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Results for “Gradient estimation”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

The effects of turbulence on the flame structure and NO formation of ammonia turbulent premixed combustion at various equivalence ratios

Ammonia is carbon-free and is regarded as a potential fuel to address global warming issues. Here, in this work, three-dimensional direct numerical simulations (DNS) of ammonia/air turbulent premixed flames were performed to explore the influence of turbulence and equivalence ratio on the flame structure and NO formation characteristics. Two equivalence ratios were considered, i.e. Φ=0.9 and Φ=1.1. The general flame structures were presented and species distributions were examined. The NO mass fraction was found to be the highest in the product for the lean case and in the reaction zone for the rich case. The conditional mean values of species mass fractions and reaction rates were compared with those of the unstrained and strained laminar premixed flames to explore how well the laminar flame structures can approach those of the turbulent flame. The budget analysis of the species transport equations showed that turbulent diffusion plays an important role in species transport. The turbulent diffusivity D T was estimated using the gradient hypothesis based on the DNS data. Various laminar flame simulations with different diffusivities were carried out. It was shown that the conditional means of the DNS agree well with those of the laminar flames including D T in the transport property calculation. The global and local NO formation characteristics were investigated. It was found that the mean NO production conditioned on the progress variable is lower compared with the corresponding laminar flame in the rich case. However, the relative contributions from various NO pathways are rarely affected by turbulence. The NO mass fraction is higher in negative curvature regions compared with positive curvature regions of the flame surface for the rich case, which is due to the preferential diffusion of H 2 and other radicals and the enhanced NO pathways in negatively curved regions.

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

Optimization of nonlinear turbulence in stellarators

We present new stellarator equilibria that have been optimized for reduced turbulent transport using nonlinear gyrokinetic simulations within the optimization loop. The optimization routine involves coupling the pseudo-spectral GPU-native gyrokinetic code GX with the stellarator equilibrium and optimization code DESC . Since using GX allows for fast nonlinear simulations, we directly optimize for reduced nonlinear heat fluxes. To handle the noisy heat flux traces returned by these simulations, we employ the simultaneous perturbation stochastic approximation (SPSA) method that only uses two objective function evaluations for a simple estimate of the gradient. We show several examples that optimize for both reduced heat fluxes and good quasi-symmetry as a proxy for low neoclassical transport. Finally, we run full transport simulations using the T3D stellarator transport code to evaluate the changes in the macroscopic profiles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Resource frugal optimizer for quantum machine learning

Quantum-enhanced data science, also known as quantum machine learning (QML), is of growing interest as an application of near-term quantum computers. Variational QML algorithms have the potential to solve practical problems on real hardware, particularly when involving quantum data. However, training these algorithms can be challenging and calls for tailored optimization procedures. Specifically, QML applications can require a large shot-count overhead due to the large datasets involved. In this work, we advocate for simultaneous random sampling over both the dataset as well as the measurement operators that define the loss function. We consider a highly general loss function that encompasses many QML applications, and we show how to construct an unbiased estimator of its gradient. This allows us to propose a shot-frugal gradient descent optimizer called Refoqus (REsource Frugal Optimizer for QUantum Stochastic gradient descent). Our numerics indicate that Refoqus can save several orders of magnitude in shot cost, even relative to optimizers that sample over measurement operators alone.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Inexact Newton-CG algorithms with complexity guarantees

Abstract We consider variants of a recently developed Newton-CG algorithm for nonconvex problems (Royer, C. W. & Wright, S. J. (2018) Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization. SIAM J. Optim., 28, 1448–1477) in which inexact estimates of the gradient and the Hessian information are used for various steps. Under certain conditions on the inexactness measures, we derive iteration complexity bounds for achieving $\epsilon $-approximate second-order optimality that match best-known lower bounds. Our inexactness condition on the gradient is adaptive, allowing for crude accuracy in regions with large gradients. We describe two variants of our approach, one in which the step size along the computed search direction is chosen adaptively, and another in which the step size is pre-defined. To obtain second-order optimality, our algorithms will make use of a negative curvature direction on some steps. These directions can be obtained, with high probability, using the randomized Lanczos algorithm. In this sense, all of our results hold with high probability over the run of the algorithm. We evaluate the performance of our proposed algorithms empirically on several machine learning models. Our approach is a first attempt to introduce inexact Hessian and/or gradient information into the Newton-CG algorithm of Royer & Wright (2018, Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization. SIAM J. Optim., 28, 1448–1477).

Mathematics↗
DOE OSTI2022

Quantifying radial migration in the Milky Way: inefficient over short time-scales but essential to the very outer disc beyond ∼15 kpc

ABSTRACT Stellar radial migration plays an important role in reshaping a galaxy’s structure and the radial distribution of stellar population properties. In this work, we revisit reported observational evidence for radial migration and quantify its strength using the age–[Fe/H] distribution of stars across the Milky Way with APOGEE data. We find a broken age–[Fe/H] relation in the Galactic disc at r > 6 kpc, with a more pronounced break at larger radii. To quantify the strength of radial migration, we assume stars born at each radius have a unique age and metallicity, and then decompose the metallicity distribution function (MDF) of mono-age young populations into different Gaussian components that originated from various birth radii at rbirth < 13 kpc. We find that, at ages of 2 and 3 Gyr, roughly half the stars were formed within 1 kpc of their present radius, and very few stars (<5 per cent) were formed more than 4 kpc away from their present radius. These results suggest limited short-distance radial migration and inefficient long-distance migration in the Milky Way during the last 3 Gyr. In the very outer disc beyond 15 kpc, the observed age–[Fe/H] distribution is consistent with the prediction of pure radial migration from smaller radii, suggesting a migration origin of the very outer disc. We also estimate intrinsic metallicity gradients at ages of 2 and 3 Gyr of −0.061 and −0.063 dex kpc−1, respectively.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Smoothing Lexis diagrams using kernel functions: A contemporary approach

Lexis diagrams are rectangular arrays of event rates indexed by age and period. Analysis of Lexis diagrams is a cornerstone of cancer surveillance research. Typically, population-based descriptive studies analyze multiple Lexis diagrams defined by sex, tumor characteristics, race/ethnicity, geographic region, etc. Inevitably the amount of information per Lexis diminishes with increasing stratification. Several methods have been proposed to smooth observed Lexis diagrams up front to clarify salient patterns and improve summary estimates of averages, gradients, and trends. In this article, we develop a novel bivariate kernel-based smoother that incorporates two key innovations. First, for any given kernel, we calculate its singular values decomposition, and select an optimal truncation point—the number of leading singular vectors to retain—based on the bias-corrected Akaike information criterion. Second, we model-average over a panel of candidate kernels with diverse shapes and bandwidths. The truncated model averaging approach is fast, automatic, has excellent performance, and provides a variance-covariance matrix that takes model selection into account. We present an in-depth case study (invasive estrogen receptor-negative breast cancer incidence among non-Hispanic white women in the United States) and simulate operating characteristics for 20 representative cancers. The truncated model averaging approach consistently outperforms any fixed kernel. Our results support the routine use of the truncated model averaging approach in descriptive studies of cancer.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Field Sensitivity Analysis of Turbulence Model Parameters for Flow Over a Wing

Reynolds-averaged-Navier-Stokes (RANS) turbulence models are a critical tool in computational-fluid-dynamics simulations of aerodynamic systems, but simulation results can be highly sensitive to RANS-model parameter choices. Sensitivity analysis can be used to quantify these impacts, and the objective of this study is to demonstrate field sensitivity analysis with respect to ten parameters in the 2003 Menter shear-stress-transport (SST) turbulence model. Here, the analysis is demonstrated for an application relevant to wind energy, namely, flow over a NACA 0015 wing at 12 degree angle of attack and a Reynolds number of 1.5 x 10 6 . We quantify sensitivity using Sobol indices and the mean-squared gradient, which are estimated using polynomial chaos and active subspace models, respectively. Our results indicate that there are substantial spatial variations in parameter sensitivities, with different sets of most-sensitive parameters near the wing, as well as in the downstream wake, consistent with the physical interpretations of the turbulence model inputs. We show that, for this particular turbulence model and flow, simultaneous dimension reduction is possible across all quantities of interest, enabling efficient exploration of model outcomes. Ultimately, this analysis provides new insights into turbulence model parameter sensitivities in incompressible flows, and also demonstrates the implementation of field sensitivity analysis for applications relevant to aerodynamics simulations.

17 WIND ENERGY↗
DOE OSTI2026

Analysis of vapor diffusion Nb$^{3}$Sn coating at Fermilab: Minimizing impurities using TOF-SIMS

Nb₃Sn demonstrates steady advancements nowadays offering reduced power cost in superconducting radio-frequency cavities due to its high critical temperature, quality factor, and achieved accelerating gradient. However, theoretical estimates of its radio-frequency parameters have not been achieved due to several potentially limiting mechanisms: tin spots, patchy regions, defects, thermal impedance, and impurities. While some of these limitations have been intensively studied, impurity analysis in Nb$_3$Sn coatings have received less attention. We report an investigation of impurities in several vapor-diffused Nb₃Sn coated samples using time-of-flight secondary ion mass spectroscopy (TOF-SIMS) and show allowable impurity levels in view of superconducting cavity performance. Challenges and lessons learned in maintaining clean Nb$_3$Sn coatings are also discussed.

Tagdulang, Nikki [Fermilab]↗
DOE OSTI2025

Challenges of Vapor Diffusion $Nb_3Sn$ Coating at Fermilab: Minimizing Impurities Using TOF-SIMS

Nb$_3$Sn demonstrates steady advancements nowadays offering reduced power cost in superconducting radio-frequency cavities due to its high critical temperature, quality factor, and achieved accelerating gradient. However, theoretical estimates of its radio-frequency parameters have not been achieved due to several potentially limiting mechanisms: tin spots, patchy regions, defects, thermal impedance, and impurities. While some of these limitations have been intensively studied, impurity analysis in Nb$_3$Sn coatings have received less attention. We report an investigation of impurities in several vapor-diffused Nb$_3$Snn coated samples using time-of-flight secondary ion mass spectroscopy (TOF-SIMS) and show allowable impurity levels in view of superconducting cavity performance. Challenges and lessons learned in maintaining clean Nb$_3$Sn coatings are also discussed.

Tagdulang, N. [Fermilab]↗
DOE OSTI2021

Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer

Restricted Boltzmann Machine (RBM) is an energy-based, undirected graphical model. It is commonly used for unsupervised and supervised machine learning. Typically, RBM is trained using contrastive divergence (CD). However, training with CD is slow and does not estimate the exact gradient of the log-likelihood cost function. In this work, the model expectation of gradient learning for RBM has been calculated using a quantum annealer (D-Wave 2000Q), where obtaining samples is faster than Markov chain Monte Carlo (MCMC) used in CD. Training and classification results of RBM trained using quantum annealing are compared with the CD-based method. The performance of the two approaches is compared with respect to the classification accuracies, image reconstruction, and log-likelihood results. The classification accuracy results indicate comparable performances of the two methods. Image reconstruction and log-likelihood results show improved performance of the CD-based method. It is shown that the samples obtained from quantum annealer can be used to train an RBM on a 64-bit “bars and stripes” dataset with classification performance similar to an RBM trained with CD. Though training based on CD showed improved learning performance, training using a quantum annealer could be useful as it eliminates computationally expensive MCMC steps of CD.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Estimation and uncertainty quantification for the output from quantum simulators

The problem of estimating certain distributions over {0, 1} d is considered here. The distribution represents a quantum system of d qubits, where there are non-trivial dependencies between the qubits. A maximum entropy approach is adopted to reconstruct the distribution from exact moments or observed empirical moments. The Robbins Monro algorithm is used to solve the intractable maximum entropy problem, by constructing an unbiased estimator of the un-normalized target with a sequential Monte Carlo sampler at each iteration. In the case of empirical moments, this coincides with a maximum likelihood estimator. A Bayesian formulation is also considered in order to quantify uncertainty a posteriori. Several approaches are proposed in order to tackle this challenging problem, according to recently developed methodologies. In particular, unbiased estimators of the gradient of the log posterior are constructed and used within a provably convergent Langevin-based Markov chain Monte Carlo method. The methods are illustrated on classically simulated output from quantum simulators.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1982

Detection and evaluation of mixed pixels in Landsat agricultural scenes

A major problem area encountered in the identification and estimation of agricultural crop proportions in Landsat imagery involves the large proportion of the pixels which are mixed pixels, whose spectral response is influenced by more than one ground cover type. The development of methods for the detection and estimation of crop proportions in mixed pixels is presently reported. The procedure designated CASCADE, based on the estimation of the gradient image for the detection of mixed pixels, considers the consequences of a linear mixing model and is found to provide a method for the allocation of mixed pixels to the surrounding homogeneous region.

Merickel, M. B.↗
NASA NTRS1984

Efficient calculation of optimum design sensitivity

Two methods for obtaining the sensitivity of an optimized design to changes in problem parameters are presented. The first-order method uses gradient information to estimate the required sensitivity. The second-order method uses second derivatives of the design objective and constraint functions to provide a quadratic approximation to the new design which results from changing the specified parameter. It is shown that the sensitivity of the optimized design may be discontinuous with respect to the new parameter. This discontinuity is accounted for in the present methods. These methods are compared to a previous approach based on the Kuhn-Tucker necessary conditions for optimality. It is shown that the present methods provide the appropriate sensitivity information in an efficient manner. The methods are demonstrated by a structural synthesis example.

Vanderplaats, G. N.↗
NASA NTRS1985

Modeling gravity and magnetic fields for crustal and upper mantle structures

Research was conducted to: (1) make a direct comparison between the gravity and magnetic fields near the ellipsoid and at the height expected for the Geopotential Research Mission (GRM) for the same geologic model, (2) obtain realistic estimates of the gradients that can be expected at the orbit height of the GRM, and (3) demonstrate the value of data that the GRM could provide for investigating upper mantle and deep crustal anomalies.

Denoyer, J. M.↗
NASA NTRS1987

Transport and photochemical modeling. Studies of atmospheric species

A program of research studies related to the photochemistry, radiative transfer, and dynamics of the stratosphere is described. Investigations were conducted in two broad areas: (1) studies of the stratospheric processes and their response to external perturbations, and (2) analysis of satellite measurements in conjunction with theoretical models. Contemporary one dimensional photochemical, radiative-convective model was used to assess the impact of perturbations such as solar flux variability, increases in atmospheric carbon dioxide, chlorofluoromethanes and other greenhouse gases. Data from satellite experiments such as LIMS and SBUV, were used along with theoretical models to develop a climatology of trace species in the stratosphere. The consistency of contemporary ozone photochemistry was examined in the light of LIMS data. Research work also includes analysis of stratospheric nitrogen dioxide distributions from different satellite experiments, investigation of the wintertime latitudinal gradients in NO2, estimation of the stratospheric odd nitrogen level and its variability, and studies related to the changes in ozone in the Antarctic, and mid latitude Southern Hemisphere.

Natarajan, M.↗
NASA NTRS1990

Improved LMS algorithm for adaptive beamforming

Two adaptive algorithms which make use of all the available samples to estimate the required gradient are proposed and studied. The first algorithm is referred to as the recursive LMS (least mean squares) and is applicable to a general array. The second algorithm is referred to as the improved LMS algorithm and exploits the Toeplitz structure of the ACM (array correlation matrix); it can be used only for an equispaced linear array.

Godara, Lal C.↗
NASA NTRS1993

Residual strain gradient determination in metal matrix composites by synchrotron X-ray energy dispersive diffraction

An X-ray technique for the measurement of internal residual strain gradients near the continuous reinforcements of metal matrix composites has been investigated. The technique utilizes high intensity white X-ray radiation from a synchrotron radiation source to obtain energy spectra from small (0.001 cu mm) volumes deep within composite samples. The viability of the technique was tested using a model system with 800 micron Al203 fibers and a commercial purity titanium matrix. Good agreement was observed between the measured residual radial and hoop strain gradients and those estimated from a simple elastic concentric cylinders model. The technique was then used to assess the strains near (SCS-6) silicon carbide fibers in a Ti-14Al-21Nb matrix after consolidation processing. Reasonable agreement between measured and calculated strains was seen provided the probe volume was located 50 microns or more from the fiber/matrix interface.

Kuntz, Todd A.↗