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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,297 records · Page 72
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A Fast Solver for the Fractional Helmholtz Equation

The purpose of this paper is to study a Helmholtz problem with a spectral fractional Laplacian, instead of the standard Laplacian. Recently, it has been established that such a fractional Helmholtz problem better captures the underlying behavior in Geophysical Electromagnetics. In this work, we establish the well-posedness and regularity of this problem. We introduce a hybrid spectral-finite element approach to discretize it and show well-posedness of the discrete system. In addition, we derive a priori discretization error estimates. Finally, we introduce an efficient solver that scales aswell as the best possible solver for the classical integer-order Helmholtz equation. We conclude withseveral illustrative examples that confirm our theoretical findings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

On the Training and Generalization of Deep Operator Networks

Here, we present a novel training method for deep operator networks (DeepONets), one of the most popular neural network models for operators. DeepONets are constructed by two subnetworks, namely the branch and trunk networks. Typically, the two subnetworks are trained simultaneously, which amounts to solving a complex optimization problem in a high dimensional space. In addition, the nonconvex and nonlinear nature makes training very challenging. To tackle such a challenge, we propose a two-step training method that trains the trunk network first and then sequentially trains the branch network. The core mechanism is motivated by the divide-and-conquer paradigm and is the decomposition of the entire complex training task into two subtasks with reduced complexity. Therein the Gram–Schmidt orthonormalization process is introduced which significantly improves stability and generalization ability. On the theoretical side, we establish a generalization error estimate in terms of the number of training data, the width of DeepONets, and the number of input and output sensors. Numerical examples are presented to demonstrate the effectiveness of the two-step training method, including Darcy flow in heterogeneous porous media.

deep operator networks↗
DOE OSTI2025

Comparison of CERES SYN1deg Radiative Fluxes with Those Derived from Observations at the ARM ENA Site

Profiles of radiative fluxes simulated from thermodynamic and cloud observations made at the Atmospheric Radiation Measurement (ARM) eastern North Atlantic (ENA) site for a 6-yr period are termed as ENARad. ENARad radiative fluxes are compared to those from the Clouds and the Earth’s Radiant Energy System (CERES) 1°-resolution synoptic product (SYN1deg)-simulated radiative flux profiles as well as the CERES instrument observed top-of-the-atmosphere (TOA) fluxes and ground site broadband radiometer measurements. Monthly average differences between ENARad and surface radiometer reported fluxes and differences between ENARad, SYN1deg, and observed fluxes at TOA were statistically insignificant. SYN1deg significantly overestimated surface downwelling shortwave flux by 12 ± 52 W m −2 and surface downwelling longwave flux by 5 ± 20 W m −2 on monthly time scales. Such overestimations were traced to a moister and warmer subcloud layer, a drier cloud layer, and a moister and colder above-cloud-free troposphere in the ancillary thermodynamic and cloud properties used by SYN1deg than observed. Similarly, low-cloud coverage, boundaries, and liquid water paths utilized by SYN1deg were also significantly higher than observed. Intramodel differences in the hourly values of shortwave fluxes exceeded 100 W m−2 at the TOA and the surface. These differences were also due to inaccuracies in the representation of low-cloud properties within the SYN1deg product relative to those determined by ENA ARM instrumentation and used as ENARad ancillary data. Results presented are relevant to investigations employing the CERES SYN1deg data product, studies that estimate radiative fluxes from surface-based or satellite-borne observations, and comparative analyses of radiative fluxes derived using different methodological approaches.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Visual inspection reliability for precision manufactured parts

Sandia National Laboratories conducted an experiment for the National Nuclear Security Administration to determine the reliability of visual inspection of precision manufactured parts used in nuclear weapons. In addition visual inspection has been extensively researched since the early 20th century; however, the reliability of visual inspection for nuclear weapons parts has not been addressed. In addition, the efficacy of using inspector confidence ratings to guide multiple inspections in an effort to improve overall performance accuracy is unknown. Further, the workload associated with inspection has not been documented, and newer measures of stress have not been applied.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2017

Variationally Derived Discontinuity Factors for the Asymptotic Homogenized Diffusion Equation

Here in this work, we derive and test variational discontinuity factors (DFs) for the asymptotic homogenized diffusion equation. We begin with a functional for optimally estimating the reactor multiplication factor, then introduce asymptotic expressions for the forward and adjoint angular fluxes, and finally require that all first-order error terms vanish. In this way, the reactor multiplication factor can be calculated with second-order error. The analysis leads to (1) an alternate derivation of the asymptotic homogenized diffusion equation, (2) variational boundary conditions for large periodic systems, and (3) variational DFs to be applied between adjacent periodic regions (e.g., fuel assemblies). Numerical tests show that applying the variational DFs to the asymptotic homogenized diffusion equation yields the most accurate estimates of the reactor multiplication factor compared to other DFs for a wide range of problems. However, the resulting assembly powers are less accurate than those obtained using other DFs for many realistic problems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Utilizing Adjoint-Based Error Estimates for Surrogate Models to Accurately Predict Probabilities of Events

In thist study, we develop a procedure to utilize error estimates for samples of a surrogate model to compute robust upper and lower bounds on estimates of probabilities of events. We show that these error estimates can also be used in an adaptive algorithm to simultaneously reduce the computational cost and increase the accuracy in estimating probabilities of events using computationally expensive high-fidelity models. Specifically, we introduce the notion of reliability of a sample of a surrogate model, and we prove that utilizing the surrogate model for the reliable samples and the high-fidelity model for the unreliable samples gives precisely the same estimate of the probability of the output event as would be obtained by evaluation of the original model for each sample. The adaptive algorithm uses the additional evaluations of the high-fidelity model for the unreliable samples to locally improve the surrogate model near the limit state, which significantly reduces the number of high-fidelity model evaluations as the limit state is resolved. Numerical results based on a recently developed adjoint-based approach for estimating the error in samples of a surrogate are provided to demonstrate (1) the robustness of the bounds on the probability of an event, and (2) that the adaptive enhancement algorithm provides a more accurate estimate of the probability of the QoI event than standard response surface approximation methods at a lower computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

The stacked Lyα emission profile from the circum-galactic medium of z ∼ 2 quasars

In the context of the FLASHLIGHT survey, we obtained deep narrowband images of 15 z ∼ 2 quasars with the Gemini Multi-object Spectrograph on Gemini South in an effort to measure Lyα emission from circum- and intergalactic gas on scales of hundreds of kpc from the central quasar. We do not detect bright giant Lyα nebulae (SB ∼ 10{sup −17} erg s{sup −1} cm{sup −2} arcsec{sup −2} at distances >50 kpc) around any of our sources, although we routinely (≃47%) detect smaller-scale <50 kpc Lyα emission at this surface brightness level emerging from either the extended narrow emission line regions powered by the quasars or by star formation in their host galaxies. We stack our 15 deep images to study the average extended Lyα surface brightness profile around z ∼ 2 quasars, carefully PSF-subtracting the unresolved emission component and paying close attention to sources of systematic error. Our analysis, which achieves an unprecedented depth, reveals a surface brightness of SB{sub Lyα} ∼ 10{sup −19} erg s{sup −1} cm{sup −2} arcsec{sup −2} at ∼200 kpc, with a 2.3σ detection of Lyα emission at SB {sub Lyα}=(5.5±3.1)×10{sup −20} erg s{sup −1} cm{sup −2} arcsec{sup −2} within an annulus spanning 50 kpc < R < 500 kpc from the quasars. Assuming that this Lyα emission is powered by fluorescence from highly ionized gas illuminated by the bright central quasar, we deduce an average volume density of n {sub H} = 0.6 × 10{sup −2} cm{sup −3} on these large scales. Our results are in broad agreement with the densities suggested by cosmological hydrodynamical simulations of massive (M ≃ 10{sup 12.5} M {sub ⊙}) quasar hosts; however, they indicate that the typical quasars at these redshifts are surrounded by gas that is a factor of ∼100 times less dense than the (∼1 cm{sup −3}) gas responsible for the giant bright Lyα nebulae around quasars recently discovered by our group.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Deep nonparametric estimation of operators between infinite dimensional spaces

Learning operators between infinitely dimensional spaces is an important learning task arising in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric estimation of Lipschitz operators using deep neural networks. Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class. Under the assumption that the target operator exhibits a low dimensional structure, our error bounds decay as the training sample size increases, with an attractive fast rate depending on the intrinsic dimension in our estimation. Our assumptions cover most scenarios in real applications and our results give rise to fast rates by exploiting low dimensional structures of data in operator estimation. We also investigate the influence of network structures (e.g., network width, depth, and sparsity) on the generalization error of the neural network estimator and propose a general suggestion on the choice of network structures to maximize the learning efficiency quantitatively.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1969

The effect of mismatched components on microwave noise-temperature calibrations

Analysis of errors on microwave noise-temperature measurements is important due to development of very low-noise antenna receiving systems and in the absolute accuracies to which the noise temperatures of these systems can be calibrated. Scattering parameters describe properties of the microwave network connected between noise source and receiver.

Otoshi, T. Y.↗
NASA NTRS1974

Coherent optical noise suppression device

The present work describes a scheme for a noise suppression system to be used with an afocal coherent optical data processor. The noise averaging scheme is based on the simple principle of moving input and output film planes together during exposure; the noise pattern remains stationary while the desired (filtered) image moves through it. The noise suppression system consists of a drive motor, right-angle gear box, reversing gear assemblage, right-angle gear drive, and micrometer adjusting translation tables. The device was tested by using a Sayce target containing fundamental spatial frequencies from 5 lines/mm to 100 lines/mm as the input signal. The output was photographed on Pan-X 35-mm film with and without the noise suppression system in operation. Microdensitometer scans of the exposed output film show that without noise averaging, resolution is good to about 80 lines/mm, while with noise averaging, it is good to about 35 lines/mm. A brief analysis of errors in the mechanical parts of the system reponsible for the upper limit of resolution is presented.

Horner, J. L.↗
NASA NTRS1979

Onset of condensation effects with an NACA 0012-64 airfoil tested in the Langley 0.3-meter transonic cryogenic tunnel

The onset of condensation effects as determined by varying the stagnation temperature was found to correlate better with the amount of supercooling in the free stream than it did with the supercooling in the region of maximum local Mach number over the air foil. Effects in the pressure distribution over the air foil were seen to appear over its entire length at nearly the same total temperature. Both observations suggest that heterogeneous nucleation does occur in the free stream. The benefits realized from supercooling are presented in terms of increased Reynolds number capability at a given tunnel total pressure and reduced drive-fan power and liquid nitrogen consumption if Reynolds number is held constant. Depending on total pressure and free-stream Mach number, these three benefits are found to vary respectively from 8 to 19 percent, 12 to 24 percent, and 9 to 19 percent. The data analysis and error estimates are given.

Hall, R. M.↗