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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 D.; Phipps, Eric T.; Edwards, Harold C.; Hu, Jonathan J.; Rajamanickam, Sivasankaran R.

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
OSTIDOI

Ensemble grouping strategies for embedded stochastic collocation methods applied to anisotropic diffusion problems

SIAM-ASA Journal on Uncertainty Quantification

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

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 work 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. 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 Conference Poster YEAR 2018
ScopusOSTI

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
ScopusOSTIDOI

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
OSTIDOI
Results 1–25 of 142
Results 1–25 of 142