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 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Phase equilibrium of methane and nitrogen at low temperatures - Application to Titan

Since the vapor phase composition of Titan's methane-nitrogen lower atmosphere is uniquely determined as a function of the Gibbs phase rule, these data are presently computed via integration of the Gibbs-Duhem equation. The thermodynamic consistency of published measurements and calculations of the vapor phase composition is then examined, and the saturated mole fraction of gaseous methane is computed as a function of altitude up to the 700-mbar level. The mole fraction is found to lie approximately halfway between that computed from Raoult's law, for a gas in equilibrium with an ideal solution of liquid nitrogen and methane, and that for a gas in equilibrium with pure liquid methane.

Kouvaris, Louis C.↗
NASA NTRS1952

Practical Calculation of Second-order Supersonic Flow past Nonlifting Bodies of Revolution

Calculation of second-order supersonic flow past bodies of revolution at zero angle of attack is described in detail, and reduced to routine computation. Use of an approximate tangency condition is shown to increase the accuracy for bodies with corners. Tables of basic functions and standard computing forms are presented. The procedure is summarized so that one can apply it without necessarily understanding the details of the theory. A sample calculation is given, and several examples are compared with solutions calculated by the method of characteristics.

Van Dyke, Milton D↗
NASA NTRS1986

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.↗
DOE OSTI2018

Dissociative recombination by frame transformation to Siegert pseudostates: A comparison with a numerically solvable model

Here, we present a simple two-dimensional model of the indirect dissociative recombination process. The model has one electronic and one nuclear degree of freedom and it can be solved to high precision, without making any physically motivated approximations, by employing the exterior complex scaling method together with the finite-elements method and discrete variable representation. The approach is applied to solve a model for dissociative recombination of H 2 + in the singlet ungerade channels, and the results serve as a benchmark to test validity of several physical approximations commonly used in the computational modeling of dissociative recombination for real molecular targets. The second, approximate, set of calculations employs a combination of multichannel quantum defect theory and frame transformation into a basis of Siegert pseudostates. The cross sections computed with the two methods are compared in detail for collision energies from 0 to 2 eV.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Computational analysis of the tryptophan cation radical energetics in peroxidase Compound $\mathrm{I}$

Three well-characterized heme peroxidases (cytochrome c peroxidase = CCP, ascorbate peroxidase = APX, and Leishmania major peroxidase = LMP) all have a Trp residue tucked under the heme stacked against the proximal His heme ligand. The reaction of peroxidases with H 2 O 2 to give Compound I results in the oxidation of this Trp to a cationic radical in CCP and LMP but not in APX. Considerable experimental data indicate that the local electrostatic environment controls whether this Trp or the porphyrin is oxidized in Compound I. Attempts have been made to place the differences between these peroxidases on a quantitative basis using computational methods. These efforts have been somewhat limited by the approximations required owing to the computational cost of using fully solvated atomistic models with well-developed forcefields. This now has changed with available GPU computing power and the associated development of software. Here we employ thermodynamic integration and multistate Bennett acceptance ratio methods to help fine-tune our understanding on the energetic differences in Trp radical stabilization in all three peroxidases. These results indicate that the local solvent structure near the redox active Trp plays a significant role in stabilization of the cationic Trp radical.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Discrete Hahn polynomials for numerical solution of two-dimensional variable-order fractional Rayleigh–Stokes problem

The main aim of this paper is to find the numerical solutions of 2D Rayleigh–Stokes problem with the variable-order fractional derivatives in the Riemann–Liouville sense. The presented method is based on collocation procedure in combination with the new operational matrix of the variable-order fractional derivatives, in the Caputo sense, for the discrete Hahn polynomials. The main advantage of the proposed method is obtaining a global approximation for spatial and temporal discretizations, and it reduced the problem to an algebraic system, which is easier to solve. Also, the profit of approximating a continuous function by Hahn polynomials is that for computing the coefficients of the expansion, we only have to compute a summation and the calculation of coefficients is exact. The error bound for the approximate solution is estimated. Finally, we evaluate results of the presented method with other numerical methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2018

An Abstract Interpretation Framework for the Round-Off Error Analysis of Floating-Point Programs

This paper presents an abstract interpretation framework for the round-off error analysis of floating-point programs. This framework defines a parametric abstract analysis that computes, for each combination of ideal and floating-point execution path of the program, a sound over-approximation of the accumulated floating-point round-off error that may occur. In addition, a Boolean expression that characterizes the input values leading to the computed error approximation is also computed. An abstraction on the control flow of the program is proposed to mitigate the explosion of the number of elements generated by the analysis. Additionally, a widening operator is defined to ensure the convergence of recursive functions and loops. An instantiation of this framework is implemented in the prototype tool PRECiSA that generates formal proof certificates stating the correctness of the computed round-off errors.

Titolo, Laura↗
DOE OSTI2022

Quantum computational phase transition in combinatorial problems

Quantum Approximate Optimization algorithm (QAOA) aims to search for approximate solutions to discrete optimization problems with near-term quantum computers. As there are no algorithmic guarantee possible for QAOA to outperform classical computers, without a proof that bounded-error quantum polynomial time (BQP) ≠ nondeterministic polynomial time (NP), it is necessary to investigate the empirical advantages of QAOA. We identify a computational phase transition of QAOA when solving hard problems such as SAT—random instances are most difficult to train at a critical problem density. We connect the transition to the controllability and the complexity of QAOA circuits. Moreover, we find that the critical problem density in general deviates from the SAT-UNSAT phase transition, where the hardest instances for classical algorithms lies. Then, we show that the high problem density region, which limits QAOA’s performance in hard optimization problems (reachability deficits), is actually a good place to utilize QAOA: its approximation ratio has a much slower decay with the problem density, compared to classical approximate algorithms. Indeed, it is exactly in this region that quantum advantages of QAOA over classical approximate algorithms can be identified.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Advanced Computing Annual Report 2023

In 2023, advanced computing saw the arrival of Kestrel, the National Renewable Energy Laboratory's (NREL's) newest high-performance computing (HPC) system. Kestrel will accelerate clean energy research at a pace and scale more than five times greater than Eagle, with approximately 44 petaflops of computing power. Kestrel's heterogeneous architecture - which includes both CPU-only and GPU-accelerated nodes - is designed to bring a much greater GPU capacity to EERE workloads compared to Eagle, enabling rapidly advancing applications in artificial intelligence and expanding research in new directions for computing. In Fiscal Year (FY) 2023, 333 projects utilized NREL's HPC system, advancing the U.S. Department of Energy's (DOE's) Office of Energy Efficiency and Renewable Energy (EERE) mission across 13 funding areas. Cross-disciplinary collaboration among researchers yielded more than 800 technical outputs, including 177 peer-reviewed journal articles in FY 2023. All this great work continues to advance the science of energy efficiency and renewable energy. This report highlights research that utilized HPC resources in FY 2023.

advanced computing↗
DOE OSTI2022

Performance Evaluations of Noisy Approximate Quantum Fourier Arithmetic

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route towards a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor’s algorithm, weighted sum optimization problems in data processing and machine learning and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM’s superconducting qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands’ superposed integer states. We analyze performance, and identify the most effective approximation depths for quantum add and quantum multiply within the given context. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges - relevant to signed, unsigned, modular and non-modular versions - that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. Here, we analyze performance trends in our results and speculate on possible future development within this computational paradigm.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1978

Use of a computer model in the understanding of erythropoietic control mechanisms

During an eight-week visit approximately 200 simulations using the computer model for the regulation of erythopoiesis were carries out in four general areas: with the human model simulating hypoxia and dehydration, evaluation of the simulation of dehydration using the mouse model. The experiments led to two considerations for the models. Firstly, a direct relationship between erythropoietin concentration and bone marrow sensitivity to the hormone and, secondly, a partial correction of tissue hypoxia prior to compensation by an increased hematocrit. This latter change in particular produced a better simuation of the effects of hypoxia on plasma erythropoietin concentrations.

Dunn, C. D. R.↗
NASA NTRS1979

A vectorization of the Hess McDonnell Douglas potential flow program NUED for the STAR-100 computer

The computer program NUED for analyzing potential flow about arbitrary three dimensional lifting bodies using the panel method was modified to use vector operations and run on the STAR-100 computer. A high speed of computation and ability to approximate the body surface with a large number of panels are characteristics of NUEDV. The new program shows that vector operations can be readily implemented in programs of this type to increase the computational speed on the STAR-100 computer. The virtual memory architecture of the STAR-100 facilitates the use of large numbers of panels to approximate the body surface.

Boney, L. R.↗
DOE OSTI2018

Minimum fuel trajectories for round trip lunar missions

In this work, a study about minimum fuel trajectories in a round trip journey to the Moon is presented. It is assumed that the velocity changes are instantaneous, that is, the propulsion system is capable of delivering impulses such that the fuel consumption is represented by the total velocity increment applied to the space vehicle. It is also assumed that the velocity increments are applied tangentially to the terminal orbits, and, the outgoing trip and the return trip are analyzed separately such that the whole mission is performed with four impulses (two impulses in each trip). The mathematical models used to describe the motion of the space vehicle are three: the lunar patched-conic approximation; the classic planar circular restricted three-body problem, and, the planar bi-circular restricted four-body problem (PBR4BP). For computing the optimal trajectories, the Sequential Gradient-Restoration Algorithm with constraints is used. The influence of the Sun on round trip lunar missions is analyzed through the PBR4BP model. For all models, the trajectories studied are direct ascent maneuvers, and, both the outgoing and return trips are considered. The results obtained through the different models are compared with each other. The optimal results for the PBR4BP model show that a small reduction of the fuel consumption can be achieved if the initial phase angle of the Sun is chosen properly.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1988

Three-dimensional inelastic approximate analysis code (MOMM)

The Mechanics of Materials Model (MOMM) is one of a series of new stand-alone three dimensional nonlinear structural analysis codes. Incorporation of a general purpose finite element computer code into the hot section design process was severely limited by the high costs involved. MOMM is a stiffness method finite element code that uses an internally generated network of beams to characterize hot section component behavior. The method was proposed as a fast, easy to use, computationally efficient tool for approximate analyses. MOMM incorporates a wide variety of analysis capabilities, material models, and load type specifiers instrumental for the analysis of hot section components.

Meister, Jeffrey P.↗
DOE OSTI2023

Compression of tokamak boundary plasma simulation data using a maximum volume algorithm for matrix skeleton decomposition

This report demonstrates satisfactory data compression of SOLPS-ITER simulation output ranging from 2D fields, 1D profiles, and 0D scalar variables with a novel matrix decomposition approach. The singular value decomposition (SVD) scales poorly for large matrix sizes and is unsuited to the application on high dimensional data common to fusion plasma physics simulation. In this work, we employ the columns-submatrix-rows (CUR) matrix factorization technique in order to compute a low-rank approximation up to two orders of magnitude faster than the SVD, but within a nominal L2-norm relative error of ε = 10 –2 . In addition, the CUR approach maintains the original format of the data, in its extracted columns and rows, allowing for interpretable data storage at the original resolution of the simulation. We utilize an iterative algorithm to compute the CUR decomposition of simulation output by maximizing the volume, or linearly independent information content, of a low-rank submatrix contained within the data. Experiments over $\textit{n} × \textit{n}$ randomized test matrices with embedded rank-deficient features show that this maximum volume implementation of CUR matrix approximation has reduced asymptotic computational complexity on the order of n compared to the SVD, which scales approximately as $n^3$. These results show that the CUR technique can be used to effectively select time step snapshots (columns) of over 140 SOLPS-ITER output variables and the associated discretized coordinate timeseries (rows) allowing for reconstruction of the complete simulation dynamics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Digital quantum magnetism on a trapped-ion quantum computer

Digital quantum matter—realized when discrete quantum gates approximate continuous time evolution—is susceptible to heating into chaotic, structureless states. If digitization errors are adequately suppressed, a long-lived transient regime of approximately energy-conserving dynamics can be observed on gate-based quantum computers. Conservation of energy, in turn, enables the exploration of a wide variety of complex behaviours observed in equilibrium systems, ranging from the non-trivial microscopic origins of thermalization itself to the stabilization of effective models hosting exotic emergent properties. Here we use Quantinuum’s H2 quantum computer to simulate digitized dynamics of the quantum Ising model, suppressing digitization errors well enough to observe thermalization on timescales that severely challenge classical simulation methods. Relaxation of an inhomogeneous state reveals an emergent hydrodynamics owing to approximate energy conservation and we compute the associated diffusion constant. By reprogramming our simulations to take place on a triangular lattice with periodic boundary conditions, we observe thermalization consistent with emergent gauge and topological constraints resulting from lattice frustration. Furthermore, our results were enabled by continued advances in two-qubit gate quality (native partial entangler fidelities of 99.94(1)%) and establish digital quantum computers as powerful tools for studying (effectively) continuous-time dynamics.

Information theory and computation↗
DOE OSTI2021

Parameterization of the Stoner-Wohlfarth model of magnetic hysteresis

The Stoner-Wohlfarth (SW) is the most used model of magnetic hysteresis, but its computation is time-consuming. We approximate piecewise this model by easy-to-compute analytic functions. Overall, our parametrization is suitable for fast quantitative evaluations and fitting experimental data, which we exemplify. Applicability of this parametrization is as broad as that of the SW model, which can be extended to include more parameters.

36 MATERIALS SCIENCE↗