Search NASA⌕ Search

SEARCH · Search NASA

Results for “gradient projection”

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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

What is the gradient of a scalar function defined on a subspace of square matrices?

We illustrate a technique to calculate the gradient of scalar functions that are defined on any arbitrary matrix subspace. It generalizes our earlier work titled “What is the gradient of a scalar function of a symmetric matrix ?”(Indian Journal of Pure and Applied Mathematics (2022), doi:10.1007/s13226-022-00313-x), in which we considered the special case of the subspace of symmetric matrices. Extant methods to calculate the gradient in such cases have an inherent flaw which leads to spurious results that populate several publications, as well as respected textbooks and handbooks on matrix calculus. We examine these sources and results in a rigorous and concrete mathematical setting of a finite-dimensional inner-product space and discover the inherent flaw and also a remedy. We demonstrate two ways to calculate the derivative/gradient and second derivative for scalar functions of matrices defined over an arbitrary matrix subspace; the first method is by considering any (differentiable) extension to the space of square matrices and projection of its gradient onto the given subspace. The second method utilizes an ordered basis and computes each component of the gradient through evaluation of the directional derivative. All the ideas presented are illustrated by non-trivial examples, namely, considering the subspace of 3 × 3 circulant and Toeplitz matrices and presenting the results of gradient-descent with both the spurious and correct gradients. Moreover, our bibliography makes it clear that a rigorous approach to matrix calculus is not common in practice, and our presentation of matrix calculus in the language of inner-product spaces will be significant and meaningful for applied mathematicians, engineers and researchers working in inter-disciplinary fields to avoid the conceptual pitfalls that exist.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

What is the gradient of a scalar function defined on a subspace of square matrices?

We illustrate a technique to calculate the gradient of scalar functions that are defined on any arbitrary matrix subspace. It generalizes our earlier work titled “What is the gradient of a scalar function of a symmetric matrix ?”(Indian Journal of Pure and Applied Mathematics (2022), https://doi.org/10.1007/s13226-022-00313-x), in which we considered the special case of the subspace of symmetric matrices. Extant methods to calculate the gradient in such cases have an inherent flaw which leads to spurious results that populate several publications, as well as respected textbooks and handbooks on matrix calculus. Here, we examine these sources and results in a rigorous and concrete mathematical setting of a finite-dimensional inner-product space and discover the inherent flaw and also a remedy. We demonstrate two ways to calculate the derivative/gradient and second derivative for scalar functions of matrices defined over an arbitrary matrix subspace; the first method is by considering any (differentiable) extension to the space of square matrices and projection of its gradient onto the given subspace. The second method utilizes an ordered basis and computes each component of the gradient through evaluation of the directional derivative. All the ideas presented are illustrated by non-trivial examples, namely, considering the subspace of 3 x 3 circulant and Toeplitz matrices and presenting the results of gradient-descent with both the spurious and correct gradients. Moreover, our bibliography makes it clear that a rigorous approach to matrix calculus is not common in practice, and our presentation of matrix calculus in the language of inner-product spaces will be significant and meaningful for applied mathematicians, engineers and researchers working in inter-disciplinary fields to avoid the conceptual pitfalls that exist.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A rotorcraft in-flight ice detection framework using computational aeroacoustics and Bayesian neural networks

Abstract This work develops a novel ice detection framework specifically suitable for rotorcraft using computational aeroacoustics and Bayesian neural networks. In an offline phase of the work, the acoustic signature of glaze and rime ice shapes on an oscillating wing are computed. In addition, the aerodynamic performance indicators corresponding to the ice shapes are also monitored. These performance indicators include the lift, drag, and moment coefficients. A Bayesian neural network is subsequently trained using projected Stein variational gradient descent to create a mapping from the acoustic signature generated by the iced wings to predict their performance indicators along with quantified uncertainty that is highly important for time- and safety-critical decision-making scenarios. While the training is carried out fully offline, usage of the Bayesian neural network to make predictions can be conducted rapidly online allowing for an ice detection system that can be used in real time and in-flight.

42 ENGINEERING↗
DOE OSTI2021

Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilities

Here we propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities, which is characterized by time-dependent stochastic processes and time-independent parameters in ~ 1500 dimensions after discretization. To infer these parameters, we use reported data on the number of confirmed, hospitalized, and deceased cases with suitable post-processing in both a deterministic inversion approach with appropriate regularization as a first step, followed by Bayesian inversion with proper prior distributions. To address the curse of dimensionality and the ill-posedness of the high-dimensional inference problem, we propose use of a dimension-independent projected Stein variational gradient descent method, and demonstrate the intrinsic low-dimensionality of the inverse problem. We present inference results with quantified uncertainties for both New Jersey and Texas, which experienced different epidemic phases and patterns. Moreover, we also present forecasting and validation results based on the empirical posterior samples of our inference for the future trajectory of COVID-19.

42 ENGINEERING↗
DOE OSTI2024

A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions

Neural network wavefunctions optimized using the variational Monte Carlo method have been shown to produce highly accurate results for the electronic structure of atoms and small molecules, but the high cost of optimizing such wavefunctions prevents their application to larger systems. We propose the Subsampled Projected-Increment Natural Gradient Descent (SPRING) optimizer to reduce this bottleneck. SPRING combines ideas from the recently introduced minimum-step stochastic reconfiguration optimizer (MinSR) and the classical randomized Kaczmarz method for solving linear least-squares problems. We demonstrate that SPRING outperforms both MinSR and the popular Kronecker-Factored Approximate Curvature method (KFAC) across a number of small atoms and molecules, given that the learning rates of all methods are optimally tuned. For example, on the oxygen atom, SPRING attains chemical accuracy after forty thousand training iterations, whereas both MinSR and KFAC fail to do so even after one hundred thousand iterations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Development of an Ultrahigh-bandwidth Phase Contrast Imaging System for detection of electron scale turbulence and Gigahertz Radio-Frequency Waves

The study of waves and turbulence is vital to the development of future reactor-grade plasma devices developed in the quest for fusion energy. These fluctuations are responsible for moving heat and particles across the magnetic field, and a predictive understanding of them is needed to achieve the density and temperature required to sustain a plasma fusion reaction. While many techniques have been developed for measuring waves and fluctuations, every measurement method has limitations. There are relatively few techniques for measuring very high frequency fluctuations, such as radio frequency waves injected to heat the plasma, unstable waves driven by suprathermal particles, or short wavelength electrostatic waves driven by electron temperature or density gradients. The present project builds upon the proven phase contrast imaging (PCI) technique to extend the response of the diagnostic by orders of magnitude in frequency and almost a factor of ten in spatial resolution. PCI provides a measurement of electron density based on small angle scattering of a CO-2 laser beam by using optical techniques to render a phase shift as an intensity change on a detector. Due to the telecommunications revolution, technological development by manufacturers has focused on components in the near -infrared, so that high- quality lasers and detectors at 1.55 µm are readily available. Shifting PCI design to a new, shorter wavelength has numerous advantages and challenges. Similar detector performance is available with room-temperature arrays with GHz bandwidth, while the detector arrays for 10.6 µm required liquid nitrogen cooling and were therefore limited to a bandwidth of about 1 MHz. Shifting to a shorter wavelength reduces the angle at which the laser beam scatters off of plasma waves, allowing more such scattered components to pass through the aperture of the vacuum vessel port and be collected by the PCI, which increases the spatial resolution. Concomitant with these benefits, various questions of performance arise. At shorter laser wave- length, the sensitivity to mirror and lens quality is increased, the contribution of the laser to the overall system noise is increased, and the sensitivity to vibrations is increased. The custom optical components at the heart of the PCI technique were required to be properly scaled for the shorter wavelength, so fabrication technologies needed to be explored. This project was designed to show that a low noise, high response PCI system at 1.55 µm could be constructed and operated, and then to quantify potential issues to allow extrapolation to a full-size production system providing physics measurements on a large plasma device. The first stage, producing the custom optical component called a Phase Plate, was successfully achieved using two methods. First, an easily reproduced masking and coating technique was able to produce good phase plates with the required parameters. Second, a nanofabrication technique was found to produce extremely high quality phase plates at a competitive price. The PCI constructed with the new phase plates and 1.55 µm laser was found to provide excellent wavelength measurements with the theoretically expected response. The sensitivity to optical surface quality was found to be in line with previous measurements at 10.6 µm. The observed signal-to-noise ratio was similar to the theoretically expected value. The effect of vibrations on PCI was studied with the first measurement of the effect of beam motion on PCI response and comparison to theory, allowing for a quantitative prediction of the effect of vibrations on a production PCI system and the requirements for improved beam stabilization. PCI is an extremely cost-effective method to provide a low noise, absolutely calibrated measurement of plasma fluctuations across a wide spatial scale. This project has shown that a 1.55 µm PCI using modern techniques and components is less expensive than the 10.6 µm PCI of a few years ago, with the largest savings in phase plate fabrication and the infrared detector array.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1996

Pattern Search Algorithms for Bound Constrained Minimization

We present a convergence theory for pattern search methods for solving bound constrained nonlinear programs. The analysis relies on the abstract structure of pattern search methods and an understanding of how the pattern interacts with the bound constraints. This analysis makes it possible to develop pattern search methods for bound constrained problems while only slightly restricting the flexibility present in pattern search methods for unconstrained problems. We prove global convergence despite the fact that pattern search methods do not have explicit information concerning the gradient and its projection onto the feasible region and consequently are unable to enforce explicitly a notion of sufficient feasible decrease.

Lewis, Robert Michael↗
DOE OSTI2024

Excellent performance of 650 MHz single-cell niobium cavity after electropolishing

Electropolishing process and cathodes have undergone modification and optimization for both low- and high-beta 650 MHz five-cell niobium cavities for PIP-II. Cavities treated with these modified electropolishing conditions exhibited smooth surfaces and good performance in baseline tests. Nonetheless, due to administrative constraints on project cavities, maximum gradient performance testing was not conducted. This paper presents a study conducted on a single-cell 650 MHz cavity utilizing the optimized electropolishing conditions, highlighting the maximum performance attained for this specific cavity. The cavity tested at 2 K in a vertical cryostat reached a superior accelerating field gradient of 53.3 MV/m at Q0 of 1.6x1010, which is the highest gradient attained for this type of large-sized cavities.

43 PARTICLE ACCELERATORS↗
NASA NTRS1988

A multivariate variational objective analysis-assimilation method. Part 1: Development of the basic model

The variational method of undetermined multipliers is used to derive a multivariate model for objective analysis. The model is intended for the assimilation of 3-D fields of rawinsonde height, temperature and wind, and mean level temperature observed by satellite into a dynamically consistent data set. Relative measurement errors are taken into account. The dynamic equations are the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation. The model Euler-Lagrange equations are eleven linear and/or nonlinear partial differential and/or algebraic equations. A cyclical solution sequence is described. Other model features include a nonlinear terrain-following vertical coordinate that eliminates truncation error in the pressure gradient terms of the horizontal momentum equations and easily accommodates satellite observed mean layer temperatures in the middle and upper troposphere. A projection of the pressure gradient onto equivalent pressure surfaces removes most of the adverse impacts of the lower coordinate surface on the variational adjustment.

Achtemeier, Gary L.↗
NASA NTRS2020

Unprecedented Drought Challenges for Texas Water Resources in a Changing Climate: What Do Researchers and Stakeholders Need to Know?

Long‐range water planning is complicated by factors that are rapidly changing in the 21st century, including climate, population, and water use. Here, we analyze climate factors and drought projections for Texas as an example of a diverse society straddling an aridity gradient to examine how the projections can best serve water stakeholder needs. We find that climate models are robust in projecting drying of summer‐season soil moisture and decreasing reservoir supplies for both the eastern and western portions of Texas during the 21st century. Further, projections indicate drier conditions during the latter half of the 21st century than even the most arid centuries of the last 1,000 years that included megadroughts. To illustrate how accounting for drought non‐stationarity may increase water resiliency, we consider generalized case studies involving four key stakeholder groups: agricultural producers, large surface water suppliers, small groundwater management districts, and regional water planning districts. We also examine an example of customized climate information being used as input to long‐range water planning. We find that while stakeholders value the quantitative capability of climate model outputs, more specific climate‐related information better supports resilience planning across multiple stakeholder groups. New suites of tools could provide necessary capacity for both short and long‐term, stakeholder‐specific adaptive planning.

drought↗
DOE OSTI2024

Experimental and Computational Studies of Crystal Nucleation in Composition Gradients (Final Report)

The major goals of this project were to develop and validate a predictive nucleation model that incorporates composition gradients and is applicable to a large range of metallic systems which form both stochiometric and non-stochiometric compounds. Computationally we planned to expand the extent of thermodynamics-based theories and lay the groundwork to improve the general understanding and predictive capabilities of the role that gradients play in phase formation, glass formability and stability, and nucleation and growth events. To address these goals, we used Molecular Dynamics (MD) simulations and both isothermal and isochronal nanocalorimetric experiments on amorphous phases with a controlled composition gradient with the hopes of validating and improving the classical nucleation model and its use in solid solutions. While the computations were successful and identified ways to improve the classical nucleation model, the in situ nanocalorimetry studies proved very challenging due to unexpected difficulties in fabricating effective calorimeters and samples. Thus, we could not experimentally validate our predicted influence of composition gradients on nucleation. Nonetheless, important insights were gained and modifications to the classical nucleation theory were suggested.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Western Sector In-Situ Chemical Oxidation Project: Additional Injection Pilot Testing Supplemental Results (U)

Trichloroethylene (TCE) and tetrachloroethylene (PCE) are persistent at elevated concentrations in the Western Sector of the M-Area Hazardous Waste Management Facility (HWMF) groundwater plume. Migration of these chlorinated ethenes as Dense Non-Aqueous Phase Liquids (DNAPLs) occurred from the M-Area Settling Basin along geologic strata resulting in a high concentration groundwater plume in Western Sector. Pump-and-treat has been active for over 30 years at the M-Area HWMF to hydraulically contain the primary sources of the plume in addition to other remediation strategies throughout the contaminated zone, like soil vapor extraction, dynamic underground stripping, groundwater recirculation wells, and bioremediation. In-situ chemical oxidation (ISCO) has been identified as a viable treatment method for removal of these volatile organic compounds (VOCs) due to the complex lithology and high concentrations in this part of the aquifer. In addition to ISCO, a new recovery well (i.e., RWM018) was also installed in Western Sector to contain the high concentration VOC plume. The ISCO projects have utilized the gradient induced by RWM018 to help plan the injection and monitoring locations. The combination of ISCO and the additional pump and treat in Western Sector with the installation of RWM018 will help to control the plume and maximize remediation efforts.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1980

Salton Sea solar pond project

The feasibility of constructing salt gradient solar ponds within the Salton Sea is being studied. These ponds would serve a dual purpose: (1) become a depository for unwanted salt and (2) supply thermal energy for driving turbine electric power systems. Under present circumstances, the rise in salinity is expected to eliminate fish life and create other unfavorable conditions. The proposed concept would have a power generation potential of 600 MWe.

French, R. L.↗
DOE OSTI2023

AmeriFlux FLUXNET-1F US-EML Eight Mile Lake Permafrost thaw gradient, Healy Alaska.

This is the AmeriFlux Management Project (AMP) created FLUXNET-1F version of the carbon flux data for the site US-EML Eight Mile Lake Permafrost thaw gradient, Healy Alaska.. This is the FLUXNET version of the carbon flux data for the site US-EML Eight Mile Lake Permafrost thaw gradient, Healy Alaska. produced by applying the standard ONEFlux (1F) software. Site Description - Tundra permafrost degrading

Bracho, Rosvel↗
DOE OSTI2024

Poleward Migration of the Latitude of Maximum Tropical Cyclone Intensity—Forced or Natural?

Abstract Past studies have shown a significant observed poleward trend in the latitude at which tropical cyclones reach their lifetime maximum intensity (LMI), especially in the northwest Pacific basin. Given the brevity of the historical record, it remains difficult to separate the forced trend from internal variability of the climate system. A recently developed tropical cyclone downscaling model is used to downscale the Community Earth System Model, version 2 (CESM2), preindustrial control simulation. It is found that the observed trend in the latitude at which tropical cyclones reach their LMI in the northwest Pacific is very unlikely to be caused by internal variability. The same downscaling model is then used to downscale CESM2 simulations under historical forcing. The resulting trend distribution shows a significant poleward migration of tropical cyclone LMI even after regressing out both natural variability and the part of the forced warming pattern that projects onto natural variability. The results indicate that the observed poleward migration of the latitude at which tropical cyclones reach their LMI in the northwest Pacific basin is likely to be, at least in part, forced. However, the magnitude of the projected poleward trend in climate models can be significantly modulated by the simulated spatial pattern of ocean warming. This highlights how discrepancies between models and observations, with regard to projected changes to the equatorial zonal sea surface temperature gradient under anthropogenic forcing, can lead to large uncertainties in projected changes to the LMI latitude of tropical cyclones. Significance Statement Observations in the northwest Pacific basin show that the latitude at which tropical cyclones are at their most intense has been trending northward in the recent half century. These changes are important since tropical cyclones could bring hazardous weather to coastal areas that are poorly equipped to handle them. Here, we show that natural variations in Earth’s climate are very unlikely to explain the observed poleward trend in the latitude that tropical cyclone reach their maximum intensity. We find that it is much more likely that the observed trend is forced by human-related emissions, though the spatial pattern of warming in response to greenhouse emissions can have significant impacts on the magnitude of the trend.

Lin, Jonathan↗
DOE OSTI2024

Implementation and Exploration of Parameterizations of Large-Scale Dynamics in NCAR's Single Column Atmosphere Model SCAM6

A single column model with parameterized large-scale (LS) dynamics is used to better understand the response of steady-state tropical precipitation to relative sea surface temperature under various representations of radiation, convection, and circulation. The large-scale dynamics are parametrized via the weak temperature gradient (WTG), damped gravity wave (DGW), and spectral weak temperature gradient (Spectral WTG) method in NCAR's Single Column Atmosphere Model (SCAM6). Radiative cooling is either specified or interactive, and the convective parameterization is run using two different values of a parameter that controls the degree of convective inhibition. Results are interpreted in the context of the Global Atmospheric System Studies -Weak Temperature Gradient (GASS-WTG) Intercomparison project. Using the same parameter settings and simulation configuration as in the GASS-WTG Intercomparison project, SCAM6 under the WTG and DGW methods produces erratic results, suggestive of numerical instability. However, when key parameters are changed to weaken the large-scale circulation's damping of tropospheric temperature variations, SCAM6 performs comparably to single column models in the GASS-WTG Intercomparison project. The Spectral WTG method is less sensitive to changes in convection and radiation than are the other two methods, performing qualitatively similarly across all configurations considered. Under all three methods, circulation strength, represented in 1D by grid-scale vertical velocity, is decreased when barriers to convection are reduced. This effect is most extreme under specified radiative cooling, and is shown to come from increased static stability in the column's reference radiative-convective equilibrium profile. This argument can be extended to interactive radiation cases as well, though perhaps less conclusively.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Elemental Abundances in M31: Gradients in the Giant Stellar Stream

We analyze existing measurements of [Fe/H] and [α/Fe] for individual red giant branch (RGB) stars in the Giant Stellar Stream (GSS) of M31 to determine whether spatial abundance gradients are present. These measurements were obtained from low- (R ~ 3000) and moderate- (R ~ 6000) resolution Keck/DEIMOS spectroscopy using spectral synthesis techniques as part of the Elemental Abundances in M31 survey. From a sample of 62 RGB stars spanning the GSS at 17, 22, and 33 projected kpc, we measure a [Fe/H] gradient of -0.018 ± 0.003 dex kpc{sup -1} and negligible [α/Fe] gradient with M31-centric radius. We investigate GSS abundance patterns in the outer halo using additional [Fe/H] and [α/Fe] measurements for six RGB stars located along the stream at 45 and 58 projected kpc. These abundances provide tentative evidence that the trends in [Fe/H] and [α/Fe] beyond 40 kpc in the GSS are consistent with those within 33 kpc. We also compare the GSS abundances to 65 RGB stars located along the possibly related Southeast (SE) shelf substructure at 12 and 18 projected kpc. The abundances of the GSS and SE shelf are consistent, supporting a common origin hypothesis, although this interpretation may be complicated by the presence of [Fe/H] gradients in the GSS. We discuss the abundance patterns in the context of photometric studies from the literature and explore implications for the properties of the GSS progenitor, suggesting that the high ⟨[α/Fe]⟩ of the GSS (+0.40 ± 0.05 dex) favors a major merger scenario for its formation.

47 OTHER INSTRUMENTATION↗
NASA NTRS1992

Characterization of radiation-induced damage in high performance polymers by electron paramagnetic resonance imaging spectroscopy

The potential for long-term human activity beyond the Earth's protective magnetosphere is limited in part by the lack of detailed information on the effectiveness and performance of existing structural materials to shield the crew and spacecraft from highly penetrating space radiations. The two radiations of greatest concern are high energy protons emitted during solar flares and galactic cosmic rays which are energetic ions ranging from protons to highly oxidized iron. Although the interactions of such high-energy radiations with matter are not completely understood at this time, the effects of the incident radiation are clearly expected to include the formation of paramagnetic spin centers via ionization and bond-scission reactions in the molecular matrices of structural materials. Since this type of radiation damage is readily characterized by Electron Paramagnetic Resonance (EPR) spectroscopy, the NASA Langley Research Center EPR system was repaired and brought on-line during the 1991 ASEE term. A major goal of the 1992 ASEE term was to adapt the existing core of the LaRC EPR system to meet the requirements for EPR Imaging--a powerful new technique which provides detailed information on the internal structure of materials by mapping the spatial distribution of unpaired spin density in bulk media. Major impetus for this adaptation arises from the fact that information derived from EPRI complements other methods such as scanning electron microscopy which primarily characterize surface phenomena. The modification of the EPR system has been initiated by the construction of specially designed, counterwound Helmholtz coils which will be mounted on the main EPR electromagnet. The specifications of the coils have been set to achieve a static linear magnetic field gradient of 10 gauss/mm/amp along the principal (Z) axis of the Zeeman field. Construction is also in progress of a paramagnetic standard in which the spin distribution is known in all three dimensions. This sample will be used to assess the linearity of the magnetic field gradient and to ensure authentic image reconstruction. A second major task was to secure the computer capability to enable image reconstruction from projection data generated by the magnetic field gradients. To this end, commercially available and public domain software packages which perform inverse Fourier Transform and convoluted (filtered) back projection functions are being integrated into the existing EPR data processing system.

Suleman, Naushadalli K.↗