Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Function approximation”

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 1,513 records · Page 84
All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

A Patch Density Recommendation based on Convergence Studies for Vehicle Panel Vibration Response resulting from Excitation by a Diffuse Acoustic Field

Fluid structural interaction problems that estimate panel vibration from an applied pressure field excitation are quite dependent on the spatial correlation of the pressure field. There is a danger of either over estimating a low frequency response or under predicting broad band panel response in the more modally dense bands if the pressure field spatial correlation is not accounted for adequately. Even when the analyst elects to use a fitted function for the spatial correlation an error may be introduced if the choice of patch density is not fine enough to represent the more continuous spatial correlation function throughout the intended frequency range of interest. Both qualitative and quantitative illustrations evaluating the adequacy of different patch density assumptions to approximate the fitted spatial correlation function are provided. The actual response of a typical vehicle panel system is then evaluated in a convergence study where the patch density assumptions are varied over the same finite element model. The convergence study results are presented illustrating the impact resulting from a poor choice of patch density. The fitted correlation function used in this study represents a Diffuse Acoustic Field (DAF) excitation of the panel to produce vibration response.

Smith, Andrew↗
DOE OSTI2018

Exact Fluctuations of Nonequilibrium Steady States from Approximate Auxiliary Dynamics

We describe a framework to reduce the computational effort to evaluate large deviation functions of time integrated observables within nonequilibrium steady states. We do this by incorporating an auxiliary dynamics into trajectory based Monte Carlo calculations, through a transformation of the system's propagator using an approximate guiding function. This procedure importance samples the trajectories that most contribute to the large deviation function, mitigating the exponential complexity of such calculations. Here, we illustrate the method by studying driven diffusion and interacting lattice models in one and two spatial dimensions. Finally, our work offers an avenue to calculate large deviation functions for high dimensional systems driven far from equilibrium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Exponential Synthesis in the Kernel of a Symmetric Convolution

The paper describes a certain class of homogeneous equations of convolution type in spaces of analytic functions on convex domains. We obtain sufficient conditions under which every solution of an equation from this class is approximated by its elementary solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

An n -material thresholding method for improving integerness of solutions in topology optimization

It is common in solving topology optimization problems to replace an integer-valued characteristic function design field with the material volume fraction field, a real-valued approximation of the design field that permits "fictitious" mixtures of materials during intermediate iterations in the optimization process. This is reasonable so long as one can interpolate properties for such materials and so long as the final design is integer valued. For this purpose, we present a method for smoothly thresholding the volume fractions of an arbitrary number of material phases which specify the design. This method is trivial for two-material design problems, for example, the canonical topology design problem of specifying the presence or absence of a single material within a domain, but it becomes more complex when three or more materials are used, as often occurs in material design problems. We take advantage of the similarity in properties between the volume fractions and the barycentric coordinates on a simplex to derive a thresholding, method which is applicable to an arbitrary number of materials. As we show in a sensitivity analysis, this method has smooth derivatives, allowing it to be used in gradient-based optimization algorithms. Finally, we present results, which show synergistic effects when used with Solid Isotropic Material with Penalty and Rational Approximation of Material Properties material interpolation functions, popular methods of ensuring integerness of solutions.

42 ENGINEERING↗
DOE OSTI2018

Excited-State Diffusion Monte Carlo Calculations: A Simple and Efficient Two-Determinant Ansatz

We perform excited-state variational Monte Carlo and diffusion Monte Carlo calculations using a simple and efficient wave function ansatz. This ansatz follows the recent variation-after-response formalism, accurately approximating a configuration interaction singles wave function as a sum of only two nonorthogonal Slater determinants and further including important orbital relaxation. The ansatz is used to perform diffusion Monte Carlo calculations with large augmented basis sets, comparing to benchmarks from near-exact quantum chemical methods. Here, the significance of orbital optimization in excited-state diffusion Monte Carlo is demonstrated, and the excited-state optimization procedure is discussed in detail. Diffuse excited states in water and formaldehyde are studied, in addition to the formaldimine and benzonitrile molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Deep probabilistic direction prediction in 3D with applications to directional dark matter detectors

Abstract We present the first method to probabilistically predict 3D direction in a deep neural network model. The probabilistic predictions are modeled as a heteroscedastic von Mises-Fisher distribution on the sphere S 2 , giving a simple way to quantify aleatoric uncertainty. This approach generalizes the cosine distance loss which is a special case of our loss function when the uncertainty is assumed to be uniform across samples. We develop approximations required to make the likelihood function and gradient calculations stable. The method is applied to the task of predicting the 3D directions of electrons, the most complex signal in a class of experimental particle physics detectors designed to demonstrate the particle nature of dark matter and study solar neutrinos. Using simulated Monte Carlo data, the initial direction of recoiling electrons is inferred from their tortuous trajectories, as captured by the 3D detectors. For 40 keV electrons in a 70% He 30% CO 2 gas mixture at STP, the new approach achieves a mean cosine distance of 0.104 (26 ∘ ) compared to 0.556 (64 ∘ ) achieved by a non-machine learning algorithm. We show that the model is well-calibrated and accuracy can be increased further by removing samples with high predicted uncertainty. This advancement in probabilistic 3D directional learning could increase the sensitivity of directional dark matter detectors.

Computer Science↗
NASA NTRS1994

Coagulation algorithms with size binning

The Smoluchowski equation describes the time evolution of an aerosol particle size distribution due to aggregation or coagulation. Any algorithm for computerized solution of this equation requires a scheme for describing the continuum of aerosol particle sizes as a discrete set. One standard form of the Smoluchowski equation accomplishes this by restricting the particle sizes to integer multiples of a basic unit particle size (the monomer size). This can be inefficient when particle concentrations over a large range of particle sizes must be calculated. Two algorithms employing a geometric size binning convention are examined: the first assumes that the aerosol particle concentration as a function of size can be considered constant within each size bin; the second approximates the concentration as a linear function of particle size within each size bin. The output of each algorithm is compared to an analytical solution in a special case of the Smoluchowski equation for which an exact solution is known . The range of parameters more appropriate for each algorithm is examined.

Statton, David M.↗
DOE OSTI2015

A regulatory perspective on the response function method for determining allowable content of a radioactive materials transportation package or storage cask - 15023

In order to simplify shielding design, there has been an increasingly use of a so-called dose rate response function method for determining the allowable contents in radioactive materials (including spent fuel) transportation package and spent fuel storage cask designs. In essence, this approach uses a pre-calculated dose rate at a given location outside the storage cask or transportation package for a given source inside the cask. It assumes that there is a one-to-one relationship between a source inside the cask and the dose rate outside the cask, i.e., a dose rate response function of a source. Thus, the allowable content is obtained by simply dividing the targeted dose rate by the response function. This method converts the complex particle transport problem into a simple arithmetic calculation. If used correctly and prudently, this approach can greatly simplify the shielding design of casks. However, the use of this method must demonstrate the validity of the assumption, that is, the nuclear physics property of the media through which the particle transverses must be similar to that used in computing the response function. Because of the assumptions and approximations, either implicitly or explicitly, made in the models for dose rate response functions, to assure safety the users should also consider the errors in the models and the bias and uncertainties associated with the code used to calculate the response function. This paper reviewed the advantages and some of the major potential pitfalls of this method from the regulatory perspective. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

Fully thermal meta-GGA exchange correlation free-energy density functional

The application of density functional theory to materials in the warm dense matter regime has motivated the development of exchange-correlation functionals which incorporate proper, explicit temperature dependence. Previous work has yielded fully-thermal exchange-correlation free energy functionals at the local density approximation (LDA) and generalized gradient approximation (GGA) levels of refinement. Recently an additive thermal correction scheme was utilized to construct a meta-GGA exchange-correlation (XC) functional in which thermal effects are treated at the GGA level. Here, the f TSCAN free-energy XC functional presented here includes thermal effects through the meta-GGA level in the context of the SCAN (strongly constrained and appropriately normed) ground-state functional. The f TSCAN functional provides generality while achieving similar performance to a thermal GGA functional at high temperatures, e.g. pressures within 1% of path integral Monte Carlo simulations of warm dense hydrogen, and a significant improvement over ground-state functionals. At low temperatures, f TSCAN demonstrates improvements in accuracy relative to lower-level and deorbitalized functionals, indicating that calculations using f TSCAN may be expected to perform well across experimentally relevant densities and pressures.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Leverage Score Sampling for Parametric PDEs (Final Technical Report)

This final technical report summarizes the accomplishments of work performed under DOE Office of Science Award DE-SC0022266, which is titled “Leverage Score Sampling for Parametric PDEs”. The goal of the project was to extend methods from Randomized Numerical Linear Algebra (RandNLA) to tackle central computational challenges in model order reduction and uncertainty quantification (UQ) for parametric partial differential equations (PDEs). In particular, we sought to use importance sampling methods originally developed for RandNLA to develop sample efficient active learning algorithms for approximating high-dimensional scalar functions, e.g. by polynomials, Gaussian process models, and simple neural networks. Such methods can be immediately applied to developing surrogate models or to approximating quantity of interest (QoI) surfaces. In the context of PDEs, each sample used for learning equates to the solution of the differential equation for a particular set of parameters, so sample efficiency translates to improved computational efficiency for a variety of downstream tasks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Collective charge and spin dynamics in low-dimensional itinerant electron systems with spin-orbit coupling

This research project in theoretical condensed-matter physics aims to study the collective charge and spin excitations of itinerant quasi-two-dimensional electronic systems such as doped semiconductor nanostructures and carbon-based materials, in the presence of impurities and spin-orbit coupling. In previous work under DOE support, we had discovered an interesting interplay between many-body effects and Rashba and Dresselhaus spin-orbit interactions: contrary to many situation in spintronics where spin-orbit interactions lead to loss of spin coherence, collective spin modes are robust against such coherence losses, and behave as macroscopic quantum objects with a collective magnetic moment precessing about an effective spin-orbit magnetic field. Experimental data for GaAs and CdMnTe quantum wells, obtained by our collaborators at the University Pierre et Marie Curie in Paris, confirmed our predictions and suggested that the observed effect is universal. However, a full theoretical explanation of the effect is still missing, and a wealth of new experimental data remains to be analyzed. We therefore plan to address the following three interrelated objectives: 1. Theory of collective modes in chiral systems. We will explore the various ways in which spin-orbit interactions affect collective spin-density and spin-flip excitations in semiconductor quantum wells. The goal will be to develop a universal formalism for chiral collective modes, with a particular emphasis on analytic results for dispersion relations, which will be compared with experimental results from inelastic light scattering. We will calculate the linewidths of spin plasmons and spin-flip waves due to impurity scattering and spin Coulomb drag from first principles. 2.Many-body effects in noncollinear magnetism. We will describe electronic many-body effects using time-dependent density-functional theory (TDDFT) in the linear-response regime. Quantum wells with spin-orbit coupling are noncollinear itinerant magnetic systems at the crossover between two and three dimensions, which poses subtle challenges for standard exchange-correlation (xc) functionals such as the local-density approximation (LDA). We will develop new orbital-dependent xc functionals for noncollinear magnetic systems by generalizing the so-called STLS approach. 3. Beyond single semiconductor quantum wells. We will consider quantum well bilayer or multilayer systems with spin-orbit coupling, where the coupling between the quasi-2D electron systems leads to acoustic and optical modes (in phase and out of phase). How are these modes affected if the two layers have the same or different chirality? Plasmon modes have been widely studied in graphene and other topological materials, and we will study collective spin excitations in graphene and other carbon-based materials in the presence of spin-orbit coupling and magnetic fields. The potential impact of the proposed research will be both on a fundamental and a practical level. A universal theory of chiral collective modes will advance our understanding of the interplay between many-body effects and spin-orbit interactions in a wide variety of materials and systems. A generalized STLS approach for noncollinear magnetism will be of wide interest beyond the systems studied here. This work may also point towards new ways of manipulating and controlling spin waves in low-dimensional itinerant electron systems: this could be used to encode, transport and process information, which would be of interest to the field of magnon spintronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1991

Temperature dependence of optical properties of GaAs

The effect of temperature on the optical properties of GaAs was investigated using spectroscopic ellipsometry measurements, between room temperature and about 610 C in increments of 50 C, of pseudodielectric functions and related optical constants of GaAs. A quantitative analysis of the pseudodielectric function spectrum was carried out using a harmonic-oscillator approximation (HOA) to fit the measured dielectric functions. Good fits were obtained with this model, which provides a convenient means of reproducing the GaAs dielectric function at any temperature, by using the temperature-dependent oscillator parameters. The HOA analysis also provides information about band-gap variation with temperature. Using the measured optical constants at a number of fixed temperatures, an algorithm was developed for computing the dielectric function spectrum at an arbitrary temperature in the range 22-610 C.

Yao, Huade↗
NASA NTRS1998

Three-dimensional organization of otolith-ocular reflexes in rhesus monkeys. III. Responses To translation

The three-dimensional (3-D) properties of the translational vestibulo-ocular reflexes (translational VORs) during lateral and fore-aft oscillations in complete darkness were studied in rhesus monkeys at frequencies between 0.16 and 25 Hz. In addition, constant velocity off-vertical axis rotations extended the frequency range to 0.02 Hz. During lateral motion, horizontal responses were in phase with linear velocity in the frequency range of 2-10 Hz. At both lower and higher frequencies, phase lags were introduced. Torsional response phase changed more than 180 degrees in the tested frequency range such that torsional eye movements, which could be regarded as compensatory to "an apparent roll tilt" at the lowest frequencies, became anticompensatory at all frequencies above approximately 1 Hz. These results suggest two functionally different frequency bandwidths for the translational VORs. In the low-frequency spectrum (<<0.5 Hz), horizontal responses compensatory to translation are small and high-pass-filtered whereas torsional response sensitivity is relatively frequency independent. At higher frequencies however, both horizontal and torsional response sensitivity and phase exhibit a similar frequency dependence, suggesting a common role during head translation. During up-down motion, vertical responses were in phase with translational velocity at 3-5 Hz but phase leads progressively increased for lower frequencies (>90 degrees at frequencies <0.2 Hz). No consistent dependence on static head orientation was observed for the vertical response components during up-down motion and the horizontal and torsional response components during lateral translation. The frequency response characteristics of the translational VORs were fitted by "periphery/brain stem" functions that related the linear acceleration input, transduced by primary otolith afferents, to the velocity signals providing the input to the velocity-to-position neural integrator and the oculomotor plant. The lowest-order, best-fit periphery/brain stem model that approximated the frequency dependence of the data consisted of a second order transfer function with two alternating poles (at 0.4 and 7.2 Hz) and zeros (at 0.035 and 3.4 Hz). In addition to clearly differentiator dynamics at low frequencies (less than approximately 0.5 Hz), there was no frequency bandwidth where the periphery/brain stem function could be approximated by an integrator, as previously suggested. In this scheme, the oculomotor plant dynamics are assumed to perform the necessary high-frequency integration as required by the reflex. The detailed frequency dependence of the data could only be precisely described by higher order functions with nonminimum phase characteristics that preclude simple filtering of afferent inputs and might be suggestive of distributed spatiotemporal processing of otolith signals in the translational VORs.

Non-NASA Center↗
DOE OSTI2016

Perspective: How good is DFT for water?

Kohn-Sham density functional theory (DFT) has become established as an indispensable tool for investigating aqueous systems of all kinds, including those important in chemistry, surface science, biology, and the earth sciences. Nevertheless, many widely used approximations for the exchange-correlation (XC) functional describe the properties of pure water systems with an accuracy that is not fully satisfactory. The explicit inclusion of dispersion interactions generally improves the description, but there remain large disagreements between the predictions of different dispersion-inclusive methods. We present here a review of DFT work on water clusters, ice structures, and liquid water, with the aim of elucidating how the strengths and weaknesses of different XC approximations manifest themselves across this variety of water systems. Our review highlights the crucial role of dispersion in describing the delicate balance between compact and extended structures of many different water systems, including the liquid. By referring to a wide range of published work, we argue that the correct description of exchange-overlap interactions is also extremely important, so that the choice of semi-local or hybrid functional employed in dispersion-inclusive methods is crucial. The origins and consequences of beyond-2-body errors of approximate XC functionals are noted, and we also discuss the substantial differences between different representations of dispersion. We propose a simple numerical scoring system that rates the performance of different XC functionals in describing water systems, and we suggest possible future developments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Single scale cluster expansions with applications to many Boson and unbounded spin systems

We develop a cluster expansion to show exponential decay of correlations for quite general single scale spin systems, as they arise in lattice quantum field theory and discretized functional integral representations for observables of quantum statistical mechanics. We apply our results to the small field approximation to the coherent state correlation functions of the grand canonical Bose gas at negative chemical potential, constructed by Balaban et al. [Ann. Henri Poincaré 11, 151–350 (2010c)], and to N component unbounded spin systems with repulsive two body interaction and massive, possibly complex, covariance. Our cluster expansion is derived by a single application of the Brydges-Kennedy-Abdesselam-Rivasseau interpolation formula.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1979

Linear Approximation SAR Azimuth Processing Study

A segmented linear approximation of the quadratic phase function that is used to focus the synthetic antenna of a SAR was studied. Ideal focusing, using a quadratic varying phase focusing function during the time radar target histories are gathered, requires a large number of complex multiplications. These can be largely eliminated by using linear approximation techniques. The result is a reduced processor size and chip count relative to ideally focussed processing and a correspondingly increased feasibility for spaceworthy implementation. A preliminary design and sizing for a spaceworthy linear approximation SAR azimuth processor meeting requirements similar to those of the SEASAT-A SAR was developed. The study resulted in a design with approximately 1500 IC's, 1.2 cubic feet of volume, and 350 watts of power for a single look, 4000 range cell azimuth processor with 25 meters resolution.

Lindquist, R. B.↗