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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Bringing randomized algorithms to mainstream numerical linear algebra

Numerical linear algebra (NLA) underpins huge swaths of computational science and engineering. For scientists and engineers to make the most of the DOE’s computing resources, it is essential that they have access to high-performance implementations of algorithms with best-in-class scalability and reliability. Despite this, prevailing NLA libraries have little to no support for breakthrough algorithms from the field of randomized numerical linear algebra (RandNLA) that have been developed over the past twenty years. The goal of this LDRD was to break a log-jam that had prevented broad adoption of RandNLA. Our work had two thrusts. The first was to develop RandBLAS: a trustworthy and high-performance C++ library for randomized dimension reduction (an operation widely known as sketching). The second was the development of a novel randomized algorithm for computing a challenging type of matrix decomposition known as Householder QR with column pivoting (Householder QRCP). In this one-year late-start LDRD we successfully delivered RandBLAS 1.0 and new CPU and GPU codes for Householder QRCP. RandBLAS has extensive documentation at https://randblas.readthedocs.io/en/stable/. Papers on RandBLAS and and our high-performance QRCP codes are forthcoming.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

HALA: Handy Accelerated Linear Algebra

Accelerated linear algebra libraries often come with C-style of interfaces or even older Fortran77 standards, which makes it difficult to use within generic template programming environment of modern C++. For example, the BLAS and derived standards such as cuBLAS do not accept overloads and a different functions have to be called for each input type, thus it is very challenging to write a single template that handles multiple precision modes and works well with different C++ containers. HALA offers a series of templates that wrap around the BLAS/cuBLAS and other similar methods, automatically infer the relevant types and call the appropriate back-end. The templates work out-of-the-box with all C++ standard vector-like containers and can be easily extended (with template specializations) to handle user-provided containers. The HALA API is also overloaded to handle both GPU and CPU cases with a single "engine" class, thus a single high-level algorithms can utilize both CPU or GPU backends, i.e., the HALA API is unified and handles the variations between cuBLAS and BLAS. In addition to BLAS and cuBLAS, wrapper templates are provided for subset of LAPACK, cuSparse, and Cholmod methods. Work is in progress to complete as many of these standards as possible. HALA also includes a module for low-level extended register vectorization for complex number arithmetic and several simple solvers that build on the basic linear algebra capabilities. A single unified C++ API will benefit fast prototyping and easily writing code that is portable across GPU/CPU platforms as well as precision types and user containers. Note that HALA does not provide any accelerated algorithms, it simply serves as a "handy" front-end to other standards.

Stoyanov, MiroslavK.↗
DOE OSTI2024

Evolution of the SLATE linear algebra library

SLATE (Software for Linear Algebra Targeting Exascale) is a distributed, dense linear algebra library targeting both CPU-only and GPU-accelerated systems, developed over the course of the Exascale Computing Project (ECP). While it began with several documents setting out its initial design, significant design changes occurred throughout its development. In some cases, these were anticipated: an early version used a simple consistency flag that was later replaced with a full-featured consistency protocol. In other cases, performance limitations and software and hardware changes prompted a redesign. Sequential communication tasks were parallelized; host-to-host MPI calls were replaced with GPU device-to-device MPI calls; more advanced algorithms such as Communication Avoiding LU and the Random Butterfly Transform (RBT) were introduced. Early choices that turned out to be cumbersome, error prone, or inflexible have been replaced with simpler, more intuitive, or more flexible designs. Applications have been a driving force, prompting a lighter weight queue class, nonuniform tile sizes, and more flexible MPI process grids. Of paramount importance has been building a portable library that works across several different GPU architectures – AMD, Intel, and NVIDIA – while keeping a clean and maintainable codebase. Here we explore the evolving design choices and their effects, both in terms of performance and software sustainability.

Gates, Mark↗
DOE OSTI2025

Enabling Efficient Sparse Computations using Linear Algebra Aware Compilers

This project developed the LAPIS compiler framework, built on the Multilevel Intermediate Representation (MLIR), to optimize sparse linear algebra operations and support performance portability across diverse architectures. The main innovation of LAPIS is the Kokkos dialect, which allows for lowering codes from a high productivity language to different architectures in an elegant way. The dialect also allows the conversion of lower-level MLIR code to C++ Kokkos code, facilitating the integration of scientific machine learning (SciML) models into applications. To extend LAPIS for distributed memory architectures, a new partition dialect was created to manage the distribution of sparse tensors and express communication patterns for sparse linear algebra operations. This dialect also supports the distributed execution of operators and includes algorithmic optimizations to minimize communication to improve performance. The project also demonstrates that MLIR can enable effective linear algebra-level optimizations, improving performance on different GPUs for both sparse and dense linear algebra kernels. Key applications of LAPIS include sparse linear algebra and graph kernels, TenSQL, a relational database management solution built on GraphBLAS, and the development of subgraph isomorphism and monomorphism kernels, showcasing performance portability. In summary, the LAPIS framework supports productivity, performance, portability, and distributed memory execution, while also enabling linear algebra-level optimizations that are challenging in traditional programming languages, with successful applications ranging from simple sparse linear algebra to complex graph kernels.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A survey of numerical linear algebra methods utilizing mixed-precision arithmetic

The efficient utilization of mixed-precision numerical linear algebra algorithms can offer attractive acceleration to scientific computing applications. Especially with the hardware integration of low-precision special-function units designed for machine learning applications, the traditional numerical algorithms community urgently needs to reconsider the floating point formats used in the distinct operations to efficiently leverage the available compute power. In this study, we provide a comprehensive survey of mixed-precision numerical linear algebra routines, including the underlying concepts, theoretical background, and experimental results for both dense and sparse linear algebra problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

LAPIS: Linear Algebra Performance for Intermediate Subprograms

SAND2025-11594O LAPIS (Linear Algebra Performance for Intermediate Subprograms) is a compiler infrastructure for linear algebra that targets both high productivity and performance portability. It is based on the open-source MLIR package from the LLVM project. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Kelley, Brian↗
DOE OSTI2019

Constant depth, near constant depth, and subcubic size threshold circuits for linear algebraic calculations

A method of increasing an efficiency at which a plurality of threshold gates arranged as neuromorphic hardware is able to perform a linear algebraic calculation having a dominant size of N. The computer-implemented method includes using the plurality of threshold gates to perform the linear algebraic calculation in a manner that is simultaneously efficient and at a near constant depth. “Efficient” is defined as a calculation algorithm that uses fewer of the plurality of threshold gates than a naïve algorithm. The naïve algorithm is a straightforward algorithm for solving the linear algebraic calculation. “Constant depth” is defined as an algorithm that has an execution time that is independent of a size of an input to the linear algebraic calculation. The near constant depth comprises a computing depth equal to or between O(log(log(N)) and the constant depth.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Quantum many-body linear algebra, Hamiltonian moments, and a coupled-cluster inspired framework

Here, we propose a general strategy to develop quantum many-body approximations of primitives in linear algebra algorithms. As a practical example, we introduce a coupled-cluster inspired framework to produce approximate Hamiltonian moments and demonstrate its application in various linear algebra algorithms for ground state estimation. Through numerical examples, we illustrate the difference between the ground-state energies arising from quantum many-body linear algebra and those from the analogous many-body perturbation theory. Our results support the general idea of designing quantum many-body approximations outside of perturbation theory, providing a route to new algorithms and approximations.

Algorithms and data structure↗
DOE OSTI2021

Replicated Computational Results (RCR) Report for “Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software”

The article by Flegar et al. titled “Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software” presents a novel, practical implementation of an adaptive precision block-Jacobi preconditioner. Performance results using state-of-the-art GPU architectures for the block-Jacobi preconditioner generation and application demonstrate the practical usability of the method, compared to a traditional full-precision block-Jacobi preconditioner. A production-ready implementation is provided in the Ginkgo numerical linear algebra library. In this report, the Ginkgo library is reinstalled and performance results are generated to perform a comparison to the original results when using Ginkgo’s Conjugate Gradient solver with either the full or the adaptive precision block-Jacobi preconditioner for a suite of test problems on an NVIDIA GPU accelerator. After completing this process, the published results are deemed reproducible.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Parallel algorithms for finding connected components using linear algebra

Finding connected components is one of the most widely used operations on a graph. Optimal serial algorithms for the problem have been known for half a century, and many competing parallel algorithms have been proposed over the last several decades under various different models of parallel computation. This paper presents a class of parallel connected-component algorithms designed using linear-algebraic primitives. These algorithms are based on a PRAM algorithm by Shiloach and Vishkin and can be designed using standard GraphBLAS operations. Here, we demonstrate two algorithms of this class, one named LACC for Linear Algebraic Connected Components, and the other named FastSV which can be regarded as LACC’s simplification. With the support of the highly-scalable Combinatorial BLAS library, LACC and FastSV outperform the previous state-of-the-art algorithm by a factor of up to 12x for small to medium scale graphs. For large graphs with more than 50B edges, LACC and FastSV scale to 4K nodes (262K cores) of a Cray XC40 supercomputer and outperform previous algorithms by a significant margin. This remarkable performance is accomplished by (1) exploiting sparsity that was not present in the original PRAM algorithm formulation, (2) using high-performance primitives of Combinatorial BLAS, and (3) identifying hot spots and optimizing them away by exploiting algorithmic insights.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

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↗
DOE OSTI2023

Graph Neural Networks and Applied Linear Algebra v.1.0

SAND2024-01365O The Graph Neural Networks and Applied Linear Algebra is companion software for the educational article with the same title. The software provides illustrative examples of graph neural networks in Matlab and Python. These stand-alone algorithms are for educational purposes. The software also includes graph neural network-based algorithms for a trainable Jacobi iteration as well as diffusion coefficient estimation. The software provides human-interpretable implementations of Graph Neural Networks in Matlab and Python. These implementations are not optimized for performance and instead emphasize readability. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
DOE OSTI2025

Memristive linear algebra

The advent of memristive devices offers a promising avenue for efficient and scalable analog computing, particularly for linear algebra operations essential in various scientific and engineering applications. This paper investigates the potential of memristive crossbars in implementing matrix inversion algorithms. We explore both static and dynamic approaches, emphasizing the advantages of analog and in-memory computing for matrix operations beyond multiplication. In particular, we demonstrate that the electrical properties of memristive crossbars uniquely suit them for the evolution of a family of matrix exponentials, which can be exploited for the efficient computation of matrix inverses and online solutions for linear problems. Our results demonstrate that memristive arrays can reduce computational complexity. We also study power consumption and show a tradeoff between precision and energy. Furthermore, we address the challenges of device variability, precision, and scalability, providing insights into the practical implementation of these algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Incremental Interval Assignment by Integer Linear Algebra with Improvements

Interval Assignment (IA) is the problem of selecting the number of mesh edges (intervals) for each curve for conforming quad and hex meshing. The intervals x is fundamentally integer-valued. Many other approaches perform numerical optimization then convert a floating-point solution into an integer solution, which is slow and error prone. We avoid such steps: we start integer, and stay integer. Incremental Interval Assignment (IIA) uses integer linear algebra (Hermite normal form) to find an initial solution to the meshing constraints, satisfying the integer matrix equation Solving for reduced row echelon form provides integer vectors spanning the nullspace of A. Here we add vectors from the nullspace to improve the initial solution, maintaining Ax = b Heuristics find good integer linear combinations of nullspace vectors that provide strict improvement towards variable bounds or goals. IIA always produces an integer solution if one exists. In practice we usually achieve solutions close to the user goals, but there is no guarantee that the solution is optimal, nor even satisfies variable bounds, e.g. has positive intervals. We describe several algorithmic changes since first publication that tend to improve the final solution. The software is freely available.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Surface science insight note: A linear algebraic approach to elucidate native films on Fe 3 O 4 surface

Standard materials are often used to obtain spectra that can be compared to those from unknown samples. Spectra measured from these known substances are also used as a means of computing sensitivity factors to allow quantification by X-ray photoelectron spectroscopy (XPS) of less well-defined materials. Spectra from known materials also provide line shapes suitable for inclusion in spectral models which, when fitted to spectra, permit the chemical state for a sample to be assessed. Both types of information depend on isolating photoemission signals from the inelastically scattered signal. In this Insight note, technical issues associated with the use of XPS of as received Fe 3 O 4 powder sample surface are discussed. The Insight note is designed to show how linear algebraic techniques applied to data collected from a sample marketed as pure Fe 3 O 4 powder are used to verify that XPS has been performed on chemistry representative of the sample. The methods described in this Insight note can further be utilized in elucidating complex XPS data obtained from thin films formed or evolved during cyclic/non-steady use of complex (electro)catalyst surfaces, especially in the presence of contaminants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Replicated Computational Results (RCR) Report for "Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software''

In, a practical implementation of a novel adaptive precision block-Jacobi preconditioner is introduced. In particular, the authors present a heavily-tuned GPU implementation of the adaptive precision block-Jacobi preconditioner within the Ginkgo numerical linear algebra library. The performance of the methodology and implementation is demonstrated using the proposed preconditioning scheme within Ginkgo’s high-performance Conjugate Gradient (CG) implementation on an NVIDIA Volta GPU. In this report, we replicate a subset of the computational results presented in. The focus is generating results from Fig. 9 to evaluate the performance of using Ginkgo’s CG solver integrated with either the full or the adaptive precision block-Jacobi preconditioner applied to a variety of test cases

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Inexact iterative numerical linear algebra for neural network-based spectral estimation and rare-event prediction

Understanding dynamics in complex systems is challenging because there are many degrees of freedom, and those that are most important for describing events of interest are often not obvious. The leading eigenfunctions of the transition operator are useful for visualization, and they can provide an efficient basis for computing statistics, such as the likelihood and average time of events (predictions). Here, we develop inexact iterative linear algebra methods for computing these eigenfunctions (spectral estimation) and making predictions from a dataset of short trajectories sampled at finite intervals. We demonstrate the methods on a low-dimensional model that facilitates visualization and a high-dimensional model of a biomolecular system. Implications for the prediction problem in reinforcement learning are discussed.

Chemistry↗