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Ginkgo - A math library designed to accelerate Exascale Computing Project science applications

Large-scale simulations require efficient computation across the entire computing hierarchy. A challenge of the Exascale Computing Project (ECP) was to reconcile highly heterogeneous hardware with the myriad of applications that were required to run on these supercomputers. Mathematical software forms the backbone of almost all scientific applications, providing efficient abstractions and operations that are crucial to harness the performance of computing systems. Ginkgo is one such mathematical software library, nurtured by ECP, providing high-performance, user-friendly, and performance portable interfaces for applications in ECP and beyond. In this paper, we elaborate on Ginkgo’s philosophy of high-performance software that is sustainable, reproducible, and easy to use. We showcase the wide feature set of solvers and preconditioners available in Ginkgo and the central concepts involved in their design. We elaborate on four different ECP software integrations: MFEM, PeleLM + SUNDIALS, XGC, and ExaSGD that use Ginkgo to accelerate their science runs. Performance studies of different problems from these applications highlight the effectiveness of Ginkgo and the benefits incurred by these ECP applications.

Cojean, Terry↗

xSDK-batched Subcontract - Ginkgo Batched Iterative Solver Development (Final Report)

Iterative solvers are fundamentally different from direct solvers in terms of execution as they generally do not execute a pre-defined sequence of operations or steps, but adapt the number of iterations to the specific problem and the preset solution quality. Generally, the adaptation of the iteration count to the problem is realized by monitoring the solver convergence and stopping the iteration process once the monitored metric, e.g., the residual norm, hits a pre-defined threshold. When addressing a set of problems with different properties, it is necessary to monitor the threshold for each problem individually and break up the SIMD execution style to avoid excess iterations for “easier” problems. Ginkgo integrates a simple but customizable stopping criterion for the residual norm and generally uses a pre-defined (relative or absolute) residual norm as the stopping criterion. In order to avoid the overhead of launching a kernel at every iteration, the iteration convergence and iteration control is part of the solver kernel. Each thread maintains its own copy of the iteration count.

97 MATHEMATICS AND COMPUTING↗

Providing performance portable numerics for Intel GPUs

Summary With discrete Intel GPUs entering the high‐performance computing landscape, there is an urgent need for production‐ready software stacks for these platforms. In this article, we report how we enable the Ginkgo math library to execute on Intel GPUs by developing a kernel backed based on the DPC++ programming environment. We discuss conceptual differences between the CUDA and DPC++ programming models and describe workflows for simplified code conversion. We evaluate the performance of basic and advanced sparse linear algebra routines available in Ginkgo's DPC++ backend in the hardware‐specific performance bounds and compare against routines providing the same functionality that ship with Intel's oneMKL vendor library.

97 MATHEMATICS AND COMPUTING↗

Compressed basis GMRES on high-performance graphics processing units

Krylov methods provide a fast and highly parallel numerical tool for the iterative solution of many large-scale sparse linear systems. To a large extent, the performance of practical realizations of these methods is constrained by the communication bandwidth in current computer architectures, motivating the investigation of sophisticated techniques to avoid, reduce, and/or hide the message-passing costs (in distributed platforms) and the memory accesses (in all architectures). This article leverages Ginkgo’s memory accessor in order to integrate a communication-reduction strategy into the (Krylov) GMRES solver that decouples the storage format (i.e., the data representation in memory) of the orthogonal basis from the arithmetic precision that is employed during the operations with that basis. Given that the execution time of the GMRES solver is largely determined by the memory accesses, the cost of the datatype transforms can be mostly hidden, resulting in the acceleration of the iterative step via a decrease in the volume of bits being retrieved from memory. Together with the special properties of the orthonormal basis (whose elements are all bounded by 1), this paves the road toward the aggressive customization of the storage format, which includes some floating-point as well as fixed-point formats with mild impact on the convergence of the iterative process. We develop a high-performance implementation of the “compressed basis GMRES” solver in the Ginkgo sparse linear algebra library using a large set of test problems from the SuiteSparse Matrix Collection. We demonstrate robustness and performance advantages on a modern NVIDIA V100 graphics processing unit (GPU) of up to 50% over the standard GMRES solver that stores all data in IEEE double-precision.

97 MATHEMATICS AND COMPUTING↗

Batched Sparse Linear Algebra (Final Report for Subcontract B648960)

This report finalizes design specifications for developing batched kernels for small tensor operations for unassembled matrix-free iterative solvers, batched solvers for partially assembled operators, and batched solvers with support for various sparse formats. The outcome of the project milestones is a set of interfaces to Batched Sparse LA solvers running on hardware accelerators for use in ECP Libraries and Applications. It is part of the development of sparse batched kernels, solvers/preconditioners as well as creating interoperability in xSDK libraries with sparse and dense batched functions to benefit ECP applications. The participants included representatives from ECP libraries (not limited to the xSDK project), applications, and vendors (AMD, Intel, and NVIDIA). Batched sparse linear algebra solvers form the new frontier for algorithmic development and performance engineering. Many applications (ECP and non-ECP alike) require simultaneous solutions of small linear systems of equations that are structurally sparse. To move towards high hardware utilization, it is important to provide these applications with appropriate interfaces to efficient batched sparse solvers running on modern hardware accelerators. We present interface designs in use by HPC software libraries supporting batched sparse linear algebra and the development of sparse batched kernel codes for solvers and preconditioners. We also address the potential interoperability opportunities to keep the software portable between the major hardware accelerators from AMD, Intel, and NVIDIA. The presented interface specifications includes batched band, sparse iterative, and sparse direct solvers. This report summarizes progress in Kokkos Kernels and the xSDK libraries MAGMA, Ginkgo, hypre, SUNDIALS, and SuperLU_dist.

97 MATHEMATICS AND COMPUTING↗

Milestone 49 Report: Batched Sparse LA Phase 5 Implementation

Batched sparse linear algebra operations in general, and solvers in particular, have become the major algorithmic development activity and foremost performance engineering effort in the numerical software libraries work on modern hardware with accelerators such as GPUs. Many applications, ECP and non-ECP alike, require simultaneous solutions of many small linear systems of equations that are structurally sparse in one form or another. In order to move towards high hardware utilization levels, it is important to provide these applications with appropriate interface designs to be both functionally efficient and performance portable and give full access to the appropriate batched sparse solvers running on modern hardware accelerators prevalent across DOE supercomputing sites since the inception of ECP. To this end, we present here a summary of recent advances on the interface designs in use by HPC software libraries supporting batched sparse linear algebra and the development of sparse batched kernel codes for solvers and preconditioners. We also address the potential interoperability opportunities to keep the corresponding software portable between the major hardware accelerators from AMD, Intel, and NVIDIA, while maintaining the appropriate disclosure levels conforming to the active NDA agreements. The presented interface specifications include a mix of batched band, sparse iterative, and sparse direct solvers with their accompanying functionality that is already required by the application codes or we anticipated to be needed in the near future. This report summarizes progress in Kokkos Kernels and the xSDK libraries MAGMA, Ginkgo, hypre, PETSc, and SuperLU.

97 MATHEMATICS AND COMPUTING↗

MIBiG 4.0: advancing biosynthetic gene cluster curation through global collaboration

Specialized or secondary metabolites are small molecules of biological origin, often showing potent biological activities with applications in agriculture, engineering and medicine. Usually, the biosynthesis of these natural products is governed by sets of co-regulated and physically clustered genes known as biosynthetic gene clusters (BGCs). To share information about BGCs in a standardized and machine-readable way, the Minimum Information about a Biosynthetic Gene cluster (MIBiG) data standard and repository was initiated in 2015. Since its conception, MIBiG has been regularly updated to expand data coverage and remain up to date with innovations in natural product research. Here, we describe MIBiG version 4.0, an extensive update to the data repository and the underlying data standard. In a massive community annotation effort, 267 contributors performed 8304 edits, creating 557 new entries and modifying 590 existing entries, resulting in a new total of 3059 curated entries in MIBiG. Particular attention was paid to ensuring high data quality, with automated data validation using a newly developed custom submission portal prototype, paired with a novel peer-reviewing model. MIBiG 4.0 also takes steps towards a rolling release model and a broader involvement of the scientific community. MIBiG 4.0 is accessible online at https://mibig.secondarymetabolites.org/.

59 BASIC BIOLOGICAL SCIENCES↗