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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Modeling optical properties of silicon clusters by first principles: From a few atoms to large nanocrystals

Time dependent density functional tight binding (TDDFTB) method is implemented with sparse matrix techniques and improved parallelization algorithms. The method is employed to calculate the optical properties of various Si nanocrystals (NCs). The calculated light absorption spectra of small Si NCs from TDDFTB were found to be comparable with many body perturbation methods utilizing planewave basis sets. For large Si NCs (more than a thousand atoms) that are beyond the reach of conventional approaches, the TDDFTB method is able to produce reasonable results that are consistent with prior experiments. We also employed the method to study the effects of surface chemistry on the optical properties of large Si NCs. We learned that the optical properties of Si NCs can be manipulated with small molecule passivations such as methyl, hydroxyl, amino, and fluorine. In general, the shifts and profiles in the absorption spectra can be tuned with suitably chosen passivants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Disconnected Diagrams in Lattice QCD

In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called \disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements of the nucleon at two different values of the lattice spacing. Finally, we employ these algorithms to do a high-precision study of strange sigma terms in light nuclei; to our knowledge this is the first calculation of its kind from Lattice QCD.

Gambhir, Arjun↗
DOE OSTI2014

Robust parallel iterative solvers for linear and least-squares problems (Final Technical Report)

The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners for solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the problem of evaluating f(A)v which arises in statistical sampling. 11. As an application to the methods we developed, we tackled the problem of computing the diagonal of the inverse of a matrix. This arises in statistical applications as well as in many applications in physics. We explored probing methods as well as domain-decomposition type methods. 12. A collaboration with researchers from Toulouse, France, considered the important problem of computing the Schur complement in a domain-decomposition approach. 13. We explored new ways of preconditioning linear systems, based on low-rank approximations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Tomographic analysis of tangential viewing cameras (invited)

Many tokamaks now use visible light cameras to observe plasma-wall interactions and integrated line emission. The DIII-D coherence imaging spectroscopy diagnostic cameras image interferograms that encode line integrated velocity. By modeling the 2D camera image pixels as line of sight integrals through an axisymmetric discrete grid, it is possible to do tomographic analysis to determine the local plasma line emissivity and parallel velocity. Approaches to solve the inverse problem posed by these tangential viewing cameras are presented. The inversion begins with calculation of the sparse response matrix that encompasses all the geometry and diagnostic information and reduces the process of image formation to a sparse matrix-vector multiply. Our report includes techniques for determining the detailed geometry of the camera views and methods for handling physical quantities that vary spatially. Additionally, the size of the response matrix has driven the development of capability to distribute the coarse parallel calculation across a heterogeneous cluster of computers on the Energy Sciences Network. Iterative techniques are then used to solve the sparse matrix-vector linear system

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

SMALE: Enhancing Scalability of Machine Learning Algorithms on Extreme-Scale Computing Platforms

Deployment and execution of machine learning tasks on extreme-scale computing platforms face several significant technical challenges: 1) High computing cost incurred by dense networks – The computing workload of deep networks with densely-connected topology increases rapidly with the network size, imposing a non-scalable computing model of extreme-scale computing platforms; 2) Non-optimized workload distribution – Many advanced deep learning algorithms, e.g., sparsification and irregular net-work topology, produce very unbalanced workload distribution on extreme-scale computing platforms. The computation efficiency is greatly hindered by the incurred data and computation redundancies as well as long tails of the node with extensive workload; 3) Constraints in data movement and I/O bottle-neck – Inter-node data movement in extreme-scale computing platforms are associated with high energy and latency costs, and subject to the constraints of I/O bandwidth; and 4) Generalization of algorithm realization and acceleration on computing platforms – The large varieties of machine learning algorithms and structures of extreme-scale computing platforms make the derivation of a generalized algorithm realization and acceleration method very challenging, which, however, is the requirement by domain scientists and interested users. We call the above challenges Smale’s Problems in Machine Learning and Understanding for High-Performance Computing Scientific Discovery. The objective of our three-year research project is to develop a holistic innovation set at structure, assembly, and acceleration layers of machine learning algorithms to address the above challenges in algorithm deployment and execution. Three tasks are particularly performed, including: At the algorithm structure level, we investigate the techniques that can structurally sparsify on the topology of deep networks for computing workload reduction. We also study clustering and pruning techniques that can optimize the workload distributions over the extreme-scale computing platforms; At the algorithm assembly level, we derive a unified learning framework for unsupervised transfer learning and dynamic growing capabilities. Novel training methods are also exploited to enhance the training efficiency of the proposed framework; At the algorithm acceleration level, we will develop a series of techniques that can accelerate the computation of sparse matrix operations, which are one of the core executions in deep learning and optimize memory access of the concerned platforms. Our proposed techniques attack the fundamental problems in machine learning algorithms running on extreme-scale computing platforms by vertically integrating the solutions at three closely entangled layers, paving the long-term scaling path of machine learning applications under DOE context. Three tasks corresponding to the above respective research orientations are performed during the three-year project period with our collaborators at ORNL. The outcome of the proposed project is anticipated to form a holistic solution set of novel algorithms and network topologies, efficient training techniques, and fast acceleration methods to promote the computing scalability of the machine learning applications of particular interest to DOE.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Low-rank matrix decomposition and spatio-temporal sparse recovery for STAP radar

We develop space-time adaptive processing (STAP) methods by leveraging the advantages of sparse signal processing techniques in order to detect a slowly-moving target. We observe that the inherent sparse characteristics of a STAP problem can be formulated as the low-rankness of clutter covariance matrix when compared to the total adaptive degrees-of-freedom, and also as the sparse interference spectrum on the spatio-temporal domain. By exploiting these sparse properties, we propose two approaches for estimating the interference covariance matrix. In the first approach, we consider a constrained matrix rank minimization problem (RMP) to decompose the sample covariance matrix into a low-rank positive semidefinite and a diagonal matrix. The solution of RMP is obtained by applying the trace minimization technique and the singular value decomposition with matrix shrinkage operator. Our second approach deals with the atomic norm minimization problem to recover the clutter response-vector that has a sparse support on the spatio-temporal plane. We use convex relaxation based standard sparse-recovery techniques to find the solutions. With extensive numerical examples, we demonstrate the performances of proposed STAP approaches with respect to both the ideal and practical scenarios, involving Doppler-ambiguous clutter ridges, spatial and temporal decorrelation effects. As a result, the low-rank matrix decomposition based solution requires secondary measurements as many as twice the clutter rank to attain a near-ideal STAP performance; whereas the spatio-temporal sparsity based approach needs a considerably small number of secondary data.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2019

Evaluating Proxy Apps with FPGAs

Field-programmable gate arrays (FPGAs) are becoming more promising for high performance computing (HPC). Unlike fixed hardware specialization, reconfigurability allows FPGAs to be customized for a wide variety of HPC workloads. Our ultimate goal is to understand the viability of FPGAs as accelerators for some of the key HPC codes at LLNL and identify application characteristics that can benefit from the reconfigurability of FPGAs. More specifically, this LDRD project conducted a detailed performance study of FPGAs using sparse matrix computations and identified key optimization techniques to effectively use FPGA hardware resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Shifting Between Compute and Memory Bounds: A Compression-Enabled Roofline Model

In the evolving landscape of high-performance computing, especially to fight the end of Moore’s Law and Dennard’s Scaling, the ability to shift between compute-bound and memory-bound states is critical for enhancing adaptability and flexibility to diverse system and domain-specific architectures. Such capability is vital for optimizing performance across distinguished hardware configurations, such as accelerators, memory hierarchies, and cache systems. Despite that ad hoc optimization techniques, such as compressed/approximate computation, have been enabled for compute-/data-intensive computing for improved performance in distinct hardware settings, there lacks an understanding of 1) the rational behind performance improvement; 2) capability of different optimizations; 3) what optimization to respond to specific computational and memory demands. This work proposes a compression-enabled roofline model to facilitate this adaptability with data compression techniques to balance and transform between computational and memory demands. This model enables applications to adjust in response to the specific strengths and limitations of the underlying hardware and system to optimize resource utilization. The effectiveness of this approach is demonstrated with matrix multiplication kernels on different input sizes, with turning on/off various compression techniques, including 1) low-precision floating point; 2) sparse matrix formulation; and 3) compressed arrays with ZFP. By reducing memory transfer volumes and cache misses and increasing data locality and computational intensity through compression, the specific roofline model can transform between compute and memory bounds to align more efficiently with system capabilities. This advancement not only improves overall performance but also maximizes adaptability in diverse computing environments.

Naraparaju, Ramasoumya [University of Washington]↗
DOE OSTI2024

GPU Accelerated Sparse Cholesky Factorization

The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a Cholesky factorization of the coefficient matrix is performed using a right-looking approach and the resulting triangular factors are used to compute the solution. Sparse Cholesky factorization is compute intensive. In this work we investigate techniques for reducing the factorization time in sparse Cholesky factorization by offloading some of the dense matrix operations on a GPU. We will describe the techniques we have considered. We achieved up to 4x speedup compared to the CPU-only version.

Karsavuran, M Ozan↗
DOE OSTI2017

A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations

As on-node parallelism increases and the performance gap between the processor and the memory system widens, achieving high performance in large-scale scientific applications requires an architecture-aware design of algorithms and solvers. We focus on the eigenvalue problem arising in nuclear Configuration Interaction (CI) calculations, where a few extreme eigenpairs of a sparse symmetric matrix are needed. Here, we consider a block iterative eigensolver whose main computational kernels are the multiplication of a sparse matrix with multiple vectors (SpMM), and tall-skinny matrix operations. We then present techniques to significantly improve the SpMM and the transpose operation SpMM T by using the compressed sparse blocks (CSB) format. We achieve 3-4× speedup on the requisite operations over good implementations with the commonly used compressed sparse row (CSR) format. We develop a performance model that allows us to correctly estimate the performance of our SpMM kernel implementations, and we identify cache bandwidth as a potential performance bottleneck beyond DRAM. We also analyze and optimize the performance of LOBPCG kernels (inner product and linear combinations on multiple vectors) and show up to 15× speedup over using high performance BLAS libraries for these operations. The resulting high performance LOBPCG solver achieves 1.4× to 1.8× speedup over the existing Lanczos solver on a series of CI computations on high-end multicore architectures (Intel Xeons). We also analyze the performance of our techniques on an Intel Xeon Phi Knights Corner (KNC) processor.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Probing for the Trace Estimation of a Permuted Matrix Inverse Corresponding to a Lattice Displacement

We report thatpProbing is a general technique that is used to reduce the variance of the Hutchinson stochastic estimator for the trace of the inverse of a large, sparse matrix A. The variance of the estimator is the sum of the squares of the off-diagonal elements of A -1 . Therefore, this technique computes probing vectors that when used in the estimator annihilate the largest off-diagonal elements. For matrices that display decay of the magnitude of |A$^{-1}_{ij}$| with the graph distance between nodes i and j, this is achieved through graph coloring of increasing powers A k . Equivalently, when a matrix stems from a lattice discretization, it is computationally beneficial to find a distance-k coloring of the lattice. Previously, a hierarchical coloring was proposed so that k can be increased at runtime as needed without discarding previous work. In this work, we study probing for the more general problem of computing the trace of a permutation of A -1 , say PA -1 . The motivation comes from lattice quantum chromodynamics (QCD), where we need to construct “disconnected diagrams” to extract flavor-separated generalized parton functions. In lattice QCD, where the matrix has a four-dimensional toroidal lattice structure, these nonlocal operators correspond to a PA -1 , where P is the permutation relating to some displacement $\vec{p}$ in one or more dimensions. We focus on a single dimension displacement (p), but our methods are general. We show that probing on A k or (PA) k does not annihilate the largest magnitude elements. To resolve this issue, our displacement-based probing works on PA k using a new coloring scheme that works directly on appropriately displaced neighborhoods on the lattice. We prove lower bounds on the number of colors needed and study the effect of this scheme on variance reduction, both theoretically and experimentally on a real-world lattice QCD calculation. We achieve orders of magnitude speedup over the unprobed or the naively probed methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Adapting In Situ Accelerators for Sparsity With Granular Matrix Reordering

Neural network (NN) inference is an essential part of modern systems and is found at the heart of numerous applications ranging from image recognition to natural language processing. In situ NN accelerators can efficiently perform NN inference using resistive crossbars, which makes them a promising solution to the data movement challenges faced by conventional architectures. Although such accelerators demonstrate significant potential for dense NNs, they often do not benefit from sparse NNs, which contain relatively few non-zero weights. Processing sparse NNs on in situ accelerators results in wasted energy to charge the entire crossbar where most elements are zeros. To address this limitation, this paper proposes Granular Matrix Reordering (GMR): a preprocessing technique that enables an energy-efficient computation of sparse NNs on in situ accelerators. GMR reorders the rows and columns of sparse weight matrices to maximize the crossbars' utilization and minimize the total number of crossbars needed to be charged. The reordering process does not rely on sparsity patterns and incurs no accuracy loss. Finally, GMR achieves an average of 28% and up to 34% reduction in energy consumption over seven pruned NNs across four different pruning methods and network architectures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Programming Strategies for Irregular Algorithms on the Emu Chick

The Emu Chick prototype implements migratory memory-side processing in a novel hardware system. Rather than transferring large amounts of data across the system interconnect, the Emu Chick moves lightweight thread contexts to near-memory cores before the beginning of each remote memory read. Previous work has characterized the performance of the Chick prototype in terms of memory bandwidth and programming differences from more typical, non-migratory platforms, but there has not yet been an analysis of algorithms on this system. This work evaluates irregular algorithms that could benefit from the lightweight, memory-side processing of the Chick and demonstrates techniques and optimization strategies for achieving performance in sparse matrix-vector multiply operation (SpMV), breadth-first search (BFS), and graph alignment across up to eight distributed nodes encompassing 64 nodelets in the Chick system. We also define and justify relative metrics to compare prototype FPGA-based hardware with established ASIC architectures. The Chick currently supports up to 68x scaling for graph alignment, 80 MTEPS for BFS on balanced graphs, and 50% of measured STREAM bandwidth for SpMV.

Hein, Eric↗
DOE OSTI2026

Quantum block encoding for one-pair semiseparable matrices

Quantum block encoding (QBE) is a crucial step in the development of most quantum algorithms, as it provides an embedding of a given matrix into a suitable larger unitary matrix. Historically, the development of efficient techniques for QBE has mostly focused on sparse matrices; less effort has been devoted to data-sparse (e.g., rank-structured) matrices. In this work we examine a particular case of rank structure, namely, one-pair semiseparable matrices. We present a new block encoding approach that relies on a suitable factorization of the given matrix as the product of triangular and diagonal factors. To encode the matrix, the algorithm needs $2\log(N)+7$ ancillary qubits. Assuming that the data input oracles can be implemented with polylogarithmic depth, or that a QRAM input model is available, our proposed method requires $\mathcal{O}({\rm polylog} (N))$ time and has an error of $\mathcal{O}(N^2)$, where $N$ is the matrix size.

Antonioli, Giacomo [Pisa U.; CERN] (ORCID:00090000↗
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 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 OSTI2017

Sparse Representations to Replace TOFD Images in Non-destructive Testing of Materials

This paper describes a proposed method for the selection of relevant samples of ultrasonic signals during automatic material inspection. Instead of the well-known time of flight diffraction (TOFD) images, data are stored as a sparse matrix in which the elements only indicate whether a defect has been detected. This technique avoids storage of useless signals received during probe displacement in cases of low and high signal-to-noise ratios that correspond to coarse-grained and fine-grained materials, respectively. The approach is based on comparing the positions of maximum amplitudes, which are randomly located when signals only consist of noise but are in the same signal range when a defect is detected. The matrix elements are then applied as inputs to a self organizing map by neural networks to produce a normalized sparse matrix as the output, with a constant number of elements. This approach will be beneficial to enable the use of selected data in intelligent systems requiring a fixed number of inputs to characterize defects.

42 ENGINEERING↗