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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

Trends in Data Locality Abstractions for HPC Systems

IEEE Transactions on Parallel and Distributed Systems

Unat, Didem; Dubey, Anshu; Hoefler, Torsten; Shalf, John B.; Abraham, Mark; Bianco, Mauro; Chamberlain, Bradford L.; Cledat, Romain; Edwards, Harold C.; Finkel, Hal; Fuerlinger, Karl; Hannig, Frank; Jeannot, Emmanuel; Kamil, Amir; Keasler, Jeff; Kelly, Paul H.J.; Leung, Vitus J.; Ltaief, Hatem; Maruyama, Naoya; Newburn, Chris J.; Pericas, Miquel

The cost of data movement has always been an important concern in high performance computing (HPC) systems. It has now become the dominant factor in terms of both energy consumption and performance. Support for expression of data locality has been explored in the past, but those efforts have had only modest success in being adopted in HPC applications for various reasons. them However, with the increasing complexity of the memory hierarchy and higher parallelism in emerging HPC systems, locality management has acquired a new urgency. Developers can no longer limit themselves to low-level solutions and ignore the potential for productivity and performance portability obtained by using locality abstractions. Fortunately, the trend emerging in recent literature on the topic alleviates many of the concerns that got in the way of their adoption by application developers. Data locality abstractions are available in the forms of libraries, data structures, languages and runtime systems; a common theme is increasing productivity without sacrificing performance. This paper examines these trends and identifies commonalities that can combine various locality concepts to develop a comprehensive approach to expressing and managing data locality on future large-scale high-performance computing systems.

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TYPE Journal Article YEAR 2017
DOIOSTIScopus

Kokkos' Task DAG Capabilities

Edwards, Harold C.; Ibanez-Granados, Daniel A.

This report documents the ASC/ATDM Kokkos deliverable "Production Portable Dy- namic Task DAG Capability." This capability enables applications to create and execute a dynamic task DAG ; a collection of heterogeneous computational tasks with a directed acyclic graph (DAG) of "execute after" dependencies where tasks and their dependencies are dynamically created and destroyed as tasks execute. The Kokkos task scheduler executes the dynamic task DAG on the target execution resource; e.g. a multicore CPU, a manycore CPU such as Intel's Knights Landing (KNL), or an NVIDIA GPU. Several major technical challenges had to be addressed during development of Kokkos' Task DAG capability: (1) portability to a GPU with it's simplified hardware and micro- runtime, (2) thread-scalable memory allocation and deallocation from a bounded pool of memory, (3) thread-scalable scheduler for dynamic task DAG, (4) usability by applications.

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TYPE SAND Report YEAR 2017
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
DOIOSTI

Hierarchical Task-Data Parallelism using Kokkos and Qthreads

Edwards, Harold C.; Olivier, Stephen L.; Berry, Jonathan; Mackey, Greg E.; Rajamanickam, Sivasankaran; Wolf, Michael; Kim, Kyungjoo; Stelle, George W.

This report describes a new capability for hierarchical task-data parallelism using Sandia's Kokkos and Qthreads, and evaluation of this capability with sparse matrix Cholesky factorization and social network triangle enumeration mini-applications. Hierarchical task-data parallelism consists of a collection of tasks with executes-after dependences where each task contains data parallel operations performed on a team of hardware threads. The collection of tasks and dependences form a directed acyclic graph of tasks - a task DAG. Major challenges of this research and development effort include: portability and performance across multicore CPU; manycore Intel Xeon Phi, and NVIDIA GPU architectures; scalability with respect to hardware concurrency and size of the task DAG; and usability of the application programmer interface (API).

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TYPE SAND Report YEAR 2016
DOIOSTI

Task Parallel Incomplete Cholesky Factorization using 2D Partitioned-Block Layout

Kim, Kyungjoo; Rajamanickam, Sivasankaran; Stelle, George W.; Edwards, Harold C.; Olivier, Stephen L.

We introduce a task-parallel algorithm for sparse incomplete Cholesky factorization that utilizes a 2D sparse partitioned-block layout of a matrix. Our factorization algorithm follows the idea of algorithms-by-blocks by using the block layout. The algorithm-byblocks approach induces a task graph for the factorization. These tasks are inter-related to each other through their data dependences in the factorization algorithm. To process the tasks on various manycore architectures in a portable manner, we also present a portable tasking API that incorporates different tasking backends and device-specific features using an open-source framework for manycore platforms i.e., Kokkos. A performance evaluation is presented on both Intel Sandybridge and Xeon Phi platforms for matrices from the University of Florida sparse matrix collection to illustrate merits of the proposed task-based factorization. Experimental results demonstrate that our task-parallel implementation delivers about 26.6x speedup (geometric mean) over single-threaded incomplete Choleskyby- blocks and 19.2x speedup over serial Cholesky performance which does not carry tasking overhead using 56 threads on the Intel Xeon Phi processor for sparse matrices arising from various application problems.

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TYPE Other Report YEAR 2015
DOIOSTI

ASC Trilab L2 Codesign Milestone 2015

Trott, Christian R.; Hammond, Simon; Dinge, Dennis; Lin, Paul T.; Vaughan, Courtenay T.; Cook, Jeanine; Rajan, Mahesh; Edwards, Harold C.; Hoekstra, Robert J.

For the FY15 ASC L2 Trilab Codesign milestone Sandia National Laboratories performed two main studies. The first study investigated three topics (performance, cross-platform portability and programmer productivity) when using OpenMP directives and the RAJA and Kokkos programming models available from LLNL and SNL respectively. The focus of this first study was the LULESH mini-application developed and maintained by LLNL. In the coming sections of the report the reader will find performance comparisons (and a demonstration of portability) for a variety of mini-application implementations produced during this study with varying levels of optimization. Of note is that the implementations utilized including optimizations across a number of programming models to help ensure claims that Kokkos can provide native-class application performance are valid. The second study performed during FY15 is a performance assessment of the MiniAero mini-application developed by Sandia. This mini-application was developed by the SIERRA Thermal-Fluid team at Sandia for the purposes of learning the Kokkos programming model and so is available in only a single implementation. For this report we studied its performance and scaling on a number of machines with the intent of providing insight into potential performance issues that may be experienced when similar algorithms are deployed on the forthcoming Trinity ASC ATS platform.

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TYPE SAND Report YEAR 2015
DOIOSTI

ASC-ATDM Performance Portability Requirements for 2015-2019

Edwards, Harold C.; Trott, Christian R.

This report outlines the research, development, and support requirements for the Advanced Simulation and Computing (ASC ) Advanced Technology, Development, and Mitigation (ATDM) Performance Portability (a.k.a., Kokkos) project for 2015 - 2019 . The research and development (R&D) goal for Kokkos (v2) has been to create and demonstrate a thread - parallel programming model a nd standard C++ library - based implementation that enables performance portability across diverse manycore architectures such as multicore CPU, Intel Xeon Phi, and NVIDIA Kepler GPU. This R&D goal has been achieved for algorithms that use data parallel pat terns including parallel - for, parallel - reduce, and parallel - scan. Current R&D is focusing on hierarchical parallel patterns such as a directed acyclic graph (DAG) of asynchronous tasks where each task contain s nested data parallel algorithms. This five y ear plan includes R&D required to f ully and performance portably exploit thread parallelism across current and anticipated next generation platforms (NGP). The Kokkos library is being evaluated by many projects exploring algorithm s and code design for NGP. Some production libraries and applications such as Trilinos and LAMMPS have already committed to Kokkos as their foundation for manycore parallelism an d performance portability. These five year requirements includes support required for current and antic ipated ASC projects to be effective and productive in their use of Kokkos on NGP. The greatest risk to the success of Kokkos and ASC projects relying upon Kokkos is a lack of staffing resources to support Kokkos to the degree needed by these ASC projects. This support includes up - to - date tutorials, documentation, multi - platform (hardware and software stack) testing, minor feature enhancements, thread - scalable algorithm consulting, and managing collaborative R&D.

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TYPE SAND Report YEAR 2015
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Programming Abstractions for Data Locality

Tate, Adrian; Kamil, Amir; Dubey, Anshu; Groblinger, Armin; Chamberlain, Brad; Goglin, Brice; Edwards, Harold C.; Newburn, Chris J.; Padua, David; Unat, Didem; Jeannot, Emmanuel; Hannig, Frank; Tobias, Gysi; Ltaief, Hatem; Sexton, James; Labarta, Jesus; Shalf, John; Fuerlinger, Karl; Brien, Leonidas'; Linardakis, Leonidas; Besta, MacIej; Sawley, Marie-Christine; Abraham, Mark; Bianco, Mauro; Pericas, Miquel; Maruyama, Naoya; Kelly, Paul H.J.; Messmer, Peter; Ross, Robert B.; Ciedat, Romain; Matsuoka, Satoshi; Schulthess, Thomas; Hoefler, Torsten; Leung, Vitus J.

The goal of the workshop and this report is to identify common themes and standardize concepts for locality-preserving abstractions for exascale programming models.

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TYPE Other 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
DOIOSTI
Results 1–100 of 144
Results 1–100 of 144