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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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All sources NASA NTRS DOE OSTI

DOE OSTI2015

Variational Dirichlet Blur Kernel Estimation

Blind image deconvolution involves two key objectives: 1) latent image and 2) blur estimation. For latent image estimation, we propose a fast deconvolution algorithm, which uses an image prior of nondimensional Gaussianity measure to enforce sparsity and an undetermined boundary condition methodology to reduce boundary artifacts. For blur estimation, a linear inverse problem with normalization and nonnegative constraints must be solved. However, the normalization constraint is ignored in many blind image deblurring methods, mainly because it makes the problem less tractable. In this paper, we show that the normalization constraint can be very naturally incorporated into the estimation process by using a Dirichlet distribution to approximate the posterior distribution of the blur. Making use of variational Dirichlet approximation, we provide a blur posterior approximation that considers the uncertainty of the estimate and removes noise in the estimated kernel. Furthermore, experiments with synthetic and real data demonstrate that the proposed method is very competitive to the state-of-the-art blind image restoration methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Bayesian and variational Bayesian approaches for flows in heterogeneous random media

In this paper, we study porous media flows in heterogeneous stochastic media. We propose an efficient forward simulation technique that is tailored for variational Bayesian inversion. As a starting point, the proposed forward simulation technique decomposes the solution into the sum of separable functions (with respect to randomness and the space), where each term is calculated based on a variational approach. This is similar to Proper Generalized Decomposition (PGD). Next, we apply a multiscale technique to solve for each term (as in ) and, further, decompose the random function into 1D fields. As a result, our proposed method provides an approximation hierarchy for the solution as we increase the number of terms in the expansion and, also, increase the spatial resolution of each term. We use the hierarchical solution distributions in a variational Bayesian approximation to perform uncertainty quantification in the inverse problem. We conduct a detailed numerical study to explore the performance of the proposed uncertainty quantification technique and show the theoretical posterior concentration.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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 OSTI2025

Accelerating Hamiltonian Monte Carlo for Bayesian inference in neural networks and neural operators

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high dimensionality of the network’s parameter space and the non-convexity of their posterior distributions. Therefore, various approximation techniques, such as variational inference (VI) or stochastic gradient MCMC, are often employed to infer the posterior distribution of the network parameters. Such approximations introduce inaccuracies in the inferred distributions, resulting in unreliable uncertainty estimates. In this work, we propose a hybrid approach that combines inexpensive VI and accurate HMC methods to efficiently and accurately quantify uncertainties in neural networks and neural operators. The proposed approach leverages an initial VI training on the full network. We examine the influence of individual parameters on the prediction uncertainty, which shows that a large proportion of the parameters do not contribute substantially to uncertainty in the network predictions. This information is then used to significantly reduce the dimension of the parameter space, and HMC is performed only for the subset of network parameters that strongly influence prediction uncertainties. This yields a framework for accelerating the full batch HMC for posterior inference in neural networks. We demonstrate the efficiency and accuracy of the proposed framework on deep neural networks and operator networks, showing that inference can be performed for large networks with tens to hundreds of thousands of parameters. Finally, we show that this method can effectively learn surrogates for complex physical systems by modeling the operator that maps from upstream conditions to wall-pressure data on a cone in hypersonic flow.

Bayesian inference↗

NASA NTRS1983

Modelling atmospheric aerosol backscatter at CO2 laser wavelengths. I - Aerosol properties, modeling techniques, and associated problems. II - Modeled values in the atmosphere. III - Effects of changes in wavelength and ambient conditions

The various methods of calculating the atmospheric aerosol backscattering function, beta(CO2), both from measured aerosol characteristics and from optical measurements made at other wavelengths, are discussed in detail, with limits placed on their accuracy. The most significant factor in determining beta(CO2) is found to be the aerosol size distribution and concentration; this should be known accurately for particle radii up to at least 1 micron for stratospheric particles and 5 microns for tropospheric particles. Results are then presented from the modeling of the aerosol backscattering function at a wavelength of 10.6 microns in the lowest 20 km of the atmosphere. It is found that beta(CO2) varies from 10 to the -6th per m per sr in the planetary boundary layer to less than 10 to the -11th per m per sr in the stratosphere. It is next shown that, with the exception of (NH4)2SO4-containing aerosols, whose size distributions have relatively large numbers of small particles, the variation of backscattering with CO2 wavelength is less than a factor of approximately 3. For such (NH4)2SO4 aerosol distributions, however, the variation of backscatter function with CO2 wavelengths between 9.1 and 11.1 microns may reach one order of magnitude.

Kent, G.S.↗

DOE OSTI2016

Multivariate Predictive Analytics of Wind Power Data for Robust Control of Energy Storage

Short-term forecasting is frequently identified as an important tool for the effective management of wind generation. However, forecasting errors, inherent to the point forecasts, increase requirements for energy storage and can affect optimal system operation. Probabilistic forecasts can help tackle this issue by providing a proper characterization of forecasting errors in the optimization process. This paper proposes a multivariate model of forecasting data for wind generation. Predictive uncertainty intervals of wind power can be obtained by sampling from the proposed model. The main goal is to use empirical data models without linear or Gaussian approximations of the distributional or temporal variations. The predictive modeling is utilized within a case study of an energy storage system. Finally, a modified robust convex programming is used to maintain the practical robustness and feasibility of the solution based on the sampled scenarios from the model.

17 WIND ENERGY↗

NASA NTRS1971

Dynamics of plane stellar systems.

The evolution of initially balanced rotating disks of stars is investigated with a computer model for isolated disks of stars. An isolated, initially cold balanced disk is found to be violently unstable. Adding a sufficient amount of velocity dispersion will stabilize all small-scale disturbances. However, the disks are still unstable against slowly growing long wave-length modes and after about two rotations most disks tend to assume a bar-shaped structure. It is found that the final mass distribution over most of the disk can be closely approximated by an exponential variation, irrespective of the initial mass distribution. The gravitational two-stream instability is investigated by means of a modified computer model for infinite doubly periodic stellar systems.

Hohl, F.↗

NASA NTRS1972

Dynamics of plane stellar systems.

Hohl, F.↗

NASA NTRS1990

Fuselage design for a specified Mach-sliced area distribution

A procedure for designing a fuselage having a prescribed effective area distribution computed from -90 deg Mach slices is described. This type of calculation is an essential tool in designing a complete configuration with an effective area distribution that corresponds to a desired sonic boom signature shape. Sample calculations are given for M=2 and M=3 designs. The examples include fuselages constrained to have circular cross sections and fuselages having cross sections of arbitrary shape. It is found that, for a prescribed effective area distribution having sharp variations, the iterative procedure converges to a smoothed approximation to the prescribed distribution. For a smooth prescribed area distribution, the solution is not unique.

Barger, Raymond L.↗

DOE OSTI2024

Posterior Covariance Matrix Approximations

Here, the Davis equation of state (EOS) is commonly used to model thermodynamic relationships for high explosive (HE) reactants. Typically, the parameters in the EOS are calibrated, with uncertainty, using a Bayesian framework and Markov Chain Monte Carlo (MCMC) methods. However, MCMC methods are computationally expensive, especially for complex models with many parameters. This paper provides a comparison between MCMC and less computationally expensive Variational methods (Variational Bayesian and Hessian Variational Bayesian) for computing the posterior distribution and approximating the posterior covariance matrix based on heterogeneous experimental data. All three methods recover similar posterior distributions and posterior covariance matrices. This study demonstrates that for this EOS parameter calibration application, the assumptions made in the two Variational methods significantly reduce the computational cost but do not substantially change the results compared to MCMC.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1978

Cumulative slant path rain attenuation associated with COMSTAR beacon at 28.56 GHz for Wallops Island, Virginia

Yearly, monthly, and time of day fade statistics are presented and characterized. A 19.04 GHz yearly fade distribution, corresponding to a second COMSTAR beacon frequency, is predicted using the concept of effective path length, disdrometer, and rain rate results. The yearly attenuation and rain rate distributions follow with good approximation log normal variations for most fade and rain rate levels. Attenuations were exceeded for the longest and shortest periods of times for all fades in August and February, respectively. The eight hour time period showing the maximum and minimum number of minutes over the year for which fades exceeded 12 db were approximately between 1600 to 2400, and 0400 to 1200 hours, respectively. In employing the predictive method for obtaining the 19.04 GHz fade distribution, it is demonstrated theoretically that the ratio of attenuations at two frequencies is minimally dependent of raindrop size distribution providing these frequencies are not widely separated.

Goldhirsh, J.↗

NASA NTRS1928

The Effect of a Flap and Ailerons on the N.A.C.A. M-6 Airfoil Section

This report contains the results obtained at the Langley Memorial Aeronautical Laboratory on an N. A. C. A. M-6 airfoil, fitted with a flap and ailerons, and tested in the variable density wind tunnel at a density of 20 atmospheres. Airfoil characteristics are given for the model up to 48 degree angle of attack with the flap set at various angles, and also with the ailerons set at similar angles. The approximate lift distribution and the center of pressure variation along the span are determined with the model at 18 degree angle of attack and with the ailerons displaced at 20 degrees. Approximate rolling moment and yawing moment coefficients are determined for the various aileron settings. A comparison of the calculated angles of zero lift and the calculated lift and moment coefficiencies with those observed is given in the appendix.

Higgins, George J↗

DOE OSTI2021

How Snow Aggregate Ellipsoid Shape and Orientation Variability Affects Fall Speed and Self-Aggregation Rates

Snow aggregate shapes and orientations have long been known to exhibit substantial variability. Despite this observed variability, most weather and climate prediction models use fixed power-law functions that deterministically map particle size to mass and fall speed. As such, integrated quantities like precipitation and self-aggregation rates currently ignore nonlinear effects resulting from variation in shape and orientation for aggregates of the same size. This study therefore develops an analytic framework that couples an empirically based bivariate distribution of ellipsoid shapes to classical hydrodynamic theory so as to capture an appropriate dispersion of masses, projected areas, and fall speeds for an assumed size distribution. For a fixed aggregate size, shape variations produce approximately ±0.13 m s -1 standard deviation of fall speed which increases the mass flux fall speed dispersion by more than 100% over traditional microphysics models. This increased fall speed dispersion results predominantly from shape-induced mass dispersion whereas orientation and drag dispersion play a lesser role. Shape variations can increase mass- and reflectivity-weighted fall speeds by up to 60% of traditional models whereas self-aggregation rates can increase by a factor of 100 for very small slope parameters. This implies that aggregate shape variations effectively forestall the theorized onset of fall speed distribution narrowing and subsequent quenching of the aggregation process. As a result, it is likely that secondary ice formation is necessary to prevent an ever decreasing slope parameter. The mathematical theory presented in this study is used to develop simple correction factors for snow forecast and climate models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1995

The luminosity structure and objective classification of galaxies

The luminosity structure of spiral galaxies is studied using the technique of principal component analysis. It is found that approximately 94% of the variation in the luminosity distribution of galaxies can be accounted for by just two principal components. The principal luminosity components may contain valuable information about star formation history or whatever luminosity-regulating process occurs in galaxies. Practically, these principal components provide a new approach for the investigation of the luminosity structures of galaxies and their dependence on other properties. They also serve as an excellent objective classification system for galaxies. We introduce in this paper such a classification scheme and explore its various properties. The new system shows a number of very impressive characteristics. Most important, it can well segregate virtually all the important galactic properties we tested and does so much better than the conventional morphological classification systems. Of particular interest is that some distance-dependent parameters can also be determined to a surprisingly good accuracy; for example, absolute magnitude may be determined to an accuracy of approximately 0.6 mag (yet further improvement is believed to be highly possible). Second, the system is objective, and the classification procedure can be automated to a large degree; also the new system can apply to much smaller and fainter images than do eye-based clasification systems. These properties make the new system suitable for practical application, especially on very large (and deeper) digital image catalogs. Third, the classification is expressed in dimensionless numbers, yet the simple notation bears significant and easily understandable meaning, making it easy and convenient to use. Finally, the new system has another extremely useful feature: it provides a very powerful and convenient platform not only for classification, but also for easily recording, examining, and studying the variations and correlations of galaxy properties-all these may be carried out graphically by using the C-vectors and the C-diagrams introduced in the paper. We wil also give an example to demonstrate the use of the classification system for the study of the internal extinction problem in spiral galaxies.

Han, Mingshen↗

DOE OSTI2016

Measurement and Analysis of Porosity in Al-10Si-1Mg Components Additively Manufactured by Selective Laser Melting

Aluminum alloys are candidate materials for weight critical applications because of their excellent strength and stiffness to weight ratio. However, defects such as voids decrease the strength and fatigue life of these alloys, which can limit the application of Selective Laser Melting. In this study, the average volume fraction, average size, and size distribution of pores in Al10-Si-1Mg samples built using Selective Laser Melting have been characterized. Synchrotron high energy X-rays were used to perform computed tomography on volumes of order one cubic millimeter with a resolution of approximately 1.5 μm. Substantial variations in the pore size distributions were found as a function of process conditions. Even under conditions that ensured that all locations were melted at least once, a significant number density was found of pores above 5 μm in diameter.

36 MATERIALS SCIENCE↗

NASA NTRS2023

A New View of the Lunar South Pole from the Lunar Orbiter Laser Altimeter (LOLA)

Upcoming missions to the lunar south pole require detailed maps over large areas to fully characterize landing sites locally and regionally and to place their data into proper geologic context. To that end, we enhanced the Lunar Orbiter Laser Altimeter (LOLA) altimetry dataset for the south polar region, from which we produced new maps of topography, topographic roughness, and permanently shadowed regions (PSRs). The roughness maps reveal a diversity of terrains characterized by hectometer-scale roughness which is controlled in this region primarily by cratering and downslope mass transport. The south polar region is littered with linear roughness features of order ~1 – 10 km wide and ~10s – 100s of km long hypothesized to be secondary impacts within extended ejecta rays. Non uniformities in these features could reflect variations in secondary impactor properties and/or target terrain properties. Poleward of 80° S, the PSR cumulative size-frequency distribution (CSFD) shows an approximately power-law behavior whose exponent has a spatial variation of ~10%. PSRs with areas < 1 km2 contain 15 ± 5% of the total PSR area. Finally, we studied the effect of false positives and false negatives on the accuracy of the measured PSR cumulative size-frequency distribution (CSFD) and on the area for any individual PSR. The new maps presented here have many applications in the science and exploration of the lunar south polar region, such as geologic mapping and traverse planning.

Michael K. Barker↗

DOE OSTI2015

Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis–Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler’s exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the exact posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this article: when the likelihood has some local regularity, the number of model evaluations per Markov chain Monte Carlo (MCMC) step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ordinary differential equation (ODE) and partial differential equation (PDE) inference problems, with both synthetic and real data. Supplementary materials for this article are available online.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1978

Distribution of atmospheric ozone and how it is measured

The total amount of ozone in a vertical column has been measured spectroscopically at near ultraviolet and visible wavelengths, using ground- and satellite-based instruments. The vertical distribution of ozone from the surface up to approximately 100 km has been measured by a variety of techniques - chemical and optical - and from a number of observing platforms, including balloon, rocket, and satellite platforms. The various methods presently used for determining the atmospheric ozone distribution are reviewed, along with a discussion of their advantages and disadvantages. The observed average distribution of total ozone for the period 1958-1975 shows the expected geographic and seasonal variations. The variations of total ozone, including hemispheric differences, are clearly associated with large-scale circulation processes in the lower stratosphere. Approximately ten years of observations of the vertical ozone distribution, up through the ozone maximum, also show geographic and seasonal variations strongly related to the lower stratosphere circulation. The distribution above the maximum, however, results from the interaction of photochemistry and stratospheric motions.

London, J.↗