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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
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↗
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 OSTI2012

C++ Tensor Toolbox User Manual (V.1.0)

The C++ Tensor Toolbox is a software package for computing tensor decompositions. It is based on the Matlab Tensor Toolbox, and is particularly optimized for sparse data sets. This user manual briefly overviews tensor decomposition mathematics, software capabilities, and installation of the package. Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors in C++. The Toolbox compiles into libraries and is intended for use with custom applications written by users.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2026

Toward memory-efficient melt pool monitoring: a classification framework using event-based imaging and sparse sensing technique

Vision sensors like CMOS and CCD cameras are often used for in-process monitoring of melt pools in laser-based additive and welding processes, but they require transferring large amounts of data and computational processing resources. Event-based neuromorphic imagery, on the other hand, detects only the change in pixel intensity, thus potentially reducing the data amount and latency. With an event imager, this study develops a framework for melt pool condition classification, including image construction, time scale selection, optimal pixel selection, and sparse classification, to achieve a highly memory-efficient scheme. These are based on sparse sensing techniques with singular value decomposition (SVD) and QR pivoting, the two fundamental matrix transformations for linear dimensionality reduction. The framework is then validated by classifying a controlled experiment by exciting various mode shapes of liquid gallium pools of varying depths (3, 6, and 8 mm). At 200 pixels, the classifier can reach overall accuracy of 75%, while at 2000 pixels (0.013% of the total possible pixels), the accuracy is nearly 90% (89.86%). At the same number of pixels, random selection can only achieve 46% and 67%, respectively. The memory savings of the sparsely sampled event data compared to a conventional imager is about 500 times. In addition to performance, implementation and limitations of the framework are also discussed.

42 ENGINEERING↗
DOE OSTI2022

The cosine-sine decomposition with different-orbitals-for-different-spins determinants

We report the spin decomposition of a spin-contaminated different-orbitals-for-different-spins (DODS) wave function is formulated in terms of the Krylov space of the $\hat{S}^2$ ||operator. The number of determinants that contribute to the various projected spin eigenfunctions vertical | $\psi ; S, M \rangle$ depends on the sparsity of the orbital overlap matrix X between the α and β spatial orbitals. The cosine-sine decomposition (CSD) procedure may be applied to this overlap matrix, and the resulting redundant orbital transformations may be applied to the α and β spatial orbitals. This produces a sparse X' matrix in the transformed basis in which each row or column has either one or two nonzero elements. This sparse X' matrix simplifies the spin-decomposition procedure in three ways:1) it reduces the number of contributing determinants within the Krylov basis functions and within the projected spin functions, 2) it reduces the effective orbital dimension through elimination of the frozen core and frozen virtual orbitals, and 3) it simplifies the spin-decomposition procedure in both the original and transformed bases by limiting the Krylov space dimension. These simplifications all reduce the computational effort for the spin-decomposition process. This procedure is implemented within a string-based DODS determinant formulation and applied to spin projection of unrestricted Hartree-Fock determinants.

unrestricted Hartree-Fock↗
DOE OSTI2019

Accelerating and Parallelizing Lagrangian Simulations of Mixing-Limited Reactive Transport

Recent advances in random walk particle tracking have enabled direct simulation of mixing and reactions by allowing the particles to interact with each other using a multipoint mass transfer scheme. The mass transfer scheme allows separation of mixing and spreading processes, among other advantages, but it is computationally expensive because its speed depends on the number of interacting particle pairs. This note explores methods for relieving the computational bottleneck caused by the mass transfer step, and we use these algorithms to develop a new parallel, interacting particle model. The new model is a combination of a sparse search algorithm and a novel domain decomposition scheme, both of which offer significant speedup relative to the reference case—even when they are executed serially. We combine the strengths of these methods to create a parallel particle scheme that is highly accurate and efficient with run times that scale as 1/P for a fixed number of particles, where P is the number of computational cores (equivalently, subdomains, in this work) being used. Here, the new parallel model is a significant advance because it enables efficient simulation of large particle ensembles that are needed for environmental simulations and also because it can naturally pair with parallel geochemical solvers to create a practical Lagrangian tool for simulating mixing and reactions in complex chemical systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Communication-Avoiding Parallel Sparse-Dense Matrix-Matrix Multiplication

Multiplication of a sparse matrix with a dense matrix is a building block of an increasing number of applications in many areas such as machine learning and graph algorithms. However, most previous work on parallel matrix multiplication considered only both dense or both sparse matrix operands. This paper analyzes the communication lower bounds and compares the communication costs of various classic parallel algorithms in the context of sparse-dense matrix-matrix multiplication. We also present new communication-avoiding algorithms based on a 1D decomposition, called 1.5D, which - while suboptimal in dense-dense and sparse-sparse cases - outperform the 2D and 3D variants both theoretically and in practice for sparse-dense multiplication. Our analysis separates one-time costs from per iteration costs in an iterative machine learning context. Experiments demonstrate speedups up to 100x over a baseline 3D SUMMA implementation and show parallel scaling over 10 thousand cores.

Koanantakool, Penporn↗
DOE OSTI2023

Parallel Algorithms for Computing the Tensor-Train Decomposition

The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization. In this paper, we propose four parallelizable algorithms that compute the TT format from various tensor inputs: (1) Parallel-TTSVD for traditional format, (2) PSTT and its variants for streaming data, (3) Tucker2TT for Tucker format, and (4) TT-fADI for solutions of Sylvester tensor equations. We provide theoretical guarantees of accuracy, parallelization methods, scaling analysis, and numerical results. For example, for a d-dimension tensor in $\mathbb{R}$ $n\times∙∙∙$$\times$$n$ a two-sided sketching algorithm PSTT2 is shown to have a memory complexity of $O(n^{[d/2]})$, improving upon $O(n^{d—1})$ from previous algorithms.

97 MATHEMATICS AND COMPUTING↗