Search NASA⌕ Search

SEARCH · Search NASA

Results for “matrix formats”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Exploring Deep Learning and Sparse Matrix Format Selection

We proposed to explore the use of Deep Neural Networks (DNN) for addressing the longstanding barriers. The recent rapid progress of DNN technology has created a large impact in many fields, which has significantly improved the prediction accuracy over traditional machine learning techniques in image classifications, speech recognitions, machine translations, and so on. To some degree, these tasks resemble the decision makings in many HPC tasks, including the aforementioned format selection for SpMV and linear solver selection. For instance, sparse matrix format selection is akin to image classification—such as, to tell whether an image contains a dog or a cat; in both problems, the right decisions are primarily determined by the spatial patterns of the elements in an input. For image classification, the patterns are of pixels, and for sparse matrix format selection, they are of non-zero elements. DNN could be naturally applied if we regard a sparse matrix as an image and the format selection or solver selection as classification problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A Study of Clustering Techniques and Hierarchical Matrix Formats for Kernel Ridge Regression

We present memory-efficient and scalable algorithms for kernel methods used in machine learning. Using hierarchical matrix approximations for the kernel matrix the memory requirements, the number of floating point operations, and the execution time are drastically reduced compared to standard dense linear algebra routines. We consider both the general H matrix hierarchical format as well as Hierarchically Semi-Separable (HSS) matrices. Furthermore, we investigate the impact of several preprocessing and clustering techniques on the hierarchical matrix compression. Effective clustering of the input leads to a ten-fold increase in efficiency of the compression. The algorithms are implemented using the STRUMPACK solver library. These results confirm that - with correct tuning of the hyperparameters - classification using kernel ridge regression with the compressed matrix does not lose prediction accuracy compared to the exact - not compressed - kernel matrix and that our approach can be extended to O(1M) datasets, for which computation with the full kernel matrix becomes prohibitively expensive. We present numerical experiments in a distributed memory environment up to 1,024 processors of the NERSC's Cori supercomputer using well-known datasets to the machine learning community that range from dimension 8 up to 784.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Matrix-formation dynamics dictate methyl nitrite conformer abundance

Methyl nitrite has two stable conformational isomers resulting from rotation about the primary C–O–N–O dihedral angle: cis-CH 3 ONO and trans-CH 3 ONO, with cis being more stable by ∼5 kJ/mol. Here, the barrier to rotational interconversion (∼45 kJ/mol) is too large for isomerization to occur under ambient conditions. This paper presents evidence of a change in conformer abundance when dilute CH 3 ONO is deposited onto a cold substrate; the relative population of the freshly deposited cis conformer is seen to increase compared to its gas-phase abundance, measured by in situ infrared spectroscopy. We observe abundance changes depending on the identity of the bath gas (N 2 , Ar, and Xe) and deposition angle. The observations indicate that the surface properties of the growing matrix influence conformer abundance—contrary to the widely held assumption that conformer abundance in matrices reflects gas-phase abundance. We posit that differences in the angle-dependent host-gas deposition dynamics affect the growing surfaces, causing changes in conformer abundances. Quantum chemistry calculations of the binding energies between CH 3 ONO and a single bath-gas component reveal that significant energetic stabilization is not observed in 1:1 complexes of N 2 :CH 3 ONO, Ar:CH 3 ONO, or Xe:CH 3 ONO. From our results, we conclude that the growing surface plays a significant role in trapping cis-CH 3 ONO more effectively than trans-CH 3 ONO, likely because cis-CH 3 ONO is more compact. Taken together, the observations highlight the necessity for careful characterization of conformers in matrix-isolated systems, emphasizing a need for further study into the deposition dynamics and surface structure of chemically inert matrices.

Hockey, Emily K.↗
DOE OSTI2017

Structure and decomposition of the silver formate Ag(HCO{sub 2})

Crystal structure of the silver formate Ag(HCO{sub 2}) has been determined (orthorhombic, sp.gr. Pccn, a=7.1199(5), b=10.3737(4), c=6.4701(3)Å, V=477.88(4) Å{sup 3}, Z=8). The structure contains isolated formate ions and the pairs Ag{sub 2}{sup 2+} which form the layers in (001) planes (the shortest Ag–Ag distances is 2.919 in the pair and 3.421 and 3.716 Å between the nearest Ag atoms of adjacent pairs). Silver formate is unstable compound which decompose spontaneously vs time. Decomposition was studied using Rietveld analysis of the powder diffraction patterns. It was concluded that the diffusion of Ag atoms leads to the formation of plate-like metal particles as nuclei in the (100) planes which settle parallel to (001) planes of the silver formate matrix. - Highlights: • Silver formate Ag(HCO{sub 2}) was synthesized and characterized. • Layered packing of Ag-Ag pairs in the structure was found. • Decomposition of Ag(HCO{sub 2}) and formation of metal phase were studied. • Rietveld-refined micro-structural characteristics during decomposition reveal the space relationship between the matrix structure and forming Ag phase REPLACE with: Space relationship between the matrix structure and forming Ag phase.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Spectral Properties and Possibilities of meso-Substituted BODIPY Usage in Sol–Gel Process and Materials

Hybrid materials based on organically modified silica with immobilized boron-dipyrrins (BODIPY) dyes were obtained. Spectral characteristics of the dyes were measured during the matrix formation and in obtained materials. It was stated, that immobilization does not affect the character of the absorption and fluorescence spectra of the dye, but due to the effect of fluorescent molecular rotor observed for meso-substituted BODIPY, the fluorescent quantum yields were found to increase during the matrix sealing. Quantum yield increase is linear for all of the investigated matrices except phenyl-substituted one, where the π-π interactions of the dye molecule with matrix could be observed. This effect could be used for fine control of the matrix formation process and leads to increase of the dye emission in the final material for further practical applications. All obtained hybrid materials were found to be stable upon UV light irradiation, hence immobilization enhance the stability of the dye in comparison with the BODIPY in organic solvents.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2018

The basic matrix library (BML) for quantum chemistry

The basic matrix library package (BML) provides a common application programming interface (API) for linear algebra and matrix functions in C and Fortran for quantum chemistry codes. The BML API is matrix format independent. Currently the dense, compressed sparse row, and ELLPACK-R sparse matrix data types are available, each with different implementations. We show how the second-order spectral projection (SP2) algorithm used to compute the electronic structure of a molecular system represented with a tight-binding Hamiltonian can be successfully implemented with the aid of this library.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initialization

Obtaining lightweight and accurate approximations of discretized objective functional Hessians in inverse problems governed by partial differential equations (PDEs) is essential to make both deterministic and Bayesian statistical large-scale inverse problems computationally tractable. The cubic computational complexity of dense linear algebraic tasks, such as Cholesky factorization, that provide a means to sample Gaussian distributions and determine solutions of Newton linear systems is a computational bottleneck at large-scale. These tasks can be reduced to log-linear complexity by utilizing hierarchical off-diagonal low-rank (HODLR) matrix approximations. In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix format. In particular, we study inverse problems governed by PDEs that model the instantaneous viscous flow of ice sheets. In these problems, we seek a spatially distributed basal sliding parameter field such that the flow predicted by the ice sheet model is consistent with ice sheet surface velocity observations. Here, we demonstrate the use of HODLR Hessian approximation to efficiently sample the Laplace approximation of the posterior distribution with covariance further approximated by HODLR matrix compression. Computational studies are performed which illustrate ice sheet problem regimes for which the Gauss–Newton data-misfit Hessian is more efficiently approximated by the HODLR matrix format than the low-rank (LR) format. We then demonstrate that HODLR approximations can be favorable, when compared to global LR approximations, for large-scale problems by studying the data-misfit Hessian associated with inverse problems governed by the first-order Stokes flow model on the Humboldt glacier and Greenland ice sheet.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Experimental and numerical investigation of flame stabilization and pollutant formation in matrix stabilized ammonia-hydrogen combustion

Ammonia (NH 3 ) is a carbon-free fuel that offers an attractive alternative for reducing greenhouse gas emissions. However, the slow flame speed, low heating value, and emissions of nitrogen-containing pollutants present significant issues for practical combustion applications. To address these issues, we investigate the use of matrix stabilized combustion. In this type of burner, combustion is performed within an inert porous ceramic foam, heat is recirculated by solid conduction and radiation, which enhances flame speed and combustion stabilization, thereby permitting combustion over a wide range of equivalence ratio conditions. We present a new porous media burner (PMB) capable of stabilizing NH 3 /air flames at ambient conditions. An extensive experimental characterization of the stability of this burner is conducted with up to 30% by volume of hydrogen (H 2 ) in the fuel stream. A 15:1 turndown ratio is demonstrated, with a high thermal power density of 62 MW m -3 . Concentrations of NO, unburnt NH 3 , and H 2 in the exhaust stream are measured. Two regimes are identified for low NO operation: rich and very lean. For rich conditions, NO emissions decrease with increasing equivalence ratio and decreasing H 2 blending. Unburnt NH 3 emissions follow opposite trends. These measurements are complemented by simulations in which the burner is represented by a coupled solid-gas reactor network. In conclusion, this model captures the burner’s pollutant emissions to good accuracy and is used to analyze the mechanisms of pollutant formation.

42 ENGINEERING↗
DOE OSTI2020

CSBCOO SPMM: Compressed Sparse Block Coordinate format sparse matrix dense vector multiply benchmark (CSBCOO SPMM) v1.0

The purpose of this microbenchmark is to provide a means to explore different programming methodologies using a simple, but not trivial, mathematical kernel. The kernel is based on the matrix vector product in the MFDn nuclear configuration interaction code's LOBPCG eigensolver. This particular mathematical operation is a key element in the solution of systems of equations and block eigensolvers.

Cook, Brandon↗
DOE OSTI2019

Scalable Matrix-Free Adaptive Product-Convolution Approximation for Locally Translation-Invariant Operators

We present an adaptive grid matrix-free operator approximation scheme based on a "product-convolution" interpolation of convolution operators. This scheme is appropriate for operators that are locally translation-invariant, even if these operators are high rank or full rank. Such operators arise in Schur complement methods for solving partial differential equations (PDEs), as Hessians in PDE-constrained optimization and inverse problems, as integral operators, as covariance operators, and as Dirichlet-to-Neumann maps. Constructing the approximation requires computing the impulse responses of the operator to point sources centered on nodes in an adaptively refined grid of sample points. A randomized a posteriori error estimator drives the adaptivity. Once constructed, the approximation can be efficiently applied to vectors using the fast Fourier transform. The approximation can be efficiently converted to hierarchical matrix (H-matrix) format, then inverted or factorized using scalable H-matrix arithmetic. The quality of the approximation degrades gracefully as fewer sample points are used, allowing cheap lower quality approximations to be used as preconditioners. Furthermore, this yields an automated method to construct preconditioners for locally translation-invariant Schur complements. We directly address issues related to boundaries and prove that our scheme eliminates boundary artifacts. We test the scheme on a spatially varying blurring kernel, on the nonlocal component of an interface Schur complement for the Poisson operator, and on the data misfit Hessian for an advection dominated advection-diffusion inverse problem. Numerical results show that the scheme outperforms existing methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Geometry-aware training of factorized layers in tensor Tucker format

Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during train and inference of large networks. Given its easy implementation and flexibility, one promising approach is layer factorization, which reshapes weight tensors into a matrix format and parameterizes it as the product of two rank-r matrices. However, this family of approaches often requires an initial full-model warm-up phase, prior knowledge of a feasible rank, and it is sensitive to parameter initialization.In this work, we introduce a novel approach to train the factors of a Tucker decomposition of the weight tensors. Our training proposal proves to be optimal in locally approximating the original unfactorized dynamics and stable for the initialization. Furthermore, the rank of each mode is dynamically updated during training.We provide a theoretical analysis of the algorithm, showing convergence, approximation and local descent guarantees. The method's performance is further illustrated through a variety of experiments, showing remarkable training compression rates and comparable or even better performance than the full baseline and alternative layer factorization strategies.

Zangrando, Emanuele [Gran Sasso Science Institute ↗
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 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 OSTI2022

Final Technical Report for "Cloud-based Low-Scaling Quantum Chemistry Simulations for Materials"

The objective of phase I was to develop the basic infrastructure for performing efficient hybrid DFT calculations on solid materials with a turnaround time amenable to the use in large-scale data-driven approaches. To fulfill the goal we have developed a novel algorithm that significantly reduces the cost of exchange matrix formation. The algorithm does so by making use of three ingredients (a) interpolative decomposition of the electron integrals (b) robust pseudospectral method and (c) occ-RI approach. Our published work demonstrates that the algorithm is orders of magnitude faster than any other hybrid-DFT method and is on the order of only 3-4 times slower than pure DFT. All steps of the algorithm developed during phase I can be accelerated to the point that, for large enough systems, the diagonalization of the Fock matrix will become the most expensive step. To treat such large systems we have created an interface to the ASCR-funded PEXSI library. The PEXSI method is used to compute the density matrix directly from the Fock matrix in a manner that preserves the sparsity of the local representation.

Shiozaki, Toru↗
DOE OSTI2017

Expansion of CD26 positive fibroblast population promotes keloid progression

Background: Keloid is a skin fibrosis disease that characterised by invasive growth of fibroblasts and aberrant deposition of extracellular matrix. Studies indicated that keloid fibroblasts (KFs) is a class of ‘activated’ fibroblasts, which show accelerated proliferation and excessive extracellular matrix formation as compared with normal fibroblasts (NFs). However, the mechanism underlying keloid fibroblasts dysfunction is still unknown. Objective: To verify CD26 expression difference between KFs and NFs, and investigate the function of CD26 positive fibroblasts in keloid progression. Methods: KFs and NFs were isolated from Keloid tissues and normal skin tissues respectively. Flow cytometry was performed to isolate CD26+/CD26- fibroblasts from KFs and NFs. Proliferation of different fibroblasts were analyzed by CCK8 assay and Ki 67 straining. Profibrotic phenotype difference was detected by qRT-PCR, western blot, ELISA and immunofluorescence. Scratching experiment and transwell assay were used to assess invasion ability of CD26+/CD26- fibroblasts. Diprotin A was used as a CD26 inhibitor to further investigated the function of CD26 fibroblasts in keloid disease. Result: CD26 expression was increased in KFs, and the proportion of CD26+ fibroblasts was significantly increased in KFs. Cell viability analysis showed that CD26+ fibroblasts was more active in proliferation. Furthermore, the expression of profibrotic genes were increased in CD26+ fibroblasts, including TGF-β1, IGF-1, IL6, collagen 1, collagen 3 and fibronectin. And meanwhile, CD26+ fibroblasts showed stronger invasion ability as compared to CD26- fibroblasts. Moreover, Diprotin A significantly suppressed proliferation and extracellular matrix secretion of CD26+ fibroblasts isolated from keloid tissues. Conclusion: Our findings suggest that CD26+ fibroblasts possess proliferation advantage in compare to CD26- fibroblasts, and the advantage caused expansion of CD26 positive fibroblast population promotes keloid progression.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

MicroRNA-29a mitigation of toll-like receptor 2 and 4 signaling and alleviation of obstructive jaundice-induced fibrosis in mice

Highlights: • miR-29a overexpression in cholestatic mice obstructed TLR2 and TLR4 signaling in liver tissues. • miR-29a overexpression in cholestatic mice decreased IL-1β, MCP-1, TGF-β, TNF-α, as well as HMGB1, and BRD4 expression. • Overexpression of miR-29a downregulated α-SMA, TLR2, TLR4 and BRD4 expression in HSCs. Cholestasis and hepatitis can cause continuous liver damage that may ultimately result in liver fibrosis. In a previous study, we demonstrated that microRNA-29a (miR-29a) protects against liver fibrosis. Toll-like receptor 2 (TLR2) and TLR4 are pattern recognition receptors of bacterial lipoprotein and lipopolysaccharide, both of which participate in activating hepatic stellate cells and liver fibrosis. The purpose of this study is to characterize the biological influence of miR-29a on TLR2 and TLR4 signaling in livers injured with bile duct ligation (BDL). We performed BDL on both miR-29a transgenic mice (miR-29aTg) and wild-type mice to induce cholestatic liver injury. Primary HSCs were transfected with a miR-29a mimic and inhibitor. In the wild-type mice, the BDL demonstrated significant α-smooth muscle actin fibrotic matrix formation and hepatic high mobility group box-1 expression. However, in the miR-29aTg mice, these factors were significantly reduced. Furthermore, miR-29a overexpression reduced the BDL exaggeration of TLR2, TLR4, MyD88, bromodomain-containing protein 4 (BRD4), phospho-p65 as well as proinflammatory cytokines, IL-1β, MCP-1, TGF-β, and TNF-α. In vitro, miR-29a mimic transfection reduced α-SMA, BRD4,TLR2, and TLR4 expressions in HSCs. This study provides new molecular insight into the ability of miR-29a to inhibit TLR2 and TLR4 signaling, which thus slows the progression of cholestatic liver deterioration.

60 APPLIED LIFE SCIENCES↗