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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Improved Nested Sampling and Surrogate-Enabled Comparison With Other Marginal Likelihood Estimators

Estimating marginal likelihood is of central importance to Bayesian model selection and/or model averaging. The nested sampling method has been recently used together with the Metropolis-Hasting (M-H) sampling algorithm for estimating marginal likelihood. This study develops a new implementation of nested sampling by using the DiffeRential Evolution Adaptive Metropolis (DREAMzs) sampling algorithm. The two implementations of nested sampling are evaluated for four models of a synthetic groundwater flow modeling. The DREAMzs-based nested sampling outperforms the M-H-based nested sampling in terms of their accuracy, convergence, efficiency, and stability, which is attributed to the fact that DREAMzs is more robust than M-H for parameter sampling. The nested sampling method is also compared with four other methods (arithmetic mean, harmonic mean, stabilized harmonic mean, and thermodynamic integration) commonly used for estimating marginal likelihood and posterior probability of the four groundwater models. The comparative study requires hundreds of millions of model executions, which would not be possible without using surrogate models to replace the original models. Using the arithmetic mean estimator as the reference, the comparison reveals that thermodynamic integration outperforms nested sampling in terms of accuracy and stability, whereas nested sampling is more computationally efficient to reach to convergence. Here, the harmonic mean and stabilized harmonic mean methods give the worst marginal likelihood estimation. Accurate marginal likelihood estimation is important for accurate estimation of posterior model probability and better predictive performance of Bayesian model averaging.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Multistage mixed precision iterative refinement

Abstract Low precision arithmetic, in particular half precision (16‐bit) floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings in energy. Motivated by this, there has been a renewed interest in mixed precision iterative refinement schemes for solving linear systems , and new variants of GMRES‐based iterative refinement have been developed. Each particular variant with a given combination of precisions leads to different condition number‐based constraints for convergence of the backward and forward errors, and each has different performance costs. The constraints for convergence given in the literature are, as an artifact of the analyses, often overly strict in practice, and thus could lead a user to select a more expensive variant when a less expensive one would have sufficed. In this work, we develop a multistage mixed precision iterative refinement solver which aims to combine existing mixed precision approaches to balance performance and accuracy and improve usability. For a user‐specified initial combination of precisions, the algorithm begins with the least expensive approach and convergence is monitored via inexpensive computations with quantities produced during the iteration. If slow convergence or divergence is detected using particular stopping criteria, the algorithm switches to use a more expensive, but more reliable variant. A novel aspect of our approach is that, unlike existing implementations, our algorithm first attempts to use “stronger” GMRES‐based solvers for the solution update before resorting to increasing the precision(s). In some scenarios, this can avoid the need to refactorize the matrix in higher precision. We perform extensive numerical experiments on a variety of random dense problems and problems from real applications which confirm the benefits of the multistage approach.

Oktay, Eda↗
DOE OSTI2016

Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights

Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

We describe a number of recently developed techniques for improving the performance of large-scalenuclear configuration interaction calculations on high performance parallel computers. We show thebenefit of using a preconditioned block iterative method to replace the Lanczos algorithm that hastraditionally been used to perform this type of computation. The rapid convergence of the block iterativemethod is achieved by a proper choice of starting guesses of the eigenvectors and the construction of aneffective preconditioner. These acceleration techniques take advantage of special structure of the nuclearconfiguration interaction problem which we discuss in detail. The use of a block method also allows usto improve the concurrency of the computation, and take advantage of the memory hierarchy of modernmicroprocessors to increase the arithmetic intensity of the computation relative to data movement. Wealso discuss the implementation details that are critical to achieving high performance on massivelyparallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to threetimes faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system.

Shao, Meiyue↗
DOE OSTI2021

Higher-order particle representation for particle-in-cell simulations

In this paper we present an alternative approach to the representation of simulation particles for unstructured electrostatic and electromagnetic PIC simulations. In our modified PIC algorithm we represent particles as having a smooth shape function limited by some specified finite radius, r 0 . A unique feature of our approach is the representation of this shape by surrounding simulation particles with a set of virtual particles with delta shape, with fixed offsets and weights derived from Gaussian quadrature rules and the value of r 0 . As the virtual particles are purely computational, they provide the additional benefit of increasing the arithmetic intensity of traditionally memory bound particle kernels. The modified algorithm is implemented within Sandia National Laboratories' unstructured EMPIRE-PIC code, for electrostatic and electromagnetic simulations, using periodic boundary conditions. We show results for a representative set of benchmark problems, including electron orbit, a transverse electromagnetic wave propagating through a plasma, numerical heating, and a plasma slab expansion. In this work, good error reduction across all of the chosen problems is achieved as the particles are made progressively smoother, with the optimal particle radius appearing to be problem-dependent.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Evaluating MPI resource usage summary statistics

The Message Passing Interface (MPI) remains the dominant programming model for scientific applications running on today’s high-performance computing (HPC) systems. This dominance stems from MPI’s powerful semantics for inter-process communication that has enabled scientists to write applications for simulating important physical phenomena. MPI does not, however, specify how messages and synchronization should be carried out. Those details are typically dependent on low-level architecture details and the message characteristics of the application. Therefore, analyzing an application’s MPI resource usage is critical to tuning MPI’s performance on a particular platform. The result of this analysis is typically a discussion of the mean message sizes, queue search lengths and message arrival times for a workload or set of workloads. While a discussion of the arithmetic mean in MPI resource usage might be the most intuitive summary statistic, it is not always the most accurate in terms of representing the underlying data. In this paper, we analyze MPI resource usage for a number of key MPI workloads using an existing MPI trace collector and discrete-event simulator. Our analysis demonstrates that the average, while easy and efficient to calculate, is a useful metric for characterizing latency and bandwidth measurements, but may not be a good representation of application message sizes, match list search depths, or MPI inter-operation times. Additionally, we show that the median and mode are superior choices in many cases. We also observe that the arithmetic mean is not the best representation of central tendency for data that are drawn from distributions that are multi-modal or have heavy tails. Furthermore, the results and analysis of our work provide valuable guidance on how we, as a community, should discuss and analyze MPI resource usage data for scientific applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Can We Describe Graphene Confined Water Structures as Overlapping of Approaching Graphene–Water Interfacial Structures?

We investigate the microscopic mechanisms of the overlap of interfacial structures in confined fluids and attempt to answer the question whether the confined structures can be predicted from the original density profiles of individual solid–fluid interfaces. For that purpose, we perform (globally) isobaric–isothermal (locally, grand canonical) molecular dynamics simulations to extract not only the axial distribution functions of the water sites for the uncoupled graphene–water interfaces, but also those corresponding to the confined aqueous environments over the interplate range $8 ≤ h (Å) ≤ 28$ typically at ambient conditions. We have tested two (i.e., an arithmetic and a geometric) superposition approximations for the singlet density of confined water between flat graphene plates, as well as for a combination of flat and corrugated graphene plates. The outcome of this study suggests that the answer to the title’s question is a “yes”, provided that the interplate distance h is large enough to avoid fluid geometric packing frustration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Quantum mechanics problems in observer's mathematics

This work considers the ontology, guiding equation, Schrodinger's equation, relation to the Born Rule, the conditional wave function of a subsystem in a setting of arithmetic, algebra and topology provided by Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. Certain results and communications pertaining to solutions of these problems are provided. In particular, we prove the following theorems: Theorem I (Two-slit interference). Let {Psi}{sub 1} be a wave from slit 1, {Psi}{sub 2} - from slit 2, and {Psi} = {Psi}{sub 1}+{Psi}{sub 2}. Then the probability of {Psi} being a wave equals to 0.5. Theorem II (k-bodies solution). For W{sub n} from m-observer point of view with m>log{sub 10}((2 Multiplication-Sign 10{sup 2n}-1){sup 2k}+1), the probability of standard expression of Hamiltonian variation is less than 1 and depends on n,m,k.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Retention of intermediate polarization states in ferroelectric materials enabling memories for multi-bit data storage

A homogeneous ferroelectric single crystal exhibits only two remanent polarization states that are stable over time, whereas intermediate, or unsaturated, polarization states are thermodynamically instable. Commonly used ferroelectric materials however, are inhomogeneous polycrystalline thin films or ceramics. To investigate the stability of intermediate polarization states, formed upon incomplete, or partial, switching, we have systematically studied their retention in capacitors comprising two classic ferroelectric materials, viz. random copolymer of vinylidene fluoride with trifluoroethylene, P(VDF-TrFE), and Pb(Zr,Ti)O{sub 3}. Each experiment started from a discharged and electrically depolarized ferroelectric capacitor. Voltage pulses were applied to set the given polarization states. The retention was measured as a function of time at various temperatures. The intermediate polarization states are stable over time, up to the Curie temperature. We argue that the remarkable stability originates from the coexistence of effectively independent domains, with different values of polarization and coercive field. A domain growth model is derived quantitatively describing deterministic switching between the intermediate polarization states. We show that by using well-defined voltage pulses, the polarization can be set to any arbitrary value, allowing arithmetic programming. The feasibility of arithmetic programming along with the inherent stability of intermediate polarization states makes ferroelectric materials ideal candidates for multibit data storage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Spectral induced polarization monitoring of induced calcite precipitation in subsurface sediments

Co-precipitation of contaminants within the crystalline structure of calcite is a promising natural attenuation or remedial technology being considered at contaminated sites. We explore the sensitivity of the spectral induced polarization (SIP) method to induced calcite precipitation in natural sediments as a path forward to non-invasively monitor these sites. We performed time-lapse column experiments using phased (I-IV) injections over 40 days on natural sediments from the Hanford Site (Washington State, USA). In the phased injections, abiotic calcite precipitation was induced and confirmed to have occurred. Previous work in glass beads and homogeneous sand was limited to high frequency detection of calcite, however in this work we observed the development of two polarization mechanisms, one at high frequency (>100 Hz) and one at low frequency (< 100 Hz). Based on the characteristic frequencies from the SIP high and low frequency regimes, characteristic length scales (L) were computed where the adsorption mode of Na+ versus Ca2+ was compared by using diffusion coefficients corresponding to Na+ versus an arithmetically averaged value for Na+ and Ca2+. Using the diffusion coefficient of Na+, the high frequency L was found to correlate well with the size of the calcite crystals. The low frequency L correlated well with the individual natural sediment grain sizes within the columns. During late experimental times (day 36 and 40), the characteristic low frequency in two of the experimental columns shifted to lower frequencies (<0.001 Hz) which may signify SIP sensitivity of the formed calcite with the sediment grains. In field applications, the development of a low frequency polarization length scale to monitor calcite precipitation is promising for field monitoring applications, however further laboratory work needs to be performed to examine the SIP sensitivity of calcite formation in the presence of to natural sediments

calcium carbonate, calcite, precipitation, spectra↗
DOE OSTI2021

Efficient phase-factor evaluation in quantum signal processing

Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in principle be obtained for a range of tasks, such as Hamiltonian simulation and the quantum linear system problem. A further benefit of QSP is that it uses a minimal number of ancilla qubits, which facilitates its implementation on near-to-intermediate term quantum architectures. However, there is so far no classically stable algorithm allowing computation of the phase factors that are needed to build QSP circuits. Existing methods require the use of variable precision arithmetic and can only be applied to polynomials of a relatively low degree. We present here an optimization-based method that can accurately compute the phase factors using standard double precision arithmetic operations. We demonstrate the performance of this approach with applications to Hamiltonian simulation, eigenvalue filtering, and quantum linear system problems. Furthermore, our numerical results show that the optimization algorithm can find phase factors to accurately approximate polynomials of a degree larger than 10000 with errors below 10 -12 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Fast inversion, preconditioned quantum linear system solvers, fast Green's-function computation, and fast evaluation of matrix functions

Preconditioning is the most widely used and effective way for treating ill-conditioned linear systems in the context of classical iterative linear system solvers. We introduce a quantum primitive called fast inversion, which can be used as a preconditioner for solving quantum linear systems. The key idea of fast inversion is to directly block encode a matrix inverse through a quantum circuit implementing the inversion of eigenvalues via classical arithmetics. We demonstrate the application of preconditioned linear system solvers for computing single-particle Green's functions of quantum many-body systems, which are widely used in quantum physics, chemistry, and materials science. We analyze the complexities in three scenarios: the Hubbard model, the quantum many-body Hamiltonian in the plane-wave-dual basis, and the Schwinger model. We also provide a method for performing Green's function calculation in second quantization within a fixed-particle manifold and note that this approach may be valuable for simulation more broadly. Aside from solving linear systems, fast inversion also allows us to develop fast algorithms for computing matrix functions, such as the efficient preparation of Gibbs states. Furthermore, we introduce two efficient approaches for such a task, based on the contour-integral formulation and the inverse transform, respectively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

A Work-Efficient Parallel Sparse Matrix-Sparse Vector Multiplication Algorithm

We design and develop a work-efficient multithreaded algorithm for sparse matrix-sparse vector multiplication (SpMSpV) where the matrix, the input vector, and the output vector are all sparse. SpMSpV is an important primitive in the emerging GraphBLAS standard and is the workhorse of many graph algorithms including breadth-first search, bipartite graph matching, and maximal independent set. As thread counts increase, existing multithreaded SpMSpV algorithms can spend more time accessing the sparse matrix data structure than doing arithmetic. Our shared-memory parallel SpMSpV algorithm is work efficient in the sense that its total work is proportional to the number of arithmetic operations required. The key insight is to avoid each thread individually scan the list of matrix columns. Our algorithm is simple to implement and operates on existing column-based sparse matrix formats. It performs well on diverse matrices and vectors with heterogeneous sparsity patterns. A high-performance implementation of the algorithm attains up to 15x speedup on a 24-core Intel Ivy Bridge processor and up to 49x speedup on a 64-core Intel KNL manycore processor. In contrast to implementations of existing algorithms, the performance of our algorithm is sustained on a variety of different input types include matrices representing scale-free and high-diameter graphs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Reducing Communication in Graph Neural Network Training

Graph Neural Networks (GNNs) are powerful and flexible neural networks that use the naturally sparse connectivity information of the data. GNNs represent this connectivity as sparse matrices, which have lower arithmetic intensity and thus higher communication costs compared to dense matrices, making GNNs harder to scale to high concurrencies than convolutional or fully-connected neural networks. Here, we introduce a family of parallel algorithms for training GNNs and show that they can asymptotically reduce communication compared to previous parallel GNN training methods. We implement these algorithms, which are based on 1D, 1. 5D, 2D, and 3D sparse-dense matrix multiplication, using torch.distributed on GPU-equipped clusters. Our algorithms optimize communication across the full GNN training pipeline. We train GNNs on over a hundred GPUs on multiple datasets, including a protein network with over a billion edges.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

SU-D-206-02: Evaluation of Partial Storage of the System Matrix for Cone Beam Computed Tomography Using a GPU Platform

Purpose: Iterative reconstruction algorithms in computed tomography (CT) require a fast method for computing the intersections between the photons’ trajectories and the object, also called ray-tracing or system matrix computation. This work evaluates different ways to store the system matrix, aiming to reconstruct dense image grids in reasonable time. Methods: We propose an optimized implementation of the Siddon’s algorithm using graphics processing units (GPUs) with a novel data storage scheme. The algorithm computes a part of the system matrix on demand, typically, for one projection angle. The proposed method was enhanced with accelerating options: storage of larger subsets of the system matrix, systematic reuse of data via geometric symmetries, an arithmetic-rich parallel code and code configuration via machine learning. It was tested on geometries mimicking a cone beam CT acquisition of a human head. To realistically assess the execution time, the ray-tracing routines were integrated into a regularized Poisson-based reconstruction algorithm. The proposed scheme was also compared to a different approach, where the system matrix is fully pre-computed and loaded at reconstruction time. Results: Fast ray-tracing of realistic acquisition geometries, which often lack spatial symmetry properties, was enabled via the proposed method. Ray-tracing interleaved with projection and backprojection operations required significant additional time. In most cases, ray-tracing was shown to use about 66 % of the total reconstruction time. In absolute terms, tracing times varied from 3.6 s to 7.5 min, depending on the problem size. The presence of geometrical symmetries allowed for non-negligible ray-tracing and reconstruction time reduction. Arithmetic-rich parallel code and machine learning permitted a modest reconstruction time reduction, in the order of 1 %. Conclusion: Partial system matrix storage permitted the reconstruction of higher 3D image grid sizes and larger projection datasets at the cost of additional time, when compared to the fully pre-computed approach. This work was supported in part by the Fonds de recherche du Quebec - Nature et technologies (FRQ-NT). The authors acknowledge partial support by the CREATE Medical Physics Research Training Network grant of the Natural Sciences and Engineering Research Council of Canada (Grant No. 432290).

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-T-571: Objective Assessment of 3D Dosimetry for Flattened and Flattened Filter Free Stereotactic Rotational Delivery Using 729-Array Detector with Octavius 4D Phantom

Purpose: The purpose of this study was to assess the potential of 3D dosimetry for flattened and flattened filter free stereotactic rotational delivery in high definition MLC using 729-detector array with Octavius 4D phantom Methods: Twenty rapid arc plans were assessed for this study. For each patient two plans for 6X and 6FFF photon beams were generated with same prescription and critical organ constraints in Eclipse TPS version 13.0 using high definition MLC. Verification plans were generated in scanned Octavius 4D phantom in TPS. 3D dose measurements were collected from 729-ion chamber detector array in Octavius 4D phantom using verisoft software v 6.0. TPS calculated dose was compared with measured 3D dose in verisoft using the following gamma analysis parameters such as 3D volumetric, 3D planar and 2D global gamma in transverse, sagittal and coronal planes for 3mm/3% and 2mm/2% distance to agreement criteria.Passing rate and arithmetic mean of global gamma were analysed for 2D and 3D global gamma in all planes. Results: The average number of dose points passing rate for 2D global gamma with 3mm/3% criteria in transverse, sagittal and coronal planes was 99.06%±2.89%, 98.8%±0.88% and 99.06%±91%, respectively. For 2mm/2% criteria 97.86%±2.26%, 94.49± 2.64% and 94.34%±2.9% was observed. In 3D planar global gamma with 3mm/3% was 99.53%±0.49%, 98.93%±1.03% and 99.29%±1.29%, for 2mm 2% criteria was 97.50%±2.24%, 94.5%±2.5% and 95.38%±4.5%. The maximum arithmetic mean gamma deviation of 0.505%±0.13% was observed in coronal plane for 2D global gamma with 2mm/2% criteria. The 3D volumetric gamma passing rate was observed as 99.61%±0.433% for 3mm /3% and 95.91%±2.51% for 2mm/2%. Conclusion: The objective assessment of 3D dosimetry have demonstrated that the rotational delivery accuracy for flattened and flattened filter free stereotactic plans can be verified by using Octavius system comprising with 729 ion chamber array and Octavius 4D phantom.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Manycore Parallel Computing for a Hybridizable Discontinuous Galerkin Nested Multigrid Method

In this work, we present a parallel computing strategy for a hybridizable discontinuous Galerkin (HDG) nested geometric multigrid (GMG) solver. Parallel GMG solvers require a combination of coarse-grain and fine-grain parallelism to improve time-to-solution performance. In this work we focus on fine-grain parallelism. We use Intel's second generation Xeon Phi (Knights Landing) manycore processor. The GMG method achieves ideal convergence rates of 0.2 or less, for high polynomial orders. A matrix free (assembly free) technique is exploited to save considerable memory usage and increase arithmetic intensity. HDG enables static condensation, and due to the discontinuous nature of the discretization, we developed a matrix vector multiply routine that does not require any costly synchronizations or barriers. Our algorithm is able to attain 80% of peak bandwidth performance for higher order polynomials. This is possible due to the data locality inherent in the HDG method. Very high performance is realized for high order schemes, due to good arithmetic intensity, which declines as the order is reduced.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Rounding Error Analysis of Mixed Precision Block Householder QR Algorithms

Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speedups and lower storage cost if applied appropriately. The growing interest in employing mixed precision computations motivates the need for rounding error analysis that properly handles behavior from mixed precision arithmetic. We develop mixed precision variants of existing Householder QR algorithms and show error analyses supported by numerical experiments.

97 MATHEMATICS AND COMPUTING↗