Search NASA⌕ Search

SEARCH · Search NASA

Results for “sparse decomposition”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Genten: Software for Generalized Tensor Decompositions v. 1.0.0

Tensors, or multidimensional arrays, are a powerful mathematical means of describing multiway data. This software provides computational means for decomposing or approximating a given tensor in terms of smaller tensors of lower dimension, focusing on decomposition of large, sparse tensors. These techniques have applications in many scientific areas, including signal processing, linear algebra, computer vision, numerical analysis, data mining, graph analysis, neuroscience and more. The software is designed to take advantage of parallelism present emerging computer architectures such has multi-core CPUs, many-core accelerators such as the Intel Xeon Phi, and computation-oriented GPUs to enable efficient processing of large tensors.

Phipps, EricT.↗
DOE OSTI2023

A Surrogate-Based Asynchronous Decomposition Technique for Realistic Security-Constrained Optimal Power Flow Problems

Here we present a decomposition approach for obtaining good feasible solutions for the security-constrained, alternating-current, optimal power flow (SC-AC-OPF) problem at an industrial scale and under real-world time and computational limits. The approach was designed while preparing and participating in ARPA-E’s Grid Optimization Competition (GOC) Challenge 1. The challenge focused on a near-real-time version of the SC-AC-OPF problem, where a base operating point is optimized, taking into account possible single-element contingencies, after which the system adapts its operating point following the response of automatic frequency droop controllers and voltage regulators. Our solution approach for this problem relies on state-of-the-art nonlinear programming algorithms, and it employs nonconvex relaxations for complementarity constraints, a specialized two-stage decomposition technique with sparse approximations of recourse terms and contingency ranking and prescreening. The paper describes and justifies our approach and outlines the features of its implementation, including functions and derivatives evaluation, warm-starting strategies, and asynchronous parallelism. We discuss the results of the independent benchmark of our approach by ARPA-E’s GOC team in Challenge 1, where it was found to consistently produce high-quality solutions across a wide range of network sizes and difficulty, and conclude by outlining future extensions of the approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

O(N) Quantum Molecular Dynamics (QMD) Algorithms, Code Requirements, Release Notes, and Library Deployment

The Exascale Computing Project (ECP) Co-design Center for Particle Applications (CoPA) is addressing the challenges for particle applications to run on upcoming exascale computing architectures. This includes short- and long-range molecular dynamics (MD), particle-in-cell (PIC), and quantum molecular dynamics (QMD). This document addresses $\mathcal{O}(N)$ QMD. The goal of this CoPA team is to develop $\mathcal{O}(N)$ linear scaling methods for QMD optimized for new and next generation architectures. This will provide the capability to simulate larger systems and run for longer timeframes than is possible today. Focus is initially on the density matrix construction. This requires efficient matrix formats and linear algebra operations for distributed architectures. A significant reduction in the wallclock time for an MD timestep is necessary to achieve practical large scale QMD. Equally challenging is to develop scalable distributed implementations. This requires the exploration of efficient data formats (dense, sparse, etc.), data decomposition and distribution across compute nodes using block- and graph-based methods. Traditional programming models such as MPI/OpenMP, hybrid MPI/OpenMP/Accelerator, as well as asynchronous task-based models will be explored to achieve maximum parallelism. Parallelism at the level of a matrix operation, solver, and/or application needs to be explored to gain the most benefit on new and emerging architectures. This report serves as a “living document” of the additions and enhancements throughout the ECP CoPA project for $\mathcal{O}(N)$ QMD. The following sections address the applications we are working with, the quantum chemistry libraries (BML and PROGRESS), and our co-design exploration through the use of a proxy application.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems

This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures, specifically, those that are equipped with graphic processing units (GPUs). In addition to block-Jacobi, we present general purpose two-level ILU Schur complement-based approaches, where different strategies are presented to solve the coarse-level reduced system. These strategies are combined with modified ILU methods in the construction of the coarse-level operator, in order to effectively remove smooth errors by targeting an algebraically smooth vector. We leverage available GPU-based sparse matrix kernels to accelerate the setup and the solve phases of the proposed ILU preconditioner. We evaluate the efficiency of the proposed methods as a smoother for algebraic multigrid (AMG) and as a preconditioner for Krylov subspace methods on challenging anisotropic diffusion problems and a collection of general sparse matrices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

GSoFa: Scalable Sparse Symbolic LU Factorization on GPUs

Decomposing a matrix $\mathbf {A}$ into a lower matrix $\mathbf {L}$ and an upper matrix $\mathbf {U}$, which is also known as LU decomposition, is an essential operation in numerical linear algebra. For a sparse matrix, LU decomposition often introduces more nonzero entries in the $\mathbf {L}$ and $\mathbf {U}$ factors than in the original matrix. A symbolic factorization step is needed to identify the nonzero structures of $\mathbf {L}$ and $\mathbf {U}$ matrices. Attracted by the enormous potentials of the Graphics Processing Units (GPUs), an array of efforts have surged to deploy various LU factorization steps except for the symbolic factorization, to the best of our knowledge, on GPUs. This article introduces gSoFa, the first GPU-based symbolic factorization design with the following three optimizations to enable scalable LU symbolic factorization for nonsymmetric pattern sparse matrices on GPUs. First, here we introduce a novel fine-grained parallel symbolic factorization algorithm that is well suited for the Single Instruction Multiple Thread (SIMT) architecture of GPUs. Second, we tailor supernode detection into a SIMT friendly process and strive to balance the workload, minimize the communication and saturate the GPU computing resources during supernode detection. Third, we introduce a three-pronged optimization to reduce the excessive space consumption problem faced by multi-source concurrent symbolic factorization. Taken together, gSoFa achieves up to 31× speedup from 1 to 44 Summit nodes (6 to 264 GPUs) and outperforms the state-of-the-art CPU project, on average, by 5×. Notably, gSoFa also achieves up to 47 percent of the peak memory throughput of a V100 GPU in the Summit Supercomputer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A Domain Decomposition Model Reduction Method for Linear Convection-Diffusion Equations with Random Coefficients

We developed a domain decomposition model reduction method for linear steady- state convection-diffusion equations with random coefficients. Of particular interest to this effort are the diffusion equation with random diffusivity and the convection-dominated transport equation with random velocity. We investigated two types of random fields, i.e., colored noises and discrete white noises, both of which can lead to high-dimensional parametric dependence in practice. The motivation is to exploit domain decomposition to reduce the parametric dimension of local problems in subdomains, such that an entire parametric map can be approximated with a small number of expensive partial differential equation (PDE) simulations. The new method combines domain decomposition with model reduction and sparse polynomial approximation, so as to simultaneously handle the high dimensionality and irregular behavior of the PDEs under consideration. Here, the advantages of our method lie in three aspects: (i) online-offline decomposition, i.e., the online cost is independent of the size of the triangle mesh; (ii) sparse approximation of operators involving nonaffine high-dimensional random fields; (iii) an effective strategy to capture irregular behaviors, e.g., sharp transitions of the PDE solutions. Two numerical examples are provided to demonstrate the advantageous performance of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Online Voltage Event Detection Using Synchrophasor Data with Structured Sparsity-Inducing Norms

This paper develops an accurate and computationally efficient data-driven framework to detect voltage events from PMU data streams. It develops an innovative Proximal Bilateral Random Projection (PBRP) algorithm to quickly decompose the PMU data matrix into a low-rank matrix, a row-sparse event-pattern matrix and a noise matrix. Here, the row-sparse pattern matrix significantly distinguishes events from normal behavior. These matrices are then fed into a clustering algorithm to separate voltage events from normal operating conditions. Large-scale numerical study results on real-world PMU data show that the proposed algorithm is computationally more efficient and achieves higher F scores than state-of-the-art benchmarks.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

e RPCA : Robust Principal Component Analysis for Exponential Family Distributions

Abstract Robust principal component analysis (RPCA) is a widely used method for recovering low‐rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other causes for anomalies, and the joint identification of such corruptions with low‐rank background is critical for process monitoring and diagnosis. However, existing RPCA methods and their extensions largely do not account for the underlying probabilistic distribution for the data matrices, which in many applications are known and can be highly non‐Gaussian. We thus propose a new method called RPCA for exponential family distributions (), which can perform the desired decomposition into low‐rank and sparse matrices when such a distribution falls within the exponential family. We present a novel alternating direction method of multiplier optimization algorithm for efficient decomposition, under either its natural or canonical parametrization. The effectiveness of is then demonstrated in two applications: the first for steel sheet defect detection and the second for crime activity monitoring in the Atlanta metropolitan area.

Zheng, Xiaojun↗
DOE OSTI2022

Characterization of Acoustic Emissions From Analogue Rocks Using Sparse Regression‐DMDc

Abstract Moisture loss in rock is known to generate acoustic emissions (AE). Phenomena that result in AE during drying are related to the movement of fluids through the pores and induced‐cracks that arise from differential mineral shrinkage, especially in clay‐bearing rock. AE from the movement of fluids occurs from the reconfiguration of fluid interfaces during drying, while AE from mineral shrinkage involves the debonding within or between minerals. Here, analogue rock samples were used to examine the differences in the AE signatures when one or both AE source‐types are present. An unsupervised sparse regression model, Dynamic Mode Decomposition with control, that extends Dynamic Mode Decomposition is used to characterize the AE signals recorded during the drying of porous analogue rock samples fabricated with ordinary Portland cement, with and without clay. This method can effectively and accurately reconstruct acoustic signals emitted from samples that only experience moisture loss without cracking. However, the method struggles to reconstruct signals from samples with intricate crack networks that formed during drying because AE generating mechanisms can emit contemporaneously, and the resulting waves propagate through drying‐induced cracks that can lead to multiple internal reflections. Thus, the differential reconstruction accuracy of time series generated by different underlying physical processes provides a robust filter for reducing large data catalogs. In general, both dynamics and sparse initiating events are learned directly from data and this method exposes a data hierarchy based on the complexity of the intrinsic dynamics.

58 GEOSCIENCES↗
DOE OSTI2021

Linear solvers for power grid optimization problems: A review of GPU-accelerated linear solvers

The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite, and they become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing solver frameworks based on sparse LU or LDL T decompositions. Here, we benchmark five well known direct linear solver packages on CPU- and GPU-based hardware, using matrices extracted from power grid optimization problems. The achieved solution accuracy varies greatly among the packages. None of the tested packages delivers significant GPU acceleration for our test cases. For completeness of the comparison we include results for MA57, which is one of the most efficient and reliable CPU solvers for this class of problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Parallel domain decomposition method for finite element approximation of 3D steady state non‐Newtonian fluids

Summary We introduce a stabilized finite element method for the 3D non‐Newtonian Navier–Stokes equations and a parallel domain decomposition method for solving the sparse system of nonlinear equations arising from the discretization. Non‐Newtonian flow problems are, generally speaking, more challenging than Newtonian flows because the nonlinearities are not only in the convection term but also in the viscosity term, which depends on the shear rate. Many good iterative methods and preconditioning techniques that work well for the Newtonian flows do not work well for the non‐Newtonian flows. We employ a Galerkin/least squares finite element method, with stabilization parameters adjusted to count the non‐Newtonian effect, to discretize the equations, and the resulting highly nonlinear system of equations is solved by a Newton–Krylov–Schwarz algorithm. In this study, we apply the proposed method to some inelastic power‐law fluid flows through the eccentric annuli with inner cylinder rotation and investigate the robustness of the method with respect to some physical parameters, including the power‐law index and the Reynolds number ratios. We then report the superlinear speedup achieved by the domain decomposition algorithm on a computer with up to 512 processors. Copyright © 2015 John Wiley & Sons, Ltd.

Shiu, Wen‐Shin↗
DOE OSTI2025

Structural response reconstruction using a system-equivalent singular vector basis

Here, this paper develops a novel method for reconstructing the full-field response of structural dynamic systems using sparse measurements. The singular value decomposition is applied to a frequency response matrix relating the structural response to physical loads, base motion, or modal loads. The left singular vectors form a non-physical reduced basis that can be used for response reconstruction with far fewer sensors than existing methods. The contributions of the singular vectors to measured response are termed singular-vector loads (SVLs) and are used in a regularized Bayesian framework to generate full-field response estimates and confidence intervals. The reconstruction framework is applicable to the estimation of single data records and power spectral densities from multiple records. Reconstruction is successfully performed in configurations where the number of SVLs to identify is less than, equal to, and greater than the number of sensors used for reconstruction. In a simulation featuring a seismically excited shear structure, SVL reconstruction significantly outperforms modal FRF-based reconstruction and successfully estimates full-field responses with as few as two uniaxial accelerometers. SVL reconstruction is further verified in a simulation featuring an acoustically excited cylinder. Finally, response reconstruction and uncertainty quantification are performed on an experimental structure with three shaker inputs and 27 triaxial accelerometer outputs.

42 ENGINEERING↗
DOE OSTI2014

ANALYSIS OF VARIANCE-BASED MIXED MULTISCALE FINITE ELEMENT METHOD AND APPLICATIONS IN STOCHASTIC TWO-PHASE FLOWS

The stochastic partial differential systems have been widely used to model physical processes, where the inputs involve large uncertainties. Flows in random and heterogeneous porous media is one of the cases where the random inputs (e.g., permeability) are often modeled as a stochastic field with high-dimensional random parameters. To treat the high dimensionality and heterogeneity efficiently, model reduction is employed in both stochastic space and physical space. An analysis of variance (ANOVA)-based mixed multiscale finite element method MsFEM) is developed to decompose the high-dimensional stochastic problem into a set of lower-dimensional stochastic subproblems, which require much less computational complexity and significantly reduce the computational cost in stochastic space, and the mixed MsFEM can capture the heterogeneities on a coarse grid to greatly reduce the computational cost in the spatial domain. In addition, to enhance the efficiency of the traditional ANOVA method, an adaptive ANOVA method based on a new adaptive criterion is developed, where the most active dimensions can be selected to greatly reduce the computational cost before conducting ANOVA decomposition. This novel adaptive criterion is based on variance-decomposition method coupled with sparse-grid probabilistic collocation method or multilevel Monte Carlo method. The advantage of this adaptive criterion lies in its much lower computational overhead for identifying the active dimensions and interactions. A number of numerical examples in two-phase stochastic flows are presented and demonstrate the accuracy and performance of the adaptive ANOVA-based mixed Ms-FEM.

Wei, Jia↗
NASA NTRS1988

An approach to solving large reliability models

This paper describes a unified approach to the problem of solving large realistic reliability models. The methodology integrates behavioral decomposition, state trunction, and efficient sparse matrix-based numerical methods. The use of fault trees, together with ancillary information regarding dependencies to automatically generate the underlying Markov model state space is proposed. The effectiveness of this approach is illustrated by modeling a state-of-the-art flight control system and a multiprocessor system. Nonexponential distributions for times to failure of components are assumed in the latter example. The modeling tool used for most of this analysis is HARP (the Hybrid Automated Reliability Predictor).

Boyd, Mark A.↗
NASA NTRS1989

A block-corrected subdomain solution procedure for recirculating flow calculations

This paper describes a robust and efficient subdomain solution procedure for two-dimensional recirculating flows. The solution domain is divided into a number of overlapping subdomains, and a direct fully coupled solution is obtained for each subdomain using a sparse matrix form of LU decomposition. An effective parabolic block correction procedure, which calculates global corrections to the tentative solution by a marching technique similar to that used for boundary layer flows, is used to accelerate the convergence of the basic procedure. The use of effective block correction is found to be essential for the success of the subdomain approach on strongly recirculating flows. In a number of laminar two-dimensional flows, the new block-corrected method performed extremely well, rivaling the best direct methods in execution time, while requiring substantially less computer storage. The new method proved to be from two to ten times faster than conventional iterative methods, while requiring only a moderate increase in storage.

Braaten, M. E.↗
NASA NTRS2005

Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis

A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategics and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using several complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate thc steps in the formulation and large-scale (l,000,000+ unknowns) duct acoustic examples are used to evaluate the ORIGIN 2000 processors, and a duster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environmental and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.

Nguyen, Duc T.↗
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↗