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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Simulated Half-Precision Implementation of Blocked QR Factorization and Graph Clustering Applications

We explored half-precision implementation of blocked QR algorithms with the following motivations: 1. New GPUs perform fast half-precision arithmetic (4 to 16 times as fast as doubleprecision). 2. QR factorization is a basic linear algebra tool useful for many physics and data analysis applications. 3. Communication-avoiding, parallelizable QR algorithms already exist for talland- skinny matrices. While the standard QR algorithms are highly unstable in half-precision, our numerical simulations show that the Tall-and-Skinny QR (TSQR) algorithm can improve the backward error of QR factorization. When using subspace iteration for graph clustering applications, half-precision accuracy in forming the eigenspace is sufficient for clustering with high precision and recall for some medium-scale benchmark problems. Note that all half-precision arithmetic were simulated with conversions to single-precision floats. Therefore, the results from this work are somewhat optimistic.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation

Here we present a Lindblad master equation that approximates the Redfield equation, a well known master equation derived from first principles, without significantly compromising the range of applicability of the Redfield equation. Instead of full-scale coarse-graining, this approximation only truncates terms in the Redfield equation that average out over a time-scale typical of the quantum system. The first step in this approximation is to properly renormalize the system Hamiltonian, to symmetrize the gains and losses of the state due to the environmental coupling. In the second step, we swap out an arithmetic mean of the spectral density with a geometric one, in these gains and losses, thereby restoring complete positivity. This completely positive approximation, GAME (geometric-arithmetic master equation), is adaptable between its time-independent, time-dependent, and Floquet form. In the exactly solvable, three-level, Jaynes-Cummings model, we find that the error of the approximate state is almost an order of magnitude lower than that obtained by solving the coarse-grained stochastic master equation. As a test-bed, we use a ferromagnetic Heisenberg spin-chain with long-range dipole-dipole coupling between up to 25-spins, and study the differences between various master equations. We find that GAME has the highest accuracy per computational resource.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

PROPERTIES OF CARBON–OXYGEN WHITE DWARFS FROM MONTE CARLO STELLAR MODELS

We investigate properties of carbon–oxygen white dwarfs with respect to the composite uncertainties in the reaction rates using the stellar evolution toolkit, Modules for Experiments in Stellar Astrophysics (MESA) and the probability density functions in the reaction rate library STARLIB. These are the first Monte Carlo stellar evolution studies that use complete stellar models. Focusing on 3 M{sub ⊙} models evolved from the pre main-sequence to the first thermal pulse, we survey the remnant core mass, composition, and structure properties as a function of 26 STARLIB reaction rates covering hydrogen and helium burning using a Principal Component Analysis and Spearman Rank-Order Correlation. Relative to the arithmetic mean value, we find the width of the 95% confidence interval to be ΔM{sub 1TP} ≈ 0.019 M{sub ⊙} for the core mass at the first thermal pulse, Δt{sub 1TP} ≈ 12.50 Myr for the age, Δlog(T{sub c}/K) ≈ 0.013 for the central temperature, Δlog(ρ{sub c}/g cm{sup −3}) ≈ 0.060 for the central density, ΔY{sub e,c} ≈ 2.6 × 10{sup −5} for the central electron fraction, ΔX{sub c}({sup 22}Ne) ≈ 5.8 × 10{sup −4}, ΔX{sub c}({sup 12}C) ≈ 0.392, and ΔX{sub c}({sup 16}O) ≈ 0.392. Uncertainties in the experimental {sup 12}C(α,γ){sup 16}O, triple-α, and {sup 14}N(p,γ){sup 15}O reaction rates dominate these variations. We also consider a grid of 1–6 M{sub ⊙} models evolved from the pre main-sequence to the final white dwarf to probe the sensitivity of the initial–final mass relation to experimental uncertainties in the hydrogen and helium reaction rates.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Fault Diagnosis of Hybrid Computing Systems Using Chaotic-Map Method

Computing systems are becoming increasingly complex with nodes consisting of a combination of multi-core central processing units (CPUs), many integrated core (MIC) and graphics processing unit (GPU) accelerators. These computing units and their interconnections are subject to different classes of hardware and software faults, which should be detected to support mitigation measures. We present the chaotic-map method that uses the exponential divergence and wide Fourier properties of the trajectories, combined with memory allocations and assignments to diagnose component-level faults in these hybrid computing systems. We propose lightweight codes that utilize highly parallel chaotic-map computations tailored to isolate faults in arithmetic units, memory elements and interconnects. The diagnosis module on a node utilizes pthreads to place chaotic-map threads on CPU and MIC cores, and CUDA C and OpenCL kernels on GPU blocks. We present experimental diagnosis results on five multi-core CPUs; one MIC; and, seven GPUs with typical diagnosis run-times under a minute.

Rao, Nageswara↗
DOE OSTI2013

Register file soft error recovery

Register file soft error recovery including a system that includes a first register file and a second register file that mirrors the first register file. The system also includes an arithmetic pipeline for receiving data read from the first register file, and error detection circuitry to detect whether the data read from the first register file includes corrupted data. The system further includes error recovery circuitry to insert an error recovery instruction into the arithmetic pipeline in response to detecting the corrupted data. The inserted error recovery instruction replaces the corrupted data in the first register file with a copy of the data from the second register file.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Evaluation of Low Power ARM Processors for Monte Carlo Particle Transport: MCNP6 on the ARM Cortex-A8 - Paper 83

In the push towards exascale computing, the limiting factors are power requirements and heat dissipation. Using current technology, the power required to drive an exascale supercomputer would near 400-MW. Clearly, future computing hardware will have to be more energy efficient in order to achieve exascale performance. Most of the current research in advanced computing architectures is in the use of standard CPUs with accelerators. However, these accelerators are not generally supported by the traditional scientific programming languages (C, C++, and Fortran) and the scientific software must be tailored specifically to take advantage of the accelerators. Large scale scientific software (hundreds-of-thousand to millions of lines of code) can not be easily ported to the computing platform du jour. The widespread use of low power ARM based processors in the mobile computing market offer a low power alternative to accelerators that are also supported by the traditional scientific programming languages and programming paradigms such as MPI and OpenMP. Computing architectures for scientific computing are often assessed using standard benchmarks such as LINPACK benchmark or using suites of mini-applications that are greatly simplified stand-ins for scientific software. Often the real applications that will deployed on the scientific supercomputers are not ported or tested until delivery of the machines. In order to evaluate the use of ARM processors for scientific computing the Monte Carlo particle transport code, MCNP version 6 was compiled on the ARM Cortex-A8 and a set of benchmark problems were used to assess performance in comparison to an Intel Xeon E5-2670 and the low power Intel Atom N270. MCNP is a continuous energy Monte Carlo particle transport code in development at Los Alamos National Laboratory since 1977. MCNP is used to transport neutrons, photon, electrons, and charged particles using continuous energy interaction data. It is commonly used in fields of nuclear power, nuclear medicine, radiation protection, and high-energy physics through-out the world. MCNP version 6 is approximately 450 thousand lines of code, written primary in Fortran90, with some C and C++. MCNP supports distributed multiprocessing using MPI and threading with OpenMP. The ARM Cortex-A8 executes MCNP6 using about twice as much power as the Intel Xeon E5-2670 and about the same amount of power as the Intel Atom N270. However, these results are encouraging for the use of low-power ARM chips in future supercomputers. The ARM Cortex-A8 is a 32-bit CPU and it's NEON general-purpose SIMD (single-instruction multiple data) engine does not support double-precision floating-point arithmetic. More recent ARM processors (ARM Cortex-A53 and Cortex-A57) support 64-bit addressing and have NEON co-processors that support double-precision floating-point arithmetic. ARM claims that the A50 series delivers a performance increase of 15 times the Cortex-A8 performance for similar power usage. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2017

Managing the Performance/Error Tradeoff of Floating-point Intensive Applications

Modern embedded systems are becoming more reliant on real-valued arithmetic as they employ mathematically complex vision algorithms and sensor signal processing. Double-precision floating point is the most commonly used precision in computer vision algorithm implementations. A single-precision floating point can provide a performance boost due to less memory transfers, less cache occupancy, and relatively faster mathematical operations on some architectures. However, adopting it can result in loss of accuracy. Identifying which parts of the program can run in single-precision floating point with low impact on error is a manual and tedious process. In this paper, we propose an automatic approach to identify parts of the program that have a low impact on error using shadow-value analysis. Our approach provides the user with a performance/error tradeoff, using which the user can decide how much accuracy can be sacrificed in return for performance improvement. We illustrate the impact of the approach using a well known implementation of Apriltag detection used in robotics vision. In conclusion, we demonstrate that an average 1.3x speedup can be achieved with no impact on tag detection, and a 1.7x speedup with only 4% false negatives.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Modeling protected species distributions and habitats to inform siting and management of pioneering ocean industries: A case study for Gulf of Mexico aquaculture

Marine Spatial Planning (MSP) provides a process that uses spatial data and models to evaluate environmental, social, economic, cultural, and management trade-offs when siting (i.e., strategically locating) ocean industries. Aquaculture is the fastest-growing food sector in the world. The United States (U.S.) has substantial opportunity for offshore aquaculture development given the size of its exclusive economic zone, habitat diversity, and variety of candidate species for cultivation. However, promising aquaculture areas overlap many protected species habitats. Aquaculture siting surveys, construction, operations, and decommissioning can alter protected species habitat and behavior. Additionally, aquaculture-associated vessel activity, underwater noise, and physical interactions between protected species and farms can increase the risk of injury and mortality. In 2020, the U.S. Gulf of Mexico was identified as one of the first regions to be evaluated for offshore aquaculture opportunities as directed by a Presidential Executive Order. We developed a transparent and repeatable method to identify aquaculture opportunity areas (AOAs) with the least conflict with protected species. First, we developed a generalized scoring approach for protected species that captures their vulnerability to adverse effects from anthropogenic activities using conservation status and demographic information. Next, we applied this approach to data layers for eight species listed under the Endangered Species Act, including five species of sea turtles, Rice’s whale, smalltooth sawfish, and giant manta ray. Next, we evaluated four methods for mathematically combining scores (i.e., Arithmetic mean, Geometric mean, Product, Lowest Scoring layer) to generate a combined protected species data layer. The Product approach provided the most logical ordering of, and the greatest contrast in, site suitability scores. Finally, we integrated the combined protected species data layer into a multi-criteria decision-making modeling framework for MSP. This process identified AOAs with reduced potential for protected species conflict. These modeling methods are transferable to other regions, to other sensitive or protected species, and for spatial planning for other ocean-uses.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Modification of the Local Cubic Law of fracture flow for weak inertia, tortuosity, and roughness

The classical Local Cubic Law (LCL) generally overestimates flow through real fractures. We thus developed and tested a modified LCL (MLCL) which takes into account local tortuosity and roughness, and works across a low range of local Reynolds Numbers. The MLCL is based on (1) modifying the aperture field by orienting it with the flow direction and (2) correcting for local roughness changes associated with local flow expansion/contraction. In order to test the MLCL, we compared it with direct numerical simulations with the Navier-Stokes equations using real and synthetic three-dimensional rough-walled fractures, previous corrected forms of the LCL, and experimental flow tests. The MLCL performed well and the effective errors (δ) in volumetric flow rate range from -6.7% to 13.4% with an arithmetic mean of |δ| (<|δ|>) equal to 3.7%. The MLCL is more accurate than previous modifications of the LCL. We also investigated the error associated with applying the Cubic Law (CL) while utilizing modified aperture field. The δ from the CL ranges from -14.2% to 11.2%, with a slightly higher <|δ|> = 6.1% than the MLCL. The CL with the modified aperture field considering local tortuosity and roughness may also be sufficient for predicting the hydraulic properties of rough fractures.

58 GEOSCIENCES↗
DOE OSTI2015

Performance analysis of distributed symmetric sparse matrix vector multiplication algorithm for multi-core architectures

In this article, sparse matrix vector multiply (SpMVM) is an important kernel that frequently arises in high performance computing applications. Due to its low arithmetic intensity, several approaches have been proposed in literature to improve its scalability and efficiency in large scale computations. In this paper, our target systems are high end multi-core architectures and we use messaging passing interface + open multiprocessing hybrid programming model for parallelism. We analyze the performance of recently proposed implementation of the distributed symmetric SpMVM, originally developed for large sparse symmetric matrices arising in ab initio nuclear structure calculations. We also study important features of this implementation and compare with previously reported implementations that do not exploit underlying symmetry. Our SpMVM implementations leverage the hybrid paradigm to efficiently overlap expensive communications with computations. Our main comparison criterion is the "CPU core hours" metric, which is the main measure of resource usage on supercomputers. We analyze the effects of topology-aware mapping heuristic using simplified network load model. Furthermore, we have tested the different SpMVM implementations on two large clusters with 3D Torus and Dragonfly topology. Our results show that the distributed SpMVM implementation that exploits matrix symmetry and hides communication yields the best value for the "CPU core hours" metric and significantly reduces data movement overheads.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Sparse matrix‐vector and matrix‐multivector products for the truncated SVD on graphics processors

Summary Many practical algorithms for numerical rank computations implement an iterative procedure that involves repeated multiplications of a vector, or a collection of vectors, with both a sparse matrix and its transpose. Unfortunately, the realization of these sparse products on current high performance libraries often deliver much lower arithmetic throughput when the matrix involved in the product is transposed. In this work, we propose a hybrid sparse matrix layout, named CSRC, that combines the flexibility of some well‐known sparse formats to offer a number of appealing properties: (1) CSRC can be obtained at low cost from the popular CSR (compressed sparse row) format; (2) CSRC has similar storage requirements as CSR; and especially, (3) the implementation of the sparse product kernels delivers high performance for both the direct product and its transposed variant on modern graphics accelerators thanks to a significant reduction of atomic operations compared to a conventional implementation based on CSR. This solution thus renders considerably higher performance when integrated into an iterative algorithm for the truncated singular value decomposition (SVD), such as the randomized SVD or, as demonstrated in the experimental results, the block Golub–Kahan–Lanczos algorithm.

Aliaga, José I.↗
DOE OSTI2020

Matrix-free preconditioning for high-order H (curl) discretizations

The greater arithmetic intensity of high-order finite element discretizations makes them attractive for implementation on next-generation hardware, but assembly of high-order finite element operators as matrices is prohibitively expensive. As a result, the development of general algebraic solvers for such operators has been an open research challenge. Fast matrix-free application of high-order operators has received significant attention in the literature in the context of Poisson-type problems, but preconditioners and solvers for inverting more general operators are not very well-developed. In this paper, we consider the problem of preconditioning a definite Maxwell operator at high polynomial order without assembling a matrix. We show that given efficient preconditioners for high-order H 1 finite element problems on the same mesh, efficient H(curl) preconditioners can be constructed in an auxiliary space framework. We demonstrate the resulting preconditioners in a practical setting with tensor-product basis functions on an unstructured mesh of quadrilaterals. Overall, our approach uses a sparsified H 1 solver constructed on a low-order mesh of the nodal points of the underlying high-order space, and we show that the resulting H(curl) preconditioner is effective at very high polynomial orders for two-dimensional model problems with complicated geometry, varying piecewise constant coefficients, and curved elements. The resulting preconditioner scales with nearly optimal O(p d+1 ) floating point operation count and optimal O(p d ) memory transfer requirements, outperforming existing Maxwell preconditioners in the high-order regime.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

High‐order cubature rules for tetrahedra

Summary In this paper, we construct new high‐order numerical integration schemes for tetrahedra, with positive weights and integration points that are in the interior of the domain. The construction of cubature rules is a challenging problem, which requires the solution of strongly nonlinear algebraic (moment) equations with side conditions given by affine inequality constraints. We present a robust algorithm based on a sequence of three modified Newton procedures to solve the constrained minimization problem. In the literature, numerical integration rules for the tetrahedron are available up to order p =15. We obtain integration rules for the tetrahedron from p =2 to p =20, which are computed using multiprecision arithmetic. For p ≤15, our approach provides integration rules that have the same or fewer number of integration points than existing rules; for p =16 to p =20, our rules are new. Numerical tests are presented that verify the polynomial‐precision of the cubature rules. Convergence studies are performed for the integration of exponential, rational, weakly singular and trigonometric test functions over tetrahedra with flat and curved faces. In all tests, improvements in accuracy is realized as p is increased, though in some cases nonmonotonic convergence is observed.

Jaśkowiec, Jan↗
DOE OSTI2016

Bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations

Here in this paper, two novel techniques for bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations are developed. The first provides a theorem to construct interval bounds, while the second provides a theorem to construct lower bounds convex and upper bounds concave in the parameter. The convex/concave bounds can be significantly tighter than the interval bounds because of the wrapping effect suffered by interval analysis in dynamical systems. Both types of bounds are computationally cheap to construct, requiring solving auxiliary systems twice and four times larger than the original system, respectively. An illustrative numerical example of bound construction and use for deterministic global optimization within a simple serial branch-and-bound algorithm, implemented numerically using interval arithmetic and a generalization of McCormick's relaxation technique, is presented. Finally, problems within the important class of reaction-diffusion systems may be optimized with these tools.

42 ENGINEERING↗
DOE OSTI2019

Function Maximization with Dynamic Quantum Search

Finding the maximum value of a function in a dynamic model plays an important role in many application settings, including discrete optimization in the presence of hard constraints. We present an iterative quantum algorithm for finding the maximum value of a function in which prior search results update the acceptable response. Our approach is based on quantum search and utilizes a dynamic oracle function to mark items in a specified input set. As a realization of function optimization, we verify the correctness of the algorithm using numerical simulations of quantum circuits for the Knapsack problem. In conclusion, our simulations make use of an explicit oracle function based on arithmetic operations and a comparator subroutine, and we verify these implementations using numerical simulations up to 30 qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Performance Characterization of De Novo Genome Assembly on Leading Parallel Systems.

De novo genome assembly is one of the most important and challenging computational problems in modern genomics; further, it shares algorithms and communication patterns important to other graph analytic and irregular applications. Unlike simulations, it has no floating point arithmetic and is dominated by small memory transactions within and between computing nodes. In this work, we focus on the highly scalable HipMer assembler and identify the dominant algorithms and communication patterns, also using microbenchmarks to capture the workload. We evaluate HipMer on a variety of platforms from the latest HPC systems to ethernet clusters. HipMer performs well on all single node systems, including the Xeon Phi manycore architecture. Given large enough problems, it also demonstrates excellent scaling across nodes in an HPC system, but requires a high speed network with low overhead and high injection rates. Our results shed light on the architectural features that are most important for achieving good parallel efficiency on this and related problems.

Ellis, Marquita↗
DOE OSTI2024

Two-loop master integrals for leading-color $$ pp\to t\overline{t}H $$ amplitudes with a light-quark loop

Abstract We compute the two-loop master integrals for leading-color QCD scattering amplitudes including a closed light-quark loop in$$ t\overline{t}H $$ t t ¯ H production at hadron colliders. Exploiting numerical evaluations in modular arithmetic, we construct a basis of master integrals satisfying a system of differential equations inϵ-factorized form. We present the analytic form of the differential equations in terms of a minimal set of differential one-forms. We explore properties of the function space of analytic solutions to the differential equations in terms of iterative integrals which can be exploited for studying the analytic form of related scattering amplitudes. Finally, we solve the differential equations using generalized series expansions to numerically evaluate the master integrals in physical phase space. As the first computation of a set of two-loop seven-scale master integrals, our results provide valuable input for analytic studies of scattering amplitudes in processes involving massive particles and a large number of kinematic scales.

Physics↗
DOE OSTI2024

Measurement of the effective leptonic weak mixing angle

Using pp collision data at $\sqrt{s}$ = 13 TeV, recorded by the LHCb experiment between 2016 and 2018 and corresponding to an integrated luminosity of 5.4 fb −1 , the forward-backward asymmetry in the pp → Z/γ* → μ + μ − process is measured. The measurement is carried out in ten intervals of the difference between the muon pseudorapidities, within a fiducial region covering dimuon masses between 66 and 116 GeV, muon pseudorapidities between 2.0 and 4.5 and muon transverse momenta above 20 GeV. These forward-backward asymmetries are compared with predictions, at next-to-leading order in the strong and electroweak couplings. The measured effective leptonic weak mixing angle is ${\sin}^2{\theta}_{\textrm{eff}}^{\ell }=0.23147\pm 0.00044\pm 0.00005\pm 0.00023,$ where the first uncertainty is statistical, the second arises from systematic uncertainties associated with the asymmetry measurement, and the third arises from uncertainties in the fit model used to extract ${\sin}^2{\theta}_{\textrm{eff}}^{\ell }$ from the asymmetry measurement. This result is based on an arithmetic average of results using the CT18, MSHT20, and NNPDF31 parameterisations of the proton internal structure, and is consistent with previous measurements and with predictions from the global electroweak fit.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗