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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Solving large sparse eigenvalue problems on supercomputers

An important problem in scientific computing consists in finding a few eigenvalues and corresponding eigenvectors of a very large and sparse matrix. The most popular methods to solve these problems are based on projection techniques on appropriate subspaces. The main attraction of these methods is that they only require the use of the matrix in the form of matrix by vector multiplications. The implementations on supercomputers of two such methods for symmetric matrices, namely Lanczos' method and Davidson's method are compared. Since one of the most important operations in these two methods is the multiplication of vectors by the sparse matrix, methods of performing this operation efficiently are discussed. The advantages and the disadvantages of each method are compared and implementation aspects are discussed. Numerical experiments on a one processor CRAY 2 and CRAY X-MP are reported. Possible parallel implementations are also discussed.

Philippe, Bernard↗
DOE OSTI2016

A Recursive Hypergraph Bipartitioning Framework for Reducing Bandwidth and Latency Costs Simultaneously

Intelligent partitioning models are commonly used for efficient parallelization of irregular applications on distributed systems. These models usually aim to minimize a single communication cost metric, which is either related to communication volume or message count. However, both volume- and message-related metrics should be taken into account during partitioning for a more efficient parallelization. There are only a few works that consider both of them and they usually address each in separate phases of a two-phase approach. In this work, we propose a recursive hypergraph bipartitioning framework that reduces the total volume and total message count in a single phase. In this framework, the standard hypergraph models, nets of which already capture the bandwidth cost, are augmented with message nets. The message nets encode the message count so that minimizing conventional cutsize captures the minimization of bandwidth and latency costs together. Our model provides a more accurate representation of the overall communication cost by incorporating both the bandwidth and the latency components into the partitioning objective. The use of the widely-adopted successful recursive bipartitioning framework provides the flexibility of using any existing hypergraph partitioner. In conclusion, the experiments on instances from different domains show that our model on the average achieves up to 52 percent reduction in total message count and hence results in 29 percent reduction in parallel running time compared to the model that considers only the total volume.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Supercomputing on massively parallel bit-serial architectures

Research on the Goodyear Massively Parallel Processor (MPP) suggests that high-level parallel languages are practical and can be designed with powerful new semantics that allow algorithms to be efficiently mapped to the real machines. For the MPP these semantics include parallel/associative array selection for both dense and sparse matrices, variable precision arithmetic to trade accuracy for speed, micro-pipelined train broadcast, and conditional branching at the processing element (PE) control unit level. The preliminary design of a FORTRAN-like parallel language for the MPP has been completed and is being used to write programs to perform sparse matrix array selection, min/max search, matrix multiplication, Gaussian elimination on single bit arrays and other generic algorithms. A description is given of the MPP design. Features of the system and its operation are illustrated in the form of charts and diagrams.

Iobst, Ken↗
DOE OSTI2023

Sparse matrix‐vector and matrix‐multivector products for the truncated SVD on graphics processors

Summary Many practical algorithms for numerical rank computations implement an iterative procedure that involves repeated multiplications of a vector, or a collection of vectors, with both a sparse matrix and its transpose. Unfortunately, the realization of these sparse products on current high performance libraries often deliver much lower arithmetic throughput when the matrix involved in the product is transposed. In this work, we propose a hybrid sparse matrix layout, named CSRC, that combines the flexibility of some well‐known sparse formats to offer a number of appealing properties: (1) CSRC can be obtained at low cost from the popular CSR (compressed sparse row) format; (2) CSRC has similar storage requirements as CSR; and especially, (3) the implementation of the sparse product kernels delivers high performance for both the direct product and its transposed variant on modern graphics accelerators thanks to a significant reduction of atomic operations compared to a conventional implementation based on CSR. This solution thus renders considerably higher performance when integrated into an iterative algorithm for the truncated singular value decomposition (SVD), such as the randomized SVD or, as demonstrated in the experimental results, the block Golub–Kahan–Lanczos algorithm.

Aliaga, José I.↗
DOE OSTI2020

Reduce Operations: Send Volume Balancing While Minimizing Latency

Communication hypergraph model was introduced in a two-phase setting for encapsulating multiple communication cost metrics (bandwidth and latency), which are proven to be important in parallelizing irregular applications. In the first phase, computational-task-to-processor assignment is performed with the objective of minimizing total volume while maintaining computational load balance. In the second phase, communication-task-to-processor assignment is performed with the objective of minimizing total number of messages while maintaining communication-volume balance. The reduce-communication hypergraph model suffers from failing to correctly encapsulate send-volume balancing. We propose a novel vertex weighting scheme that enables part weights to correctly encode send-volume loads of processors for send-volume balancing. The model also suffers from increasing the total communication volume during partitioning. To decrease this increase, we propose a method that utilizes the recursive bipartitioning framework and refines each bipartition by vertex swaps. For performance evaluation, we consider column-parallel SpMV, which is one of the most widely known applications in which the reduce-task assignment problem arises. Extensive experiments on 313 matrices show that, compared to the existing model, the proposed models achieve considerable improvements in all communication cost metrics. Furthermore, these improvements lead to an average decrease of 30% in parallel SpMV time on 512 processors for 70 matrices with high irregularity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

FatMan vs. LittleBoy: Scaling Up Linear Algebraic Operations in Scale-Out Data Platforms

Linear algebraic operations such as matrix manipulations form the kernel of many machine learning and other crucial algorithms. Scaling up as well as scaling out such algorithms are highly desirable to enable efficient processing over millions of data points. To this end, we present a matrix manipulation approach to effectively scale-up each node in a scale-out data parallel platform such as Apache Spark. Specifically, we enable hardware acceleration for matrix multiplications in a distributed Spark setup without user intervention. Our approach supports both dense and sparse distributed matrices, and provides flexible control of acceleration by matrix density. We demonstrate the benefit of our approach for generalized matrix multiplication operations over large matrices with up to four billion elements. To connect the effectiveness of our approach with machine learning applications, we performed Gramian matrix computation via generalized matrix multiplications. Our experiments show that our approach achieves more than 2× performance speed-up, and up to 96.1% computation improvement, compared to a state of the art Spark MLlib for dense matrices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

FatMan vs. LittleBoy: Scaling up Linear Algebraic Operations in Scale-out Data Platforms

Linear algebraic operations such as matrix manipulations form the kernel of many machine learning and other crucial algorithms. Scaling up as well as scaling out such algorithms are highly desirable to enable efficient processing over millions of data points. To this end, we present a matrix manipulation approach to effectively scale-up each node in a scale-out data parallel platform such as Apache Spark. Specifically, we enable hardware acceleration for matrix multiplications in a distributed Spark setup without user intervention. Our approach supports both dense and sparse distributed matrices, and provides flexible control of acceleration by matrix density. We demonstrate the benefit of our approach for generalized matrix multiplication operations over large matrices with up to four billion elements. To connect the effectiveness of our approach with machine learning applications, we performed Gramian matrix computation via generalized matrix multiplications. Our experiments show that our approach achieves more than 2x performance speed-up, and up to 96.1% computation improvement, compared to a state of the art Spark MLlib for dense matrices.

Lim, Seung-Hwan↗
DOE OSTI2016

SU-G-TeP1-15: Toward a Novel GPU Accelerated Deterministic Solution to the Linear Boltzmann Transport Equation

Purpose: To develop a Graphic Processor Unit (GPU) accelerated deterministic solution to the Linear Boltzmann Transport Equation (LBTE) for accurate dose calculations in radiotherapy (RT). A deterministic solution yields the potential for major speed improvements due to the sparse matrix-vector and vector-vector multiplications and would thus be of benefit to RT. Methods: In order to leverage the massively parallel architecture of GPUs, the first order LBTE was reformulated as a second order self-adjoint equation using the Least Squares Finite Element Method (LSFEM). This produces a symmetric positive-definite matrix which is efficiently solved using a parallelized conjugate gradient (CG) solver. The LSFEM formalism is applied in space, discrete ordinates is applied in angle, and the Multigroup method is applied in energy. The final linear system of equations produced is tightly coupled in space and angle. Our code written in CUDA-C was benchmarked on an Nvidia GeForce TITAN-X GPU against an Intel i7-6700K CPU. A spatial mesh of 30,950 tetrahedral elements was used with an S4 angular approximation. Results: To avoid repeating a full computationally intensive finite element matrix assembly at each Multigroup energy, a novel mapping algorithm was developed which minimized the operations required at each energy. Additionally, a parallelized memory mapping for the kronecker product between the sparse spatial and angular matrices, including Dirichlet boundary conditions, was created. Atomicity is preserved by graph-coloring overlapping nodes into separate kernel launches. The one-time mapping calculations for matrix assembly, kronecker product, and boundary condition application took 452±1ms on GPU. Matrix assembly for 16 energy groups took 556±3s on CPU, and 358±2ms on GPU using the mappings developed. The CG solver took 93±1s on CPU, and 468±2ms on GPU. Conclusion: Three computationally intensive subroutines in deterministically solving the LBTE have been formulated on GPU, resulting in two orders of magnitude speedup. Funding support from Natural Sciences and Engineering Research Council and Alberta Innovates Health Solutions. Dr. Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization).

60 APPLIED LIFE SCIENCES↗
NASA NTRS1987

A hypermatrix formulation for subspace iteration

The computational efficiency of subspace iteration is addressed relative to the data structures adopted for the very large and generally sparse coefficient matrices. The frequent triangulations and matrix multiplications demand that access to the terms in the coefficient matrices be unbiased. Reliance on virtual memory (paging) operating systems with no special considerations for localized data access is not adequate. Specific data structures must be designed that accommodate the needs of the numerical algorithm yet eliminate unnecessary paging. An implementation of the subspace iteration method using hypermatrix data structures is presented. Use of hypermatrices is shown to provide unbiased and localized data access. The various modifications to the conventional formulation are described and an example problem illustrates the potential benefits of the hypermatrix formulation. Possibilities for adapting hypermatrix data structures to new supercomputer architectures are discussed.

Schmidt, Richard J.↗
NASA NTRS1999

Efficient Implementations of the Quadrature-Free Discontinuous Galerkin Method

The efficiency of the quadrature-free form of the dis- continuous Galerkin method in two dimensions, and briefly in three dimensions, is examined. Most of the work for constant-coefficient, linear problems involves the volume and edge integrations, and the transformation of information from the volume to the edges. These operations can be viewed as matrix-vector multiplications. Many of the matrices are sparse as a result of symmetry, and blocking and specialized multiplication routines are used to account for the sparsity. By optimizing these operations, a 35% reduction in total CPU time is achieved. For nonlinear problems, the calculation of the flux becomes dominant because of the cost associated with polynomial products and inversion. This component of the work can be reduced by up to 75% when the products are approximated by truncating terms. Because the cost is high for nonlinear problems on general elements, it is suggested that simplified physics and the most efficient element types be used over most of the domain.

Lockard, David P.↗
DOE OSTI2024

Shifting Between Compute and Memory Bounds: A Compression-Enabled Roofline Model

In the evolving landscape of high-performance computing, especially to fight the end of Moore’s Law and Dennard’s Scaling, the ability to shift between compute-bound and memory-bound states is critical for enhancing adaptability and flexibility to diverse system and domain-specific architectures. Such capability is vital for optimizing performance across distinguished hardware configurations, such as accelerators, memory hierarchies, and cache systems. Despite that ad hoc optimization techniques, such as compressed/approximate computation, have been enabled for compute-/data-intensive computing for improved performance in distinct hardware settings, there lacks an understanding of 1) the rational behind performance improvement; 2) capability of different optimizations; 3) what optimization to respond to specific computational and memory demands. This work proposes a compression-enabled roofline model to facilitate this adaptability with data compression techniques to balance and transform between computational and memory demands. This model enables applications to adjust in response to the specific strengths and limitations of the underlying hardware and system to optimize resource utilization. The effectiveness of this approach is demonstrated with matrix multiplication kernels on different input sizes, with turning on/off various compression techniques, including 1) low-precision floating point; 2) sparse matrix formulation; and 3) compressed arrays with ZFP. By reducing memory transfer volumes and cache misses and increasing data locality and computational intensity through compression, the specific roofline model can transform between compute and memory bounds to align more efficiently with system capabilities. This advancement not only improves overall performance but also maximizes adaptability in diverse computing environments.

Naraparaju, Ramasoumya [University of Washington]↗
DOE OSTI2024

Energy-Efficient Neuromorphic Architectures for Nuclear Radiation Detection Applications

A comprehensive analysis and simulation of two memristor-based neuromorphic architectures for nuclear radiation detection is presented. Both scalable architectures retrofit a locally competitive algorithm to solve overcomplete sparse approximation problems by harnessing memristor crossbar execution of vector–matrix multiplications. The proposed systems demonstrate excellent accuracy and throughput while consuming minimal energy for radionuclide detection. To ensure that the simulation results of our proposed hardware are realistic, the memristor parameters are chosen from our own fabricated memristor devices. Based on these results, we conclude that memristor-based computing is the preeminent technology for a radiation detection platform.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1990

Using a multifrontal sparse solver in a high performance, finite element code

We consider the performance of the finite element method on a vector supercomputer. The computationally intensive parts of the finite element method are typically the individual element forms and the solution of the global stiffness matrix both of which are vectorized in high performance codes. To further increase throughput, new algorithms are needed. We compare a multifrontal sparse solver to a traditional skyline solver in a finite element code on a vector supercomputer. The multifrontal solver uses the Multiple-Minimum Degree reordering heuristic to reduce the number of operations required to factor a sparse matrix and full matrix computational kernels (e.g., BLAS3) to enhance vector performance. The net result in an order-of-magnitude reduction in run time for a finite element application on one processor of a Cray X-MP.

King, Scott D.↗
DOE OSTI2015

BiGlobal Secondary Instabilities of Roughness-Induced Transient Growth

Roughness-induced transient disturbances distort laminar boundary layers and can lead to premature transition if the roughness is of sufficient height and shape. If transition does occur, it does so through a high-frequency "secondary" instability of the roughness wake. A BiGlobal secondaryinstability code has been developed to solve the stability problem downstream of roughness. The code implements multiple solvers for incompressible/compressible, inviscid/viscous, and temporal/spatial stability. High-order finite differences, sparse matrix linear algebra, LU decomposition, and Arnoldi iterations are used to solve the resulting generalized eigenvalue problem. The code has been used to evaluate the stability properties of experimental roughness-induced transient growth on a flat-plate at low-speed and a slightly blunted cone at M∞= 6. The resulting mode shapes, growth rates, and spatial N-factors show excellent agreement with experimental data. The viscous mode shapes show the best agreement with the experimental disturbance profiles. Yet, execution time can be reduced by an order-of-magnitude by using the inviscid solvers with only modest differences in growth rates.

BiGlobal↗
DOE OSTI2025

Why Is Attention Sparse In Particle Transformer?

Transformer-based models have achieved state-of-the-art performance in jet tagging at the CERN Large Hadron Collider (LHC), with the Particle Transformer (ParT) representing a leading example of such models. A striking feature of ParT is its sparse, nearly binary, attention structure, raising questions about the origin of this behavior and whether it encodes physically meaningful correlations. In this work, we investigate the source of ParT's sparse attention by comparing models trained on multiple benchmark datasets and examine the relative contributions of the attention term and the physics-inspired interaction matrix before softmax. We find that binary sparsity arises primarily from the attention mechanism itself, with the interaction matrix playing a secondary role. Moreove, we show that ParT is able to identify key jet substructure elements, such as leptons in semileptonic top decays, even without explicit particle identification inputs. These results provide new insight into the interpretability of transformer-based jet taggers and clarify the conditions under which sparse attention patterns emerge in ParT.

Legge, Timothy [UC, San Diego]↗
DOE OSTI2017

Scaling Up Data-Parallel Analytics Platforms: Linear Algebraic Operation Cases

Linear algebraic operations such as matrix manipulations form the kernel of many machine learning and other crucial algorithms. Scaling up as well as scaling out such algorithms are key to supporting large scale data analysis that require efficient processing over millions of data samples. To this end, we present, ARION, a hardware acceleration based approach for scaling-up individual tasks of Spark, a popular data-parallel analytics platform. We support both linear algebraic operations of between two dense matrices, and between sparse and dense matrices in distributed environments. ARION provides a flexible control of acceleration according to matrix density, along with efficient scheduling based on runtime resource utilization. We demonstrate the benefit of our approach for general matrix multiplication operations over large matrices with up to four billion elements by using Gramian matrix computation that is commonly used in machine learning. Experiments show that our approach achieves more than 2× and 1.5× end-to-end performance speedups for dense and sparse matrices, respectively, and up to 57.04× faster computation compared to MLlib, a state of the art Spark-based implementation. This work is sponsored in part by the NSF under the grants: CNS-1565314, CNS-1405697, and CNS-1615411. The manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.

Xu, Luna↗