differential equation (PDE) discretization codes to the precipice of a major refactor. To help address this challenge a workshop titled "Algorithms and Abstractions for Assembly in PDE Codes" was held in the Computer Science Research Institute at Sandia National Laboratories on May 12th-14th, 2014. This document summarizes the goals of the workshop and the results of the presentations and subsequent discussions.

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TYPE SAND Report YEAR 2014
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Numerical Continuation Methods for Intrusive Uncertainty Quantification Studies

Safta, Cosmin; Najm, Habib N.; Phipps, Eric T.

Rigorous modeling of engineering systems relies on efficient propagation of uncertainty from input parameters to model outputs. In recent years, there has been substantial development of probabilistic polynomial chaos (PC) Uncertainty Quantification (UQ) methods, enabling studies in expensive computational models. One approach, termed ”intrusive”, involving reformulation of the governing equations, has been found to have superior computational performance compared to non-intrusive sampling-based methods in relevant large-scale problems, particularly in the context of emerging architectures. However, the utility of intrusive methods has been severely limited due to detrimental numerical instabilities associated with strong nonlinear physics. Previous methods for stabilizing these constructions tend to add unacceptably high computational costs, particularly in problems with many uncertain parameters. In order to address these challenges, we propose to adapt and improve numerical continuation methods for the robust time integration of intrusive PC system dynamics. We propose adaptive methods, starting with a small uncertainty for which the model has stable behavior and gradually moving to larger uncertainty where the instabilities are rampant, in a manner that provides a suitable solution.

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TYPE SAND Report YEAR 2014
DOIOSTI

Exploring Heterogeneous Multicore Architectures for Advanced Embedded Uncertainty Quantification

Phipps, Eric T.; Edwards, Harold C.; Hu, Jonathan J.

We explore rearrangements of classical uncertainty quantification methods with the aim of achieving higher aggregate performance for uncertainty quantification calculations on emerging multicore and many core architectures. We show a rearrangement of the stochastic Galerkin method leads to improved performance and scalability on several computational architectures whereby uncertainty information is propagated at the lowest levels of the simulation code improving memory access patterns, exposing new dimensions of fine grained parallelism, and reducing communication. We also develop a general framework for implementing such rearrangements for a diverse set of uncertainty quantification algorithms as well as computational simulation codes to which they are applied.

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TYPE SAND Report YEAR 2014
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Results 51–100 of 165
Results 51–100 of 165