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At least 73 records · Page 4

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NASA NTRS1992

New literal approximations for the longitudinal dynamic characteristics of flexible flight vehicles

The goal of the literal approximation method is to obtain simple literal (analytical) approximations for key dynamic characteristics of flexible flight vehicles. A basic question regarding the method is its usefulness as an additional design tool for existing design and simulation procedures. Two aspects of this question are: (1) ease of derivation and use of the literal approximations, and (2) the suitability of one set of literal approximations to describe the dynamics of a large set of significantly different vehicles. These issues are addressed by incorporating symbolic manipulation software into the literal approximation method for the analysis of a fifth order model of the longitudinal dynamics of a flexible flight vehicle. The automated literal approximation generated in this fashion reduces the manual derivation time by an approximate factor of four. A single set of literal approximations is shown to provide adequate approximations for the dynamics of significantly different flight vehicles configurations, such as an aircraft, a missile, and a hypersonic vehicle.

Livneh, Rafael↗

NASA NTRS1993

Producing approximate answers to database queries

We have designed and implemented a query processor, called APPROXIMATE, that makes approximate answers available if part of the database is unavailable or if there is not enough time to produce an exact answer. The accuracy of the approximate answers produced improves monotonically with the amount of data retrieved to produce the result. The exact answer is produced if all of the needed data are available and query processing is allowed to continue until completion. The monotone query processing algorithm of APPROXIMATE works within the standard relational algebra framework and can be implemented on a relational database system with little change to the relational architecture. We describe here the approximation semantics of APPROXIMATE that serves as the basis for meaningful approximations of both set-valued and single-valued queries. We show how APPROXIMATE is implemented to make effective use of semantic information, provided by an object-oriented view of the database, and describe the additional overhead required by APPROXIMATE.

Vrbsky, Susan V.↗

NASA NTRS2004

A Subsonic Aircraft Design Optimization With Neural Network and Regression Approximators

The Flight-Optimization-System (FLOPS) code encountered difficulty in analyzing a subsonic aircraft. The limitation made the design optimization problematic. The deficiencies have been alleviated through use of neural network and regression approximations. The insight gained from using the approximators is discussed in this paper. The FLOPS code is reviewed. Analysis models are developed and validated for each approximator. The regression method appears to hug the data points, while the neural network approximation follows a mean path. For an analysis cycle, the approximate model required milliseconds of central processing unit (CPU) time versus seconds by the FLOPS code. Performance of the approximators was satisfactory for aircraft analysis. A design optimization capability has been created by coupling the derived analyzers to the optimization test bed CometBoards. The approximators were efficient reanalysis tools in the aircraft design optimization. Instability encountered in the FLOPS analyzer was eliminated. The convergence characteristics were improved for the design optimization. The CPU time required to calculate the optimum solution, measured in hours with the FLOPS code was reduced to minutes with the neural network approximation and to seconds with the regression method. Generation of the approximators required the manipulation of a very large quantity of data. Design sensitivity with respect to the bounds of aircraft constraints is easily generated.

Patnaik, Surya N.↗

DOE OSTI2020

Analysis of diagonal G and subspace W approximations within fully self-consistent GW calculations for bulk semiconducting systems

Fully self-consistent GW (sc-GW) methods are now available to evaluate quasiparticle and spectral properties of various molecular and bulk systems. However, such techniques based on the full matrix of G and W are computationally demanding. Additionally, the routinely used single-shot GW approximation (G 0 W 0 ) has an undesirable dependency on the choice of initial exchange-correlation functional. In the literature, many so-called self-consistent GW methods are based on diagonal approximation of G and low-ranking approximation of W. It is thus worth checking how good such approximations are in comparison with the full matrix method. In this work, we consider AlAs, AlP, GaP, and ZnS as the prototype systems to perform sc-GW calculations by expressing the full G matrix using a plane-wave basis set. We compared our sc-GW results with the diagonal G and subspace W approximated sc-GW results (sc-GW-diagG and sc-GW-subW methods). In the sc-GW-diagG method, interacting G is expanded in the eigenvectors of noninteracting G such that only diagonal elements are retained, whereas the number of eigenmodes is truncated in sc-GW-subW calculations. A systematic analysis of the results obtained from the above techniques is presented. The differences in the quasiparticle band gap between the approximated and the full matrix sc-GW approaches are mostly less than 1.7%, which validates such widely adopted approximations, and also shows how such low-ranking approximation can be used to include higher-order terms such as the vertex correction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Noise-Resilient and Reduced Depth Approximate Adders for NISQ Quantum Computing

The "Noisy intermediate-scale quantum" NISQ machine era primarily focuses on mitigating noise, controlling errors, and executing high-fidelity operations, hence requiring shallow circuit depth and noise robustness. Approximate computing is a novel computing paradigm that produces imprecise results by relaxing the need for fully precise output for error-tolerant applications including multimedia, data mining, and image processing. We investigate how approximate computing can improve the noise resilience of quantum adder circuits in NISQ quantum computing. We propose five designs of approximate quantum adders to reduce depth while making them noise-resilient, in which three designs are with carryout, while two are without carryout. We have used novel design approaches that include approximating the Sum only from the inputs (pass-through designs) and having zero depth, as they need no quantum gates. The second design style uses a single CNOT gate to approximate the SUM with a constant depth of O(1). We performed our experimentation on IBM Qiskit on noise models including thermal, depolarizing, amplitude damping, phase damping, and bitflip: (i) Compared to exact quantum ripple carry adder without carryout the proposed approximate adders without carryout have improved fidelity ranging from 8.34% to 219.22%, and (ii) Compared to exact quantum ripple carry adder with carryout the proposed approximate adders with carryout have improved fidelity ranging from 8.23% to 371%. Further, the proposed approximate quantum adders are evaluated in terms of various error metrics.

Gaur, Bhaskar↗

DOE OSTI2021

High Performance Approximate Computing

This code repository contains the implementation of the "High-Performance Approximate Computing" (HPAC) toolkit. The toolkit allows you to approximate your own C/C++. The developer uses "pragma's" to annotate code regions as approximate. The compiler extensions lower these pragmas to either compiletime approximate techniques or runtime approximation techniques. At execution time, the implemented runtime system decides which annotated regions it should approximate. HPAC also provides a set of script utilities. The utilities perform a grid search within approximation parameters and performance. The user can analyze the raw data to identify optimal approximation techniques for the application.

Parasyris, Konstantinos↗

NASA NTRS1976

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained.

Klimas, A. J.↗

NASA NTRS1982

Difference equation state approximations for nonlinear hereditary control problems

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.

Rosen, I. G.↗

NASA NTRS1984

Difference equation state approximations for nonlinear hereditary control problems

Rosen, I. G.↗

NASA NTRS1988

Mathematical algorithms for approximate reasoning

Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away from the conclusion. These algorithms allow one to reason accurately with uncertain data. The above environment can replicate state-f-the-art expert system environments which provides a continuity between the current expert systems which cannot be validated or verified and future expert systems which should be both validated and verified

Murphy, John H.↗

NASA NTRS1994

Comparison of daily averaged reflection, transmission, and absorption for selected radiative flux transfer approximations

This paper compares accuracy for the daily averaged reflection, transmission, and absorption of solar flux derived from the delta-four-stream approximation and a few selected two-stream approximations. In the chosen variety of two-stream approximations, a two-stream approximation suggested by Zhu produces the most accurate reflection and transmission for conservative scattering with optical thickness tau(sub 1) less than 3. Otherwise, the delta-Eddington approximation is superior to other two-stream approximations. The delta-four stream approximation produces errors that are smaller than the delta-Eddington approximation by at least a factor of 2.

Zhu, Xun↗

NASA NTRS1997

Geochemistry of approximately 1.9 Ga sedimentary rocks from northeastern Labrador, Canada

Fifty-eight rock chips from fifteen samples of sedimentary rocks from the Ramah Group (approximately 1.9 Ga) in northeastern Labrador, Canada, were analyzed for major and minor elements, including C and S, to elucidate weathering processes on the Earth's surface about 1.9 Ga ago. The samples come from the Rowsell Harbour, Reddick Bight, and Nullataktok Formations. Two rock series, graywackes-gray shales of the Rowsell Harbour, Reddick Bight and Nullataktok Formations, and black shales of the Nullataktok Formation, are distinguishable on the basis of lithology, mineralogy, and major and trace element chemistry. The black shales show lower concentrations than the graywackes-gray shales in TiO2 (0.3-0.7 wt% vs. 0.7-1.8 wt%), Al2O3 (9.5-20.1 wt% vs. 13.0-25.0 wt%), and sigma Fe (<1 wt% vs. 3.8-13.9 wt% as FeO). Contents of Zr, Th, U, Nb, Ce, Y, Rb, Y, Co, and Ni are also lower in the black shales. The source rocks for the Ramah Group sediments were probably Archean gneisses with compositions similar to those in Labrador and western Greenland. The major element chemistry of source rocks for the Ramah Group sedimentary rocks was estimated from the Al2O3/TiO2 ratios of the sedimentary rocks and the relationship between the major element contents (e.g., SiO2 wt%) and Al2O3/TiO2 ratios of the Archean gneisses. This approach is justified, because the Al/Ti ratios of shales generally retain their source rock values; however, the Zr/Al, Zr/Ti, and Cr/Ni ratios fractionate during the transport of sediments. The measured SiO2 contents of shales in the Ramah Group are generally higher than the estimated SiO2 contents of source rocks by approximately 5 wt%. This correction may also have to be applied when estimating average crustal compositions from shales. Two provenances were recognized for the Ramah Group sediments. Provenance I was comprised mostly of rocks of bimodal compositions, one with SiO2 contents approximately 45 wt% and the other approximately 65 wt%, and was the source for most sedimentary rocks of the Ramah Group, except for black shales of the Nullataktok Formation. The black shales were apparently derived from Provenance II that was comprised mostly of felsic rocks with SiO2 contents approximately 65 wt%. Comparing the compositions of the Ramah Group sedimentary rocks and their source rocks, we have recognized that several major elements, especially Ca and Mg, were lost almost entirely from the source rocks during weathering and sedimentation. Sodium and potassium were also leached almost entirely during the weathering of the source rocks. However, significant amounts of Na were added to the black shales and K to all the rock types during diagenesis and/or regional metamorphism. The intensity of weathering of source rocks for the Ramah Group sediments was much higher than that of typical Phanerozoic sediments, possibly because of a higher PCO2 in the Proterozoic atmosphere. Compared to the source rock values, the Fe3+/Ti ratios of many of the graywackes and gray shales of the Ramah Group are higher, the Fe2+/Ti ratios are lower, and the sigma Fe/Ti ratios are the same. Such characteristics of the Fe geochemistry indicate that these sedimentary rocks are comprised of soils formed by weathering of source rocks under an oxygen-rich atmosphere. The atmosphere about 1.9 Ga was, therefore, oxygen rich. Typical black shales of Phanerozoic age exhibit positive correlations between the organic C contents and the concentrations of S, U, and Mo, because these elements are enriched in oxygenated seawater and are removed from seawater by organic matter in sediments. However, such correlations are not found in the Ramah Group sediments. Black shales of the Ramah Group contain 1.7-2.8 wt% organic C, but are extremely depleted in sigma Fe (<1 wt% as FeO), S (<0.3 wt%), U (approximately l ppm), Mo (<5 ppm), Ni (<2 ppm), and Co (approximately 0 ppm). This lack of correlation, however, does not imply that the approximately 1.9 Ga atmosphere-ocean system was anoxic. Depletion of these elements from the Ramah Group sediments may have occurred during diagenesis.

Non-NASA Center↗

DOE OSTI2020

A step in the direction of resolving the paradox of Perdew–Zunger self-interaction correction. II. Gauge consistency of the energy density at three levels of approximation

The Perdew-Zunger(PZ) self-interaction correction (SIC) was designed to correct the one-electron limit of any approximate density functional for the exchange-correlation (xc) energy, while yielding no correction to the exact functional. Unfortunately, it spoils the slowly-varying-in-space limits of the uncorrected approximate functionals, where those functionals are right by construction. The right limits can be restored by locally scaling down the energy density of the PZ SIC in many-electron regions, but then a spurious correction to the exact functional would be found unless the self-Hartree and exact self-xc terms of the PZ SIC energy density were expressed in the same gauge. Only the local density approximation satisfies the same-gauge condition for the energy density, which explains why the recent local-scaling SIC (LSIC) is found here to work excellently for atoms and molecules only with this basic approximation, and not with the more advanced generalized gradient approximations (GGAs) and meta-GGAs, which lose the Hartree gauge via simplifying integrations by parts. The transformation of energy density that achieves the Hartree gauge for the exact xc functional can also be applied to approximate functionals. Doing so leads to a simple scaled-down self-interaction (sdSIC) correction that is typically much more accurate than PZ SIC in tests for many molecular properties (including equilibrium bond lengths). The present work shows unambiguously that the largest errors of PZ SIC applied to standard functionals at three levels of approximation can be removed by restoring their correct slowlyvarying- density limits. Here, it also confirms the relevance of these limits to atoms and molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

A Framework for Error-Bounded Approximate Computing, with an Application to Dot Products

Approximate computing techniques, which trade off the computation accuracy of an algorithm for better performance and energy efficiency, have been successful in reducing computation and power costs in several domains. However, error sensitive applications in high-performance computing are unable to benefit from existing approximate computing strategies that are not developed with guaranteed error bounds. While approximate computing techniques can be developed for individual high-performance computing applications by domain specialists, this often requires additional theoretical analysis and potentially extensive software modification. Hence, the development of low-level error-bounded approximate computing strategies that can be introduced into any high-performance computing application without requiring additional analysis or significant software alterations is desirable. In this paper, we provide a contribution in this direction by proposing a general framework for designing error-bounded approximate computing strategies and apply it to the dot product kernel to develop \bf qdot---an error-bounded approximate dot product kernel. Following the introduction of qdot, here we perform a theoretical analysis that yields a deterministic bound on the relative approximation error introduced by qdot. Empirical tests are performed to illustrate the tightness of the derived error bound and to demonstrate the effectiveness of qdot on a synthetic dataset, as well as two scientific benchmarks---the conjugate gradient (CG) and power methods. In some instances, using qdot for the dot products in CG can result in many components being quantized to half precision without increasing the iteration count required for convergence to the same solution as CG using a double precision dot product.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Recognizability of Demographically Altered Computerized Facial Approximations in an Automated Facial Recognition Context for Potential Application in Unidentified Persons Data Repositories

This study examined the recognizability of demographically altered facial approximations for potential utility in unidentified persons tracking systems. Five computer-generated approximations were generated for each of 26 African male participants using the following demographic parameters: (i) African male (true demographics), (ii) African female, (iii) Caucasian male, (iv) Asian male, and (v) Hispanic male. Overall, 62% of the true demographic facial approximations for the 26 African male participants examined were matched to a corresponding life photo within the top 50 images of a candidate list generated from an automated blind search of an optimally standardized gallery of 6159 photographs. When the African male participants were processed as African females, the identification rate was 50%. In contrast, less congruent identification rates were observed when the African male participants were processed as Caucasian (42%), Asian (35%), and Hispanic (27%) males. The observed results suggest that approximations generated using the opposite sex may be operationally informative if sex is unknown. The performance of approximations generated using alternative ancestry assignments, however, was less congruent with the performance of the true demographic approximation (African male) and may not yield as operationally constructive data as sex-altered approximations.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Robust scalable initialization for Bayesian variational inference with multi-modal Laplace approximations

Predictive modeling typically relies on Bayesian model calibration to provide uncertainty quantification. Variational inference utilizing fully independent (“mean-field”) Gaussian distributions are often used as approximate probability density functions. This simplification is attractive since the number of variational parameters grows only linearly with the number of unknown model parameters. However, the resulting diagonal covariance structure and unimodal behavior can be too restrictive to provide useful approximations of intractable Bayesian posteriors that exhibit highly non-Gaussian behavior, including multimodality. High-fidelity surrogate posteriors for these problems can be obtained by considering the family of Gaussian mixtures. Gaussian mixtures are capable of capturing multiple modes and approximating any distribution to an arbitrary degree of accuracy, while maintaining some analytical tractability. Unfortunately, variational inference using Gaussian mixtures with full-covariance structures suffers from a quadratic growth in variational parameters with the number of model parameters. The existence of multiple local minima due to strong nonconvex trends in the loss functions often associated with variational inference present additional complications, These challenges motivate the need for robust initialization procedures to improve the performance and computational scalability of variational inference with mixture models. In this work, we propose a method for constructing an initial Gaussian mixture model approximation that can be used to warm-start the iterative solvers for variational inference. The procedure begins with a global optimization stage in model parameter space. In this step, local gradient-based optimization, globalized through multistart, is used to determine a set of local maxima, which we take to approximate the mixture component centers. Around each mode, a local Gaussian approximation is constructed via the Laplace approximation. Finally, the mixture weights are determined through constrained least squares regression. The robustness and scalability of the proposed methodology is demonstrated through application to an ensemble of synthetic tests using high-dimensional, multimodal probability density functions. Here, the practical aspects of the approach are demonstrated with inversion problems in structural dynamics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Direct Nonlinear Approximation for Security Region Boundary of Integrated Energy Systems: A Polynomial Chaos Expansion Solution

The strong interdependence of electricity, gas, and heating systems can facilitate fault propagation within integrated energy systems (IESs), posing significant challenges to secure operation. This paper proposes a polynomial chaos expansion (PCE)-based approximation method to accurately characterize the IES security region boundary (IES–SRB). By integrating the Karush-Kuhn-Tucker conditions with PCE theory, the IES-SRB approximation problem is reformulated as a set of nonlinear equations concerning the approximation coefficients. Using the Galerkin projection method, these equations are further transformed into a system of projection equations that govern the polynomial approximation coefficients in the IES-SRB approximation. To reduce computational complexity while maintaining high approximation accuracy, a piecewise polynomial approximation method is proposed. Numerical studies on the E39-G20-H6 and E118-G96-H52 IES test systems demonstrate that the proposed method can accurately and effectively construct IES security regions.

Wu, Chenghao [Northeast Electric Power University]↗

NASA NTRS1988

Approximation of the dielectric properties of Maxwellian plasmas - Dispersion functions and physical constraints

The dielectric properties of Maxwellian plasmas are approximated using high Pade approximants to the dispersion function and direct approximation of the distribution. Physical constraints on permissible approximations are discussed, and it is found that some previously published results can lead to predictions of qualitatively incorrect wave properties, including unphysical negative damping. Approximate dispersion functions for Maxwellian distributions are given explicitly, and some of the effects of these approximations on the resulting dispersion are discussed. The approximations discussed here are of use both in analytical work and in accelerating large-scale numerical computations.

Robinson, P. A.↗