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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Feeder Power Disaggregation: A Data-Efficient Matrix Completion Approach

This paper presents a data-driven algorithm for the feeder power disaggregation problem in distribution systems. Leveraging spatio-temporal power patterns in residential homes, residential power is discomposed into three components: sparse-switching loads, periodic loads, and photovoltaic (PV) generation, which are characterized through the design of two sparse matrices and a low-rank matrix. The matrix completion process is data-efficient because of the matrix sparsity and low rankness, along with the use of power system models. The proposed approach is tested using real-world residential data set on a 33-bus distribution system, demonstrating accurate power disaggregation with efficient matrix completion.

distribution system↗
DOE OSTI2023

Feeder Power Disaggregation: A Data-Efficient Matrix Completion Approach: Preprint

This paper presents a data-driven algorithm for the feeder power disaggregation problem in distribution systems. Leveraging spatio-temporal power patterns in residential homes, residential power is discomposed into three components: sparse-switching loads, periodic loads, and photovoltaic generation, using two sparse matrices and a rank-one matrix. The matrix completion process is data-efficient because of the matrix sparsity and low rankness, along with the use of power system models. The proposed approach is tested using real-world residential datasets on a 33-bus distribution system, demonstrating accurate power disaggregation with efficient matrix completion.

distribution system↗
DOE OSTI2024

Quantum chaos on edge

Recently, the physics of many-body quantum chaotic systems close to their ground states has come under intensified scrutiny. Such studies are motivated by the emergence of model systems exhibiting chaotic fluctuations throughout the entire spectrum [the Sachdev-Ye-Kitaev (SYK) model being a renowned representative] as well as by the physics of holographic principles, which likewise unfold close to ground states. Interpreting the edge of the spectrum as a quantum critical point, here we combine a wide range of analytical and numerical methods to the identification and comprehensive description of two different universality classes: the near edge physics of “sparse” and the near edge of “dense” chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension, which is exponentially small or algebraically small in the sparse and dense case, respectively. Notable representatives of the two classes are generic chaotic many-body models (sparse) and invariant random matrix ensembles or chaotic gravitational systems (dense). While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different. Considering the SYK model as a representative of the sparse class, we apply a combination of field theory and exact diagonalization to a detailed discussion of its edge spectrum. Conversely, Jackiw-Teitelboim gravity is our reference model for the dense class, where an analysis of the gravitational path integral and random matrix theory reveal universal differences to the sparse class, whose implications for the construction of holographic principles we discuss. Published by the American Physical Society 2024

Altland, Alexander (ORCID:0000000229914805)↗
DOE OSTI2018

Indigo: A Domain-Specific Language for Fast, Portable Image Reconstruction

© 2018 IEEE. Linear operators used in iterative methods like conjugate gradient have typically been implemented either as ''matrix-driven'' subroutines backed by explicit sparse or dense matrices, or as ''matrix-free'' subroutines that implement specific linear operations directly (e.g. FFTs). The matrix-driven approach is generally more portable because it can target widely-Available BLAS libraries, but it can be inefficient in terms of time and space complexity. In contrast, the matrix-free approach is more performant because it leverages structure in operations, but it requires each operator be re-implemented on each new platform. To increase performance and portability, we propose a hybrid approach that represents linear operators as expression trees. Leaf nodes in the tree are either matrix-free or matrix-driven operators, and interior nodes represent mathematical compositions (sums, products, transposes) or structural compositions (stacks, block diagonals, etc.) of the leaf operators. This representation enables expert-guided reordering and fusion transformations that can improve performance or reduce memory pressure. We implement our approach in a domain-specific language called Indigo. We assess Indigo on image reconstruction problems arising in four application areas: magnetic resonance imaging, ptychography, magnetic particle imaging, and fluorescent microscopy. We give performance results from vendor BLAS libraries, and we introduce specializations to Sparse BLAS routines that achieve near-Roofline performance on multi-core, many-core, and GPU systems.

Driscoll, Michael↗
DOE OSTI2015

Basic Matrix Library (bml), Version 0.x

The basic matrix library (bml) is a collection of various matrix data formats (in dense and sparse) and their associated algorithms for basic matrix operations.

Source record↗
DOE OSTI2015

Basic Matrix Library (bml), Version 0.x

The basic matrix library (bml) is a collection of various matrix data formats (in dense and sparse) and their associated algorithms for basic matrix operations.

Source record↗
DOE OSTI2026

Block encoding of the three-dimensional heterogeneous Poisson equation with application to fracture flow

Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as state preparation, data loading, and efficient information extraction. In this work, we study the feasibility of applying QLS algorithms to solve discretized three-dimensional (3D) heterogeneous Poisson equations, with specific examples relating to groundwater flow through geologic fracture networks. We explicitly construct a block encoding for the 3D heterogeneous Poisson matrix by leveraging the sparse local structure of the discretized operator. While classical solvers benefit from preconditioning, we show that block encoding the system matrix and preconditioner separately does not improve the effective condition number that dominates the QLS run-time. This differs from classical approaches where the preconditioner and the system matrix can often be implemented independently. Nevertheless, due to the structure of the problem in three dimensions, the quantum algorithm achieves a run-time of 𝑂⁡(𝑁 2/3 polylog 𝑁 ⋅log (1/𝜖)), outperforming the best classical methods (with run times of 𝑂⁡(𝑁⁢log 𝑁 ⋅log (1/𝜖))) and offering exponential memory savings. These results highlight both the promise and limitations of QLS algorithms for practical scientific computing, and point to effective condition-number reduction as a key barrier in achieving quantum advantages.

58 GEOSCIENCES↗
DOE OSTI2022

Analysis of sparse recovery for Legendre expansions using envelope bound

We provide novel sufficient conditions for the uniform recovery of sparse Legendre expansions using ℓ 1 minimization, where the sampling points are drawn according to orthogonalization (uniform) measure. So far, conditions of the form m ≳ Θ 2 s x log factors have been relied on to determine the minimum number of samples m that guarantees successful reconstruction of s-sparse vectors when the measurement matrix is associated to an orthonormal system. However, in case of sparse Legendre expansions, the uniform bound Θ of Legendre systems is so high that these conditions are unable to provide meaningful guarantees. Here, in this paper, we present an analysis which employs the envelop bound of all Legendre polynomials instead, and prove a new recovery guarantee for s-sparse Legendre expansions, m ≳ Θs 2 x log factors, which is independent of Θ. Arguably, this is the first recovery condition established for orthonormal systems without assuming the uniform boundedness of the sampling matrix. The key ingredient of our analysis is an extension of chaining arguments, recently developed in Bourgain and Chkifa et al., to handle the envelope bound. Furthermore, our recovery condition is proved via restricted eigenvalue property, a less demanding replacement of restricted isometry property which is perfectly suited to the considered scenario. Along the way, we derive simple criteria to detect good sample sets. Our numerical tests show that sets of uniformly sampled points that meet these criteria will perform better recovery on average.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Hybrid programming-model strategies for GPU offloading of electronic structure calculation kernels

To address the challenge of performance portability and facilitate the implementation of electronic structure solvers, we developed the basic matrix library (BML) and Parallel, Rapid O(N), and Graph-based Recursive Electronic Structure Solver (PROGRESS) library. The BML implements linear algebra operations necessary for electronic structure kernels using a unified user interface for various matrix formats (dense and sparse) and architectures (CPUs and GPUs). Focusing on density functional theory and tight-binding models, PROGRESS implements several solvers for computing the single-particle density matrix and relies on BML. In this paper, we describe the general strategies used for these implementations on various computer architectures, using OpenMP target functionalities on GPUs, in conjunction with third-party libraries to handle performance critical numerical kernels. In this study, we demonstrate the portability of this approach and its performance in benchmark problems.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Efficient Parallel Sparse Symmetric Tucker Decomposition for High-Order Tensors

Tensor based methods are receiving renewed attention in recent years due to their prevalence in diverse real-world applications. There is considerable literature on tensor representations and algorithms for tensor decompositions, both for dense and sparse tensors. Many applications in hypergraph analytics, machine learning, psychometry, and signal processing result in tensors that are both sparse and symmetric, making it an important class for further study. Similar to the critical Tensor Times Matrix chain operation (TTMc) in general sparse tensors, the Sparse Symmetric Tensor Times Same Matrix chain (S3TTMc) operation is compute and memory intensive due to high tensor order and the associated factorial explosion in the number of non-zeros. In this work, we present a novel compressed storage format CSS for sparse symmetric tensors, along with an efficient parallel algorithm for the S3TTMc operation. We theoretically establish that S3TTMc on CSS achieves a better memory versus run-time trade-off compared to state-of-the-art implementations. We demonstrate experimental findings that confirm these results and achieve up to 2.9× speedup on synthetic and real datasets.

Shivakumar, Shruti↗
DOE OSTI2017

Adaptive OFDM Waveform Design for Spatio-Temporal-Sparsity Exploited STAP Radar

In this chapter, we describe a sparsity-based space-time adaptive processing (STAP) algorithm to detect a slowly moving target using an orthogonal frequency division multiplexing (OFDM) radar. The motivation of employing an OFDM signal is that it improves the target-detectability from the interfering signals by increasing the frequency diversity of the system. However, due to the addition of one extra dimension in terms of frequency, the adaptive degrees-of-freedom in an OFDM-STAP also increases. Therefore, to avoid the construction a fully adaptive OFDM-STAP, we develop a sparsity-based STAP algorithm. We observe that the interference spectrum is inherently sparse in the spatio-temporal domain, as the clutter responses occupy only a diagonal ridge on the spatio-temporal plane and the jammer signals interfere only from a few spatial directions. Hence, we exploit that sparsity to develop an efficient STAP technique that utilizes considerably lesser number of secondary data compared to the other existing STAP techniques, and produces nearly optimum STAP performance. In addition to designing the STAP filter, we optimally design the transmit OFDM signals by maximizing the output signal-to-interference-plus-noise ratio (SINR) in order to improve the STAP performance. The computation of output SINR depends on the estimated value of the interference covariance matrix, which we obtain by applying the sparse recovery algorithm. Therefore, we analytically assess the effects of the synthesized OFDM coefficients on the sparse recovery of the interference covariance matrix by computing the coherence measure of the sparse measurement matrix. Our numerical examples demonstrate the achieved STAP-performance due to sparsity-based technique and adaptive waveform design.

Sen, Satyabrata↗
DOE OSTI2021

Spray: Sparse Reductions of Arrays in OPEN MP

We present SPRAY, an open-source header-only C++ library for sparse reductions of arrays. SPRAY is meant for applications in which a large array is collaboratively updated by multiple threads using an associative and commutative operation such as +=. Especially when each thread accesses only parts of the array, SPRAY can perform significantly better than OPENMP's built-in reduction clause or atomic updates, while also using less memory than the former. SPRAY provides both an easy-to-use interface that can serve as a drop-in replacement for OPENMP reductions and a selection of reducer objects that accumulate the final result in different thread-safe ways. We demonstrate SPRAY through multiple test cases including the LULESH shock hydrodynamics code and a transpose-matrix-vector multiplication for sparse matrices stored in CSR format. SPRAY reductions outperform built-in OPENMP reductions consistently, in some cases improving run time and memory overhead by 20X, and even beating domain-specific approaches such as Intel MKI, by over 2X in some cases. Furthermore, SPRAY reductions have a minimal impact on the code base, requiring only a few lines of source code changes. Once in place, SPRAY reduction schemes can be switched easily, allowing performance portability and tuning opportunities by separating performance-critical implementation details from application code.

OpenMP↗
DOE OSTI2025

ORMATEX

The Oak Ridge Matrix Exponential (ORMATEX) software library contains methods to compute the matrix exponential and the action of the matrix exponential on a vector. Additionally, this package contains the related methods for the phi-functions which commonly appear in a wide class of exponential time integration methods. Krylov methods are provided to evaluate the matrix exponential-vector and phi-vector products for cases where the matrix is large and sparse. Utilizing these methods, ORMATEX implements performant exponential integrators for large systems of coupled ordinary differential equations (ODEs). The exponential time integration routines in ORMATEX are particularly suitable to large, stiff systems of equations. These routines may be utilized as a competitive alternative to classical implicit and explicit time integration schemes for certain classes of differential equations where the problem stiffness can be predominately explained by the linear terms.

Gurecky, William [Oak Ridge National Laboratory (O↗
DOE OSTI2025

Classical Benchmarks for Variational Quantum Eigensolver Simulations of the Hubbard Model

Simulating the Hubbard model is of great interest to a wide range of applications within condensed matter physics, however its solution on classical computers remains challenging in dimensions larger than one. The relative simplicity of this model, embodied by the sparseness of the Hamiltonian matrix, allows for its efficient implementation on quantum computers, and for its approximate solution using variational algorithms such as the variational quantum eigensolver. While these algorithms have been shown to reproduce the qualitative features of the Hubbard model, their quantitative accuracy in terms of producing true ground state energies and other properties, and the dependence of this accuracy on the system size and interaction strength, the choice of variational ansatz, and the degree of spatial inhomogeneity in the model, remains unknown. Here we present a rigorous classical benchmarking study, demonstrating the potential impact of these factors on the accuracy of the variational solution of the Hubbard model on quantum hardware, for systems with up to 32 qubits. We find that even when using the most accurate wavefunction ansätze for the Hubbard model, the error in its ground state energy and wavefunction plateaus for larger lattices, while stronger electronic correlations magnify this issue. Concurrently, spatially inhomogeneous parameters and the presence of off-site Coulomb interactions only have a small effect on the accuracy of the computed ground state energies. Our study highlights the capabilities and limitations of current approaches for solving the Hubbard model on quantum hardware, and we discuss potential future avenues of research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Single-Cell RNA-Seq Reveals Transcriptomic Heterogeneity and Post-Traumatic Osteoarthritis-Associated Early Molecular Changes in Mouse Articular Chondrocytes

Articular cartilage is a connective tissue lining the surfaces of synovial joints. When the cartilage severely wears down, it leads to osteoarthritis (OA), a debilitating disease that affects millions of people globally. The articular cartilage is composed of a dense extracellular matrix (ECM) with a sparse distribution of chondrocytes with varying morphology and potentially different functions. Elucidating the molecular and functional profiles of various chondrocyte subtypes and understanding the interplay between these chondrocyte subtypes and other cell types in the joint will greatly expand our understanding of joint biology and OA pathology. Although recent advances in high-throughput OMICS technologies have enabled molecular-level characterization of tissues and organs at an unprecedented resolution, thorough molecular profiling of articular chondrocytes has not yet been undertaken, which may be in part due to the technical difficulties in isolating chondrocytes from dense cartilage ECM. In this study, we profiled articular cartilage from healthy and injured mouse knee joints at a single-cell resolution and identified nine chondrocyte subtypes with distinct molecular profiles and injury-induced early molecular changes in these chondrocytes. We also compared mouse chondrocyte subpopulations to human chondrocytes and evaluated the extent of molecular similarity between mice and humans. This work expands our view of chondrocyte heterogeneity and rapid molecular changes in chondrocyte populations in response to joint trauma and highlights potential mechanisms that trigger cartilage degeneration.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

Acceleration of GPU-based Krylov solvers via data transfer reduction

Krylov subspace iterative solvers are often the method of choice when solving large sparse linear systems. At the same time, hardware accelerators such as graphics processing units continue to offer significant floating point performance gains for matrix and vector computations through easy-to-use libraries of computational kernels. However, as these libraries are usually composed of a well optimized but limited set of linear algebra operations, applications that use them often fail to reduce certain data communications, and hence fail to leverage the full potential of the accelerator. In this study, we target the acceleration of Krylov subspace iterative methods for graphics processing units, and in particular the Biconjugate Gradient Stabilized solver that significant improvement can be achieved by reformulating the method to reduce data-communications through application-specific kernels instead of using the generic BLAS kernels, e.g. as provided by NVIDIA’s cuBLAS library, and by designing a graphics processing unit specific sparse matrix-vector product kernel that is able to more efficiently use the graphics processing unit’s computing power. Furthermore, we derive a model estimating the performance improvement, and use experimental data to validate the expected runtime savings. Finally, considering that the derived implementation achieves significantly higher performance, we assert that similar optimizations addressing algorithm structure, as well as sparse matrix-vector, are crucial for the subsequent development of high-performance graphics processing units accelerated Krylov subspace iterative methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A radial basis function Galerkin method for inhomogeneous nonlocal diffusion

We introduce a discretization for a nonlocal diffusion problem using a localized basis of radial basis functions. The stiffness matrix entries are assembled by a special quadrature routine unique to the localized basis. Combining the quadrature method with the localized basis produces a well-conditioned, sparse, symmetric positive definite stiffness matrix. We demonstrate that both the continuum and discrete problems are well-posed and present numerical results for the convergence behavior of the radial basis function method. As a result, we explore approximating the solution to anisotropic differential equations by solving anisotropic nonlocal integral equations using the radial basis function method.

97 MATHEMATICS AND COMPUTING↗