Search NASA⌕ Search

SEARCH · Search NASA

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,387 records · Page 77
All sourcesNASA NTRSDOE OSTI
NASA NTRS2020

Multi Model Monte Carlo with Python (MXMCPy)

Multi Model Monte Carlo with Python (\mxmc {}) is a software package developed as a general capability for computing the statistics of outputs from an expensive, high-fidelity model by leveraging faster, low-fidelity models for speedup. Motivated by uncertainty propagation problems where classical Monte Carlo (MC) simulation is computationally intractable, various multi-model MC approaches have recently emerged that yield unbiased estimators with significantly reduced variance relative to MC for the same cost. These existing methods include multi-level Monte Carlo (MLMC), multi-fidelity Monte Carlo (MFMC), and approximate control variates (ACV). Given a fixed computational budget and a collection of models with varying cost/accuracy, each method seeks a sample allocation strategy across the models that results in an estimator with optimal variance reduction. \mxmc {} is a versatile tool that enables convenient access to many existing multi-model MC approaches within one modular and extensible package. With \mxmc {}, users can easily compare existing methods to determine the best choice for their particular problem, while developers have a basis for implementing and sharing new variance reduction approaches. This report introduces the \mxmc {} software, providing a summary of the problem-solving workflow for users as well as a brief overview of the code layout for developers.

Geoffrey F Bomarito↗
DOE OSTI2025

Structure-preserving neural networks for the regularized entropy-based closure of a linear, kinetic, radiative transport equation

The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural network-based approximation to the entropy-based closure method to accurately compute the solution of the multi-dimensional moment system with a low memory footprint and competitive computational time. We extend methods developed for the standard entropy-based closure to the regularized entropy-based closures. The main idea is to interpret structure-preserving neural network approximations of the regularized entropy-based closure as a two-stage approximation to the original entropy-based closure. We conduct a numerical analysis of this approximation and investigate optimal parameter choices. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive computation times and simulation accuracy. The code and all trained networks are provided on GitHub.

entropy closure↗
NASA NTRS1987

Optical communication with semiconductor laser diodes

A 25 megabit/sec direct detection optical communication system that used Q=4 PPM signalling was constructed and its performance measured under laboratory conditions. The system used a single-mode AlGaAs laser diode transmitter and low noise silicon avalanche photodiode (APD) photodetector. Comparison of measured performance with the theoretical revealed that modeling the APD output as a Gaussian process under conditions of negligible background radiation and low (less than 10 to the -12 power A) APD bulk leakage currents leads to substantial underestimates of optimal APD gain to use and overestimates of system bit error probability. A procedure is given to numerically compute system performance which uses the more accurate Webb's Approximation of the exact Conradi distribution for the APD ouput signal that does not require excessive amounts of computer time (a few minutes of VAX 8600 CPU time per system operating point). Examples are given which illustrate the breakdown of the Gaussian approximation in assessing system performance. This system achieved a bit error probability of 10 to the -6 power at a received signal energy corresponding to an average of 60 absorbed photons/bit and optimal APD gain of 700.

Davidson, F.↗
DOE OSTI2019

Semi-local Density Functional Approximations for Bulk, Surface, and Confinement Physics

Due to its balance of accuracy and computational cost, density functional theory has become the method of choice for computing the electronic structure and related properties of materials. However, present-day semi-local approximations to the exchange-correlation energy of density functional theory break down for materials containing d and f electrons. In this report we summarize the results of our research efforts within the LDRD 200202 titled "Making density functional theory work for all materials" in addressing this issue. Our efforts are grouped into two research thrusts. In the first thrust, we develop an exchange-correlation functional (BSC functional) within the subsystem functional formalism. It enables us to capture bulk, surface, and confinement physics with a single, semi-local exchange-correlation functional in density functional theory calculations. We present the analytical properties of the BSC functional and demonstrate that the BSC functional is able to capture confinement physics more accurately than standard semi-local exchange-correlation functionals. The second research thrust focusses on developing a database for transition metal binary compounds. The database consists of materials properties (formation energies, ground-state energies, lattice constants, and elastic constants) of 26 transition metal elements and 89 transition metal alloys. It serves as a reference for benchmarking computational models (such as lower-level modeling methods and exchange-correlation functionals). We expect that our database will significantly impact the materials science community. We conclude with a brief discussion on the future research directions and impact of our results.

36 MATERIALS SCIENCE↗
DOE OSTI2017

A Fresh Math Perspective Opens New Possibilities for Computational Chemistry

By reformulating the TDDFT problem as a matrix function approximation, making use of a special transformation and taking advantage of the underlying symmetry with respect to a non-Euclidean metric, Yang and his colleagues were able to apply the Lanczos algorithm and a Kernal Polynomial Method (KPM) to approximate the absorption spectrum of several molecules. Both of these algorithms require relatively low-memory compared to non-symmetrical alternatives, which is the key to the computational savings.

Vu, Linda↗
DOE OSTI2018

A Low-Rank Multigrid Method for the Stochastic Steady-State Diffusion Problem

We study a multigrid method for solving large linear systems of equations with tensor product structure here. Such systems are obtained from stochastic finite element discretization of stochastic partial differential equations such as the steady-state diffusion problem with random coefficients. When the variance in the problem is not too large, the solution can be well approximated by a low-rank object. In the proposed multigrid algorithm, the matrix iterates are truncated to low rank to reduce memory requirements and computational effort. The technique is proved convergent with an analytic error bound. Numerical experiments show its effectiveness in solving the Galerkin systems compared to the original multigrid solver, especially when the number of degrees of freedom associated with the spatial discretization is large.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1981

As-Built design specification for PARPLT

The design and implementation of the PARPLT program are described. The program produces scatter plots of the greenness profile derived parameters alpha, beta, and t sub o computed by the CLASFYG program (alpha being the approximate greenness rise time; beta, the greenness decay time; and t sub o, the spectral crop emergence date). Statistical information concerning the parameters is also computed.

Tompkins, M. A.↗
NASA NTRS1985

A physically realistic approximate form for the redistribution function R(II-A)

An approximation is proposed to the redistribution function R(II-A) (coherent, isotropic scattering in the rest frame of the atom) which is fast to compute and attains much higher accuracy than previous approximations for the astrophysically important case of small Voigt parameters. Further, the new approximation permits the diffusion in frequency of wing photons ('Doppler drifting') which is lost in one of the widely-used versions of the R(II-A) approximation schemes: Kneer's normalization of the Jefferies-White formulation.

Ayres, T. R.↗
DOE OSTI2019

Monte Carlo Second- and Third-Order Many-Body Green’s Function Methods with Frequency-Dependent, Nondiagonal Self-Energy

We fully develop the Monte Carlo many-body Green’s function (MC-GF) method with the following enhancements: (1) The truncation order of the perturbation expansion of the Dyson self-energy is raised from the second order (MC-GF2) to the third order (MC-GF3) with the aid of a computerized procedure to enumerate and transform all 84 third-order Goldstone diagrams into Monte Carlo integrable expressions and then into central processing unit (CPU)/graphical processing unit (GPU)-parallel computer codes. (2) An efficient algorithm is proposed that computes all off-diagonal and diagonal elements of the MC-GF2 and MC-GF3 self-energy matrices by common subexpression elimination. (3) The frequency-independent approximation is lifted by introducing a method that computes frequency derivatives of the MC-GF2 and MC-GF3 self-energies up to any arbitrarily high order at nearly no additional computational cost. (4) The imaginary-time integration in the Laplace-transformed expressions of the self-energy is carried out stochastically (instead of using a quadrature in the previous implementations), resulting in a 50- to 200-fold speedup. (5) The efficiency of the redundant-walker convergence acceleration scheme is analyzed numerically, and the guidelines are established to select an optimal number of walkers for maximal efficiency. When such an optimal number is used, the cost per sample is constant of molecular size on either many CPUs or many GPUs. (6) The computational cost to obtain a binding energy within a given statistical uncertainty is observed to increase as (tentatively) O(n 4 ) and O(n 5 ) of molecular size (n is the number of electrons) with and without the diagonal approximation, respectively, as opposed to O(n 5 ) and O(n 6 ) of the corresponding deterministic algorithms. With this method applied to the electron binding energies of C 60 , we show that the third-order corrections to the self-energies are much greater in electron binding energies than in ground-state energies. As a result, they display a sign of oscillatory convergence toward experimental results, not necessarily improving the agreement with increasing perturbation order, justifying MC-GF3 and motivating even higher-order methods.

Algorithms↗
NASA NTRS1983

Finite element approximations in transient analysis

Alternative techniques for finite element models for transient analyses are explored, using as an example a pinned-pinned beam. Attention is given to the relationships between desired accuracy and the available computer resources. Stiffness, mass, damping, and loading components approximations are examined with note taken of optimization methods. Generation of regular grid results indicates a linear relationship between the number of elements or degrees of freedom and the number of eigenvalues for a given accuracy. Comparisons of the finite element models in terms of accuracy/element or accuracy/degree of freedom were found to be inaccurate for determining model efficiency. Higher accuracies were available from lumped mass and damping models than assumptions of consistent loading, which was preferred to statically equivalent loading.

Melosh, R. J.↗
NASA NTRS1984

Computer-aided surface representation and design

New methods for representing and approximating three and four dimensional surfaces were created. These schemes are the core of our forthcoming Surface Software Package. Surfaces are understood adequately only through the use of dynamic computer graphics; therefore, graphics capability is also included. The numerous applications of surface methods include modeling physical phenomena (e.g., combustion) and designing objects (e.g., airplanes and cars).

Barnhill, R. E.↗
DOE OSTI2018

A new computational approach for the solutions of generalized pantograph-delay differential equations

In this study, a new computational approach is presented to solve the generalized pantograph-delay differential equations (PDDEs). The solutions obtained by our scheme represent by a linear combination of a special kind of basis functions, and can be deduced in a straightforward manner. Firstly, using the least squares approximation method and the Lagrange-multiplier method, the given PDDE is converted to a linear system of algebraic equations, and those unknown coefficients of the solution of the problem are determined by solving this linear system. Secondly, a PDDE related to the error function of the approximate solution is constructed based on the residual error function technique, and error estimation is presented for the suggested method. The convergence of the approximate solution is proved. Several numerical examples are given to demonstrate the accuracy and efficiency. Comparisons are made between the proposed method and other existing methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

Algorithm For Integer Cosine Transforms

Algorithm computes coefficients of integer cosine transforms, containing only integer coefficients approximately proportional to floating-point coefficients of discrete cosine transforms. Used in compression of image data in blocks of N x N pixels, discrete cosine transforms involve large amounts of computation, typically amounting to 80 percent of computational load in data-compression scheme. In constructing integer approximations, competing requirements are to obtain data-compression and data-decompression performances comparable to those of corresponding descrete cosine transforms while taking advantage of simplicity afforded by integer arithmetic to reduce complexity and amount of computation.

Pollara, Fabrizio↗
DOE OSTI2019

Anisotropic hydrodynamic modeling of 200 GeV Au-Au collisions

We compare phenomenological results from (3+1)-dimensional quasiparticle anisotropic hydrodynamics (aHydroQP) with experimental data collected in RHIC 200 GeV Au-Au collisions. We present comparisons of identified particle spectra in different centrality clases, charged particle multiplicity versus pseudorapidity, identified particle multiplicity versus centrality across a wide range of particle species, identified particle elliptic flow versus transverse momentum, and charged particle elliptic flow as a function of transverse momentum and rapidity. We use the same aHydroQP and hadronic production/feed down codes that were used previously to describe LHC 2.76 TeV data. The aHydroQP hydrodynamic model includes the effects of both shear and bulk viscosities in addition to an infinite number of transport coefficients computed self-consistently in the relaxation time approximation. To convert to the final state hadrons, we use anisotropic Cooper-Frye freeze-out performed on a fixed-energy-density hypersurface and compute the production/feed down using a customized version of Therminator 2. Here, we find good agreement with many heavy-ion collision observables using only smooth Glauber initial conditions parametrized by an initial central temperature of T 0 = 455 MeV, a constant shear-viscosity-to-entropy-density ratio η/s = 0.179, and a switching (freeze-out) temperature of T FO = 130 MeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1984

Numerical simulation of the transonic flowfield for wing/nacelle configurations

An efficient grid-interfacing zonal algorithm has been developed for computing the three-dimensional transonic flow field about wing/nacelle multicomponent configurations. The algorithm uses the full-potential formulation and the AF2 fully-implicit approximate factorization scheme. The flow field position is computed using a component-adaptive grid approach in which separate grids are employed for the individual components in the multicomponent configuration, where each component grid is optimized for a particular geometry such as the wing or nacelle. The wing and nacelle component grids are allowed to overlap, and flow field information is transmitted from one grid to another through the overlap region using trivariate interpolation. This paper presents a discussion of the computational methods used to generate both the wing and nacelle component grids, the technique used to interface the component grids, and the method used to obtain the inviscid multicomponent flow field solution. Computed results and correlations with experiment are presented to illustrate application of the analysis.

Atta, E. H.↗
NASA NTRS2017

3DHZETRN: Inhomogeneous Geometry Issues

Historical methods for assessing radiation exposure inside complicated geometries for space applications were limited by computational constraints and lack of knowledge associated with nuclear processes occurring over a broad range of particles and energies. Various methods were developed and utilized to simplify geometric representations and enable coupling with simplified but efficient particle transport codes. Recent transport code development efforts, leading to 3DHZETRN, now enable such approximate methods to be carefully assessed to determine if past exposure analyses and validation efforts based on those approximate methods need to be revisited. In this work, historical methods of representing inhomogeneous spacecraft geometry for radiation protection analysis are first reviewed. Two inhomogeneous geometry cases, previously studied with 3DHZETRN and Monte Carlo codes, are considered with various levels of geometric approximation. Fluence, dose, and dose equivalent values are computed in all cases and compared. It is found that although these historical geometry approximations can induce large errors in neutron fluences up to 100 MeV, errors on dose and dose equivalent are modest (<10%) for the cases studied here.

Wilson, John W.↗
DOE OSTI2025

Gaussian Process Regression under Computational and Epistemic Misspecification

Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper investigates the effect of such kernel approximations on the interpolation error. We introduce a unified framework to analyze Gaussian process regression under important classes of computational misspecification: Karhunen-Loève expansions that result in low-rank kernel approximations, multiscale wavelet expansions that induce sparsity in the covariance matrix, and finite element representations that induce sparsity in the precision matrix. Furthermore, our theory also accounts for epistemic misspecification in the choice of kernel parameters.

Gaussian process regression↗
NASA NTRS1971

Techniques for generation of control and guidance signals derived from optical fields, part 2

The development is reported of a high resolution technique for the detection and identification of landmarks from spacecraft optical fields. By making use of nonlinear regression analysis, a method is presented whereby a sequence of synthetic images produced by a digital computer can be automatically adjusted to provide a least squares approximation to a real image. The convergence of the method is demonstrated by means of a computer simulation for both elliptical and rectangular patterns. Statistical simulation studies with elliptical and rectangular patterns show that the computational techniques developed are able to at least match human pattern recognition capabilities, even in the presence of large amounts of noise. Unlike most pattern recognition techniques, this ability is unaffected by arbitrary pattern rotation, translation, and scale change. Further development of the basic approach may eventually allow a spacecraft or robot vehicle to be provided with an ability to very accurately determine its spatial relationship to arbitrary known objects within its optical field of view.

Hemami, H.↗