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Results for “approximate computing”

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 1,585 records · Page 88

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NASA NTRS1980

Thin-layer approximation for three-dimensional supersonic corner flows

The thin-layer approximation is extended to an axial corner that is formed by the intersection of two perpendicular plates, one of which has an inclination angle with respect to the free stream. A computer code developed by Hung and MacCormack (1978) is modified for the thin-layer approximation, and a case with Mach 5.9 and a wedge angle of 6 deg is computed. In addition, it is shown that it is not necessary to solve the complete Navier-Stokes equations for a three-dimensional high-Reynolds-number corner flow.

Hung, C. M.↗

DOE OSTI2026

Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nev- ertheless, the majority of these studies examine how well deep neural networks can model functions with uniform regularities. In this paper, we explore a different angle: how deep neural networks can adapt to varying degrees of smoothness in functions and nonuni- form data distributions across different locations and scales. More precisely, we focus on a broad class of functions defined by nonlinear tree-based approximation methods. This class encompasses a range of function types, such as functions with uniform regularities and discontinuous functions. We develop nonparametric approximation and estimation theories for this class using deep ReLU networks. Our results show that deep neural networks are adaptive to the nonuniform smoothness of functions and nonuniform data distributions at different locations and scales. We apply our results to several function classes, and derive the corresponding approximation and generalization errors. The validity of our results is demonstrated through numerical experiments.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1993

A note on the computation of antenna-blocking shadows

A simple and readily applied method is provided to compute the shadow on the main reflector of a Cassegrain antenna, when cast by the subreflector and the subreflector supports. The method entails some convenient minor approximations that will produce results similar to results obtained with a lengthier, mainframe computer program.

Levy, R.↗

DOE OSTI2021

A Butterfly-Accelerated Volume Integral Equation Solver for Broad Permittivity and Large-Scale Electromagnetic Analysis

In this work, a butterfly-accelerated volume integral equation (VIE) solver is proposed for fast and accurate electromagnetic (EM) analysis of scattering from heterogeneous objects. The proposed solver leverages the hierarchical off-diagonal butterfly (HOD-BF) scheme to construct the system matrix and obtain its approximate inverse, used as a preconditioner. Complexity analysis and numerical experiments validate the O(N log 2 N) construction cost of the HOD-BF-compressed system matrix and O(N log 1.5 N) inversion cost for the preconditioner, where N is the number of unknowns in the high-frequency EM scattering problem. For many practical scenarios, the proposed VIE solver requires less memory and computational time to construct the system matrix and obtain its approximate inverse compared to a H matrix-accelerated VIE solver. The accuracy and efficiency of the proposed solver have been demonstrated via its application to the EM analysis of large-scale canonical and real-world structures comprising of broad permittivity values and involving millions of unknowns.

42 ENGINEERING↗

NASA NTRS1982

Dynamic modeling of structures from measured complex modes

A technique is presented to use a set of identified complex modes together with an analytical mathematical model of a structure under test to compute improved mass, stiffness and damping matrices. A set of identified normal modes, computed from the measured complex modes, is used in the mass orthogonality equation to compute an improved mass matrix. This eliminates possible errors that may result from using approximated complex modes as normal modes. The improved mass matrix, the measured complex modes and the higher analytical modes are then used to compute the improved stiffness and damping matrices. The number of degrees-of-freedom of the improved model is limited to equal the number of elements in the measured modal vectors. A simulated experiment shows considerable improvements, in the system's analytical dynamic model, over the frequency range of the given measured modal information.

Ibrahim, s. R.↗

NASA NTRS1985

Dynamic Modeling of Structures from Measured Complex Modes

Ibrahim, S. R.↗

NASA NTRS1983

The efficient solution of transonic wing flow fields

An evaluation of the transonic-wing-analysis computer code TWING is presented. TWING utilizes a fully implicit, approximate-factorization iteration scheme to solve the full-potential equation in conservative form. A numerical elliptic-solver grid-generation scheme is used to generate the required finite-difference mesh. Several wing configurations have been analyzed, and comparisons of computed results have been made with available experimental data. Results indicate that the code is robust, accurate (when significant viscous effects are not present), and efficient. TWING generally produces solutions an order of magnitude faster than other conservative, full-potential codes using successive-line overrelaxation. The present method is applicable to a wide range of isolated wing configurations, including high-aspect-ratio transport wings and low-aspect-ratio, high-sweep, fighter configurations.

Holst, T. L.↗

NASA NTRS2007

Propagation of Computational Uncertainty Using the Modern Design of Experiments

This paper describes the use of formally designed experiments to aid in the error analysis of a computational experiment. A method is described by which the underlying code is approximated with relatively low-order polynomial graduating functions represented by truncated Taylor series approximations to the true underlying response function. A resource-minimal approach is outlined by which such graduating functions can be estimated from a minimum number of case runs of the underlying computational code. Certain practical considerations are discussed, including ways and means of coping with high-order response functions. The distributional properties of prediction residuals are presented and discussed. A practical method is presented for quantifying that component of the prediction uncertainty of a computational code that can be attributed to imperfect knowledge of independent variable levels. This method is illustrated with a recent assessment of uncertainty in computational estimates of Space Shuttle thermal and structural reentry loads attributable to ice and foam debris impact on ascent.

DeLoach, Richard↗

DOE OSTI2023

Hi-COLA: fast, approximate simulations of structure formation in Horndeski gravity

We introduce Hi-COLA, a code designed to run fast, approximate N-body simulations of non-linear structure formation in reduced Horndeski gravity. Given an input Lagrangian, Hi-COLA dynamically constructs the appropriate field equations and consistently solves for the cosmological background, linear growth, and screened fifth force of that theory. Hence Hi-COLA is a general, adaptable, and useful tool that allows the mildly non-linear regime of many Horndeski theories to be investigated for the first time, at low computational cost. In this work, we first describe the screening approximations and simulation setup of Hi-COLA for theories with Vainshtein screening. We validate the code against traditional N-body simulations for cubic Galileon gravity, finding 2.5% agreement up to k max = 1.2 h/Mpc. To demonstrate the flexibility of Hi-COLA, we additionally run the first simulations of an extended shift-symmetric gravity theory. We use the consistency and modularity of Hi-COLA to dissect how the modified background, linear growth, and screened fifth force all contribute to departures from ΛCDM in the non-linear matter power spectrum. Hi-COLA can be found at https://github.com/Hi-COLACode/Hi-COLA.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1970

Concept for a distributed processor computer

Future generation computer utilizes cell of single metal oxide semiconductor wafer containing general purpose processor section and small memory of approximately 512 words of 16 bits each. Cells are organized into groups and groups interconnected to form computer.

Bogue, P. N.↗

DOE OSTI2024

Improving the five-point bootstrap

We present a new algorithm for the numerical evaluation of five-point conformal blocks in d-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in radial coordinates, derive a set of recursion relations for the unknown coefficients in the ansatz, and evaluate the series using a Padé approximant to accelerate its convergence. We then study the 〈σσϵσσ〉 correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff ∆ ⩽ ∆cutoff. We approximate the contributions of the operators above the cutoff by the corresponding contributions in a suitable disconnected five-point correlator. Using this approach, we compute a number of OPE coefficients with greater accuracy than previous methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1983

Application of advanced reliability methods to local strain fatigue analysis

When design factors are considered as random variables and the failure condition cannot be expressed by a closed form algebraic inequality, computations of risk (or probability of failure) might become extremely difficult or very inefficient. This study suggests using a simple, and easily constructed, second degree polynomial to approximate the complicated limit state in the neighborhood of the design point; a computer analysis relates the design variables at selected points. Then a fast probability integration technique (i.e., the Rackwitz-Fiessler algorithm) can be used to estimate risk. The capability of the proposed method is demonstrated in an example of a low cycle fatigue problem for which a computer analysis is required to perform local strain analysis to relate the design variables. A comparison of the performance of this method is made with a far more costly Monte Carlo solution. Agreement of the proposed method with Monte Carlo is considered to be good.

Wu, T. T.↗

NASA NTRS1984

Advanced reliability method for fatigue analysis

When design factors are considered as random variables and the failure condition cannot be expressed by a closed form algebraic inequality, computations of risk (or probability of failure) may become extremely difficult or very inefficient. This study suggests using a simple and easily constructed second degree polynomial to approximate the complicated limit state in the neighborhood of the design point; a computer analysis relates the design variables at selected points. Then a fast probability integration technique (i.e., the Rackwitz-Fiessler algorithm) can be used to estimate risk. The capability of the proposed method is demonstrated in an example of a low cycle fatigue problem for which a computer analysis is required to perform local strain analysis to relate the design variables. A comparison of the performance of this method is made with a far more costly Monte Carlo solution. Agreement of the proposed method with Monte Carlo is considered to be good.

Wu, Y.-T.↗

NASA NTRS1994

Rapid computation of spectrally integrated non-local thermodynamic equilibrium limb emission

The interpretation of infrared radiance measurements made by satellite-borne limb-scanning broadband radiometers requires accurate and computationally fast techniques with which to evaluate the equation of radiative transfer. This requirement is made even more stringent when analyzing measurements of non-local thermodynamic equilibrium (non-LTE) emission from the terrestrial mesosphere and lower thermosphere. In principle, line-by-line calculations which explicitly account for the departure from thermodynamic equilibrium in both the source functions and the transmittances are necessary. In this paper we extend the emissivity growth approximation (EGA) technique developed for local thermodynamic equilibrium (LTE) limb radiance for the molecular oxygen dayglow (1.27 micrometers and 762 nm), ozone and carbon dioxide in the 9- to 11-micrometer spectral interval, carbon monoxide (4.6 micrometers), nitric oxide (5.3 micrometers), and the carbon dioxide bands (15 micrometers) are presented. Using the non-LTE form of the EGA, the spectrally integrated limb emission is calculated for 35 tangent heights in the mesosphere and lower thermosphere (a total of 1200 atmospheric layers) with line-by-line accuracy in approximately 0.35 s of CPU time on readily available desktop computer hardware, while the corresponding line-by-line calculations may require several minutes. The non-LTE EGA technique will allow kinetic temperature and minor constituend retrieval algorithms to readily include non-LTE efects limited only by the a priori knowledge of the departure from LTE in the observed bands.

Mlynczak, Martin G.↗

DOE OSTI2025

Scalable Algorithms for Inverse Problems With High-Dimensional Parameter Spaces

Inverse problems, which involve inferring unknown parameters from observed data, present significant computational challenges, especially in large-scale settings with high-dimensional unknown parameters and nonlinear relationships between the unknowns and observations. Bayesian inference provides an approach for addressing these problems, often relying on sequential sampling methods like Markov chain Monte Carlo (MCMC) to approximate the posterior distribution of the parameters. However, MCMC methods become computationally demanding as the dimensionality of the problem increases, particularly in large-scale systems where likelihood evaluations rely on solving partial differential equations (PDEs) on large spatial domains with finely resolved meshes. To overcome these limitations, recent advancements have focused on designing scalable computa tional techniques – for both PDE simulations and sampling strategies – to make Bayesian methods feasible for high-dimensional problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Propagation of radio frequency waves through turbulent plasmas

The practical and economic viability of tokamak fusion reactors depends, in a significant way, on the efficiency of radio frequency (RF) waves to deliver energy and momentum to the plasma in the core of the reactor. The RF electromagnetic waves, excited by antenna structures placed near the wall of a tokamak, have to propagate through the turbulent edge plasma along their path to the core of the fusion device. In present day experiments, the radial width of the edge region and scrape-off layer is of the order of a few centimeters. In ITER, and in future fusion reactors, this width will be of the order of tens of centimeters. Any effects on RF waves due to plasma turbulence have to be properly understood in order to optimize the delivery of RF energy and momentum into the core. This paper is on a multi-pronged, theoretical and computational, approach that is being pursued to quantify the effect of edge plasma turbulence on the propagation of RF waves. The theoretical and analytical models are based on solutions of the Faraday-Ampere equation in a magnetized plasma and on the Kirchhoff tangent plane approximation. An effective medium approach has been developed so as to approximate the permittivity of a turbulent plasma by analytical expressions. The computations are being carried out with a newly developed code ScaRF that is based on the finite difference finite domain technique for solving Maxwell's equations. The plasma permittivity can be assigned as desired. The code is being used to validate the analytical and theoretical models and to evaluate their limitations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2004

Implementation of a Message Passing Interface into a Cloud-Resolving Model for Massively Parallel Computing

The capability for massively parallel programming (MPP) using a message passing interface (MPI) has been implemented into a three-dimensional version of the Goddard Cumulus Ensemble (GCE) model. The design for the MPP with MPI uses the concept of maintaining similar code structure between the whole domain as well as the portions after decomposition. Hence the model follows the same integration for single and multiple tasks (CPUs). Also, it provides for minimal changes to the original code, so it is easily modified and/or managed by the model developers and users who have little knowledge of MPP. The entire model domain could be sliced into one- or two-dimensional decomposition with a halo regime, which is overlaid on partial domains. The halo regime requires that no data be fetched across tasks during the computational stage, but it must be updated before the next computational stage through data exchange via MPI. For reproducible purposes, transposing data among tasks is required for spectral transform (Fast Fourier Transform, FFT), which is used in the anelastic version of the model for solving the pressure equation. The performance of the MPI-implemented codes (i.e., the compressible and anelastic versions) was tested on three different computing platforms. The major results are: 1) both versions have speedups of about 99% up to 256 tasks but not for 512 tasks; 2) the anelastic version has better speedup and efficiency because it requires more computations than that of the compressible version; 3) equal or approximately-equal numbers of slices between the x- and y- directions provide the fastest integration due to fewer data exchanges; and 4) one-dimensional slices in the x-direction result in the slowest integration due to the need for more memory relocation for computation.

Juang, Hann-Ming Henry↗

DOE OSTI2023

Perturbative readout-error mitigation for near-term quantum computers

Readout errors on near-term quantum computers can introduce significant error to the empirical probability distribution sampled from the output of a quantum circuit. These errors can be mitigated by classical postprocessing given the access of an experimental response matrix that describes the error associated with the measurement of each computational basis state. However, the resources required to characterize a complete response matrix and to compute the corrected probability distribution scale exponentially with the number of qubits, n . In this work, we modify standard matrix inversion techniques using perturbative approximations with significantly reduced complexity and bounded error when the likelihood of high-order bit-flip events is strongly suppressed. Given a characteristic error rate q , we discuss a method to recover the probability of the all-zeros bit string p 0 by sampling only a small subspace of the response matrix before inverting readout error, resulting in a relative speedup of poly [ 2 n / ( n w ) ] , which we motivate using a simplified error model for which the approximation incurs only O ( q w ) error for some integer w . We then provide a generalized technique to efficiently recover full output distributions with O ( q w ) error in the perturbative limit. These approximate techniques for readout-error correction may greatly accelerate near-term quantum computing applications.

97 MATHEMATICS AND COMPUTING↗