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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

On the Solution of ℓ 0 -Constrained Sparse Inverse Covariance Estimation Problems

The sparse inverse covariance matrix is used to model conditional dependencies between variables in a graphical model to fit a multivariate Gaussian distribution. Estimating the matrix from data are well known to be computationally expensive for large-scale problems. Sparsity is employed to handle noise in the data and to promote interpretability of a learning model. Although the use of a convex ℓ 1 regularizer to encourage sparsity is common practice, the combinatorial ℓ 0 penalty often has more favorable statistical properties. In this paper, we directly constrain sparsity by specifying a maximally allowable number of nonzeros, in other words, by imposing an ℓ 0 constraint. Here, we introduce an efficient approximate Newton algorithm using warm starts for solving the nonconvex ℓ 0 -constrained inverse covariance learning problem. Numerical experiments on standard data sets show that the performance of the proposed algorithm is competitive with state-of-the-art methods.

$\ell_0$-Constrained↗
DOE OSTI2022

A Statistical Interpolation Code for Ocean Analysis and Forecasting

Abstract We present a data assimilation package for use with ocean circulation models in analysis, forecasting, and system evaluation applications. The basic functionality of the package is centered on a multivariate linear statistical estimation for a given predicted/background ocean state, observations, and error statistics. Novel features of the package include support for multiple covariance models, and the solution of the least squares normal equations either using the covariance matrix or its inverse—the information matrix. The main focus of this paper, however, is on the solution of the analysis equations using the information matrix, which offers several advantages for solving large problems efficiently. Details of the parameterization of the inverse covariance using Markov random fields are provided and its relationship to finite-difference discretizations of diffusion equations are pointed out. The package can assimilate a variety of observation types from both remote sensing and in situ platforms. The performance of the data assimilation methodology implemented in the package is demonstrated with a yearlong global ocean hindcast with a 1/4° ocean model. The code is implemented in modern Fortran, supports distributed memory, shared memory, multicore architectures, and uses climate and forecasts compliant Network Common Data Form for input/output. The package is freely available with an open source license from www.tendral.com/tsis/ .

Srinivasan, Ashwanth↗
NASA NTRS1976

Canonical analysis for increased classification speed and channel selection

The quadratic form can be expressed as a monotonically increasing sum of squares when the inverse covariance matrix is represented in canonical form. This formulation has the advantage that, in testing a particular class hypothesis, computations can be discontinued when the partial sum exceeds the smallest value obtained for other classes already tested. A method for channel selection is presented which arranges the original input measurements in that order which minimizes the expected number of computations. The classification algorithm was tested on data from LARS Flight Line C1 and found to reduce the sum-of-products operations by a factor of 6.7 in comparison with the conventional approach. In effect, the accuracy of a twelve-channel classification was achieved using only that CPU time required for a conventional four-channel classification.

Eppler, W.↗
NASA NTRS1992

Sulfur transformations in the sediments of a New Hampshire salt marsh

Summer sulfate reduction and sulfide and iron chemistry were monitored in marsh soils along a gradient from a creekside Spartina alterniflora region to an inland area dominated by S. patens. Sulfate reduction rates measured using S-35 increased from 0.4 in June to as much as 4.5 micro-mole/ml(sup -1)d(sup -1) in July in S. alterniflora soils with most rapid rates occurring in the upper few cm. Rates in S. patens soils were approximately equal to 5-8 fold slower with the most rapid rates occurring generally in soils deeper than 10 cm. The recovery percentage of reduced S-35 sulfur varied with depths at both locations; dissolved and acid-volatile sulfides dominating S. alterniflora regions while chromium-reducible solid phases were abundant in S. patens soils. Dissolved sulfide in S. alterniflora soils increased throughout the summer to approximately equal to 2.8 mM while sulfide in S. patens soils was abundant only in soils deeper than 15 cm. Dissolved sulfide covaried inversely with iron. Diel studies demonstrated that sulfide and iron varied approximately equal to two-fold in response to a semi-diurnal tide. Dissolved sulfide turnover was most rapid during periods of active plant growth.

Hines, Mark E.↗
NASA NTRS2002

SNC Meteorites and Martian Reservoirs

Jones first suggested that the inverse covariation of initial epsilon (Nd-143) and Sr-87/Sr-86 of the shergottites could be explained by interaction between mantle-derived magmas with another isotopic reservoir(s) (i.e., assimilation or contamination). In that model, magmas were generated in a source region that was isotopically similar to the Nakhla source and the second reservoir(s) was presumed to be crust. The text also permitted the second reservoir to be another type of mantle, but I can confirm that a second mantle reservoir was never seriously considered by that author. Other features of this model were that (i) it occurred at a particular time, 180 m.y. ago, and (ii) the interacting reservoirs had been separated at approximately 4.5 b.y. In a later paper Jones explored this mixing model more quantitatively and concluded that magmas from a Nakhla-like source region at 180 m.y. would fall on or near an isotopic Nd-Sr-Pb hyperplane defined by the shergottites. This criterion was a necessary prerequisite for the parent magma(s) of the shergottites to have initially been Nakhla-like isotopically. At this juncture, it is perhaps worthwhile to note that this mixing model was not presented to explain geochemical variations but as a justification for a 180 m.y. crystallization age for the shergottites and a 1.3 b.y. crystallization age for the nakhlites. In the mid-1980's crystallization ages estimated for Nakhla ranged from approximately 1.3 b.y to 4.5 b.y. Similarly, preferred crystallization ages for the shergottites ranged from 360 m.y., to 1.3 b.y., to 4.5 b.y. In all these models, the 180 m.y. event seen in the shergottites was deemed to be metamorphic. The fit between the Nakhla-like source region and the shergottite hyperplane was a validation both of the 1.3 b.y. igneous age of Nakhla and the 180 m.y. igneous age of the shergottites.

Jones, J. H.↗
NASA NTRS2001

Maximally Informative Statistics for Localization and Mapping

This paper presents an algorithm for localization and mapping for a mobile robot using monocular vision and odometry as its means of sensing. The approach uses the Variable State Dimension filtering (VSDF) framework to combine aspects of Extended Kalman filtering and nonlinear batch optimization. This paper describes two primary improvements to the VSDF. The first is to use an interpolation scheme based on Gaussian quadrature to linearize measurements rather than relying on analytic Jacobians. The second is to replace the inverse covariance matrix in the VSDF with its Cholesky factor to improve the computational complexity. Results of applying the filter to the problem of localization and mapping with omnidirectional vision are presented.

Deans, Matthew C.↗
DOE OSTI2020

The Sylvester Graphical Lasso (SyGlasso)

This paper introduces the Sylvester graphical lasso (SyGlasso) that captures multiway dependencies present in tensor-valued data. The model is based on the Sylvester equation that defines a generative model. The proposed model complements the tensor graphical lasso that imposes a Kronecker sum model for the inverse covariance matrix by providing an alternative Kronecker sum model that is generative and interpretable. A nodewise regression approach is adopted for estimating the conditional independence relationships among variables. The statistical convergence of the method is established, and empirical studies are provided to demonstrate the recovery of meaningful conditional dependency graphs. Here we apply the SyGlasso to an electroencephalography (EEG) study to compare the brain connectivity of alcoholic and nonalcoholic subjects. Here, we demonstrate that our model can simultaneously estimate both the brain connectivity and its temporal dependencies.

Wang, Yu↗
DOE OSTI2021

Tractable Learning in Underexcited Power Grids

Estimating the structure of physical flow networks, such as power grids, is critical to secure delivery of energy. This article discusses statistical structure estimation in power grids in the “underexcited” regime, where a subset of internal nodes has zero injection fluctuations. Prior estimation algorithms based on nodal voltages fail for such grids as the voltage covariance matrix is not invertible. Here, we propose a novel topology learning algorithm for learning underexcited general networks. Our algorithm uses physics-informed conservation laws to first identify the zero-injection buses and their neighbors, and then estimates the remaining edges in the grid. We prove the asymptotic correctness of our algorithm for grids with nonadjacent internal zero-injection nodes. More important, we theoretically analyze our algorithm’s efficacy under noisy measurements, and determine bounds on maximum noise under which asymptotically correct recovery is guaranteed. Our approach is validated through simulations with voltage samples generated on test distribution grids with real injection data and nonlinear power flow models.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1989

Analysis of modified SMI method for adaptive array weight control

An adaptive array is applied to the problem of receiving a desired signal in the presence of weak interference signals which need to be suppressed. A modification, suggested by Gupta, of the sample matrix inversion (SMI) algorithm controls the array weights. In the modified SMI algorithm, interference suppression is increased by subtracting a fraction F of the noise power from the diagonal elements of the estimated covariance matrix. Given the true covariance matrix and the desired signal direction, the modified algorithm is shown to maximize a well-defined, intuitive output power ratio criterion. Expressions are derived for the expected value and variance of the array weights and output powers as a function of the fraction F and the number of snapshots used in the covariance matrix estimate. These expressions are compared with computer simulation and good agreement is found. A trade-off is found to exist between the desired level of interference suppression and the number of snapshots required in order to achieve that level with some certainty. The removal of noise eigenvectors from the covariance matrix inverse is also discussed with respect to this application. Finally, the type and severity of errors which occur in the covariance matrix estimate are characterized through simulation.

Dilsavor, R. L.↗
NASA NTRS1977

Statistical principles of inversion theory

Statistical methods are used to deal with the inverse problem of radiative transfer. All the available information about an unknown profile can be expressed in the form of values of functions of that profile and error estimates of these values. Estimation theory shows how these values are combined to give an estimate of the unknown profile and its error covariance. Many inversion methods are expressed in this form, although the error estimate is not usually carried out. Practical applications are described, both for inversion of individual profiles, and the global analysis of satellite data.

Rodgers, C. D.↗
NASA NTRS2018

Southern California Megacity CO2, CH4, and CO Flux Estimates Using Ground- and Space-Based Remote Sensing and a Lagrangian Model

We estimate the overall CO2, CH4, and CO flux from the South Coast Air Basin using an inversion that couples Total Carbon Column Observing Network (TCCON) and Orbiting Carbon Observatory-2 (OCO-2) observations, with the Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) model and the Open-source Data Inventory for Anthropogenic CO2 (ODIAC). Using TCCON data we estimate the direct net CO2 flux from the So-CAB to be 104±26 Tg CO2 yr(exp -1) for the study period of July 2013–August 2016. We obtain a slightly higher estimate of 120±30 Tg CO2 yr(exp -1) using OCO-2 data. These CO2 emission estimates are on the low end of previous work. Our net CH4 (360±90 Gg CH4 y(exp -1)) flux estimate is in agreement with central values from previous top-down studies going back to 2010 (342–440 Gg CH4 yr(exp -1)). CO emissions are estimated at 487±122 Gg CO yr(exp -1), much lower than previous top-down estimates (1440 Gg CO yr(exp -1)). Given the decreasing emissions of CO, this finding is not unexpected. We perform sensitivity tests to estimate how much errors in the prior, errors in the covariance, different inversion schemes, or a coarser dynamical model influence the emission estimates. Overall, the uncertainty is estimated to be 25%, with the largest contribution from the dynamical model. Lessons learned here may help in future inversions of satellite data over urban areas.

Total Carbon Column Observing Network (TCCON)↗
DOE OSTI2024

TICC Clustering Library v.1.0

SAND2024-01234O TICC is a clustering algorithm that labels a sequence of data points according to numerical properties. This library is a Python implementation of the algorithm described in "Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data" (Hallac et al. 2017). It includes documentation, performance improvements, examples, and test coverage. This library allows users to automatically segment a series of multivariate data points according to their covariance—that is, the way the values at each data point are changing in relation to one another. This is useful for identifying periods in which a system is behaving. For example, if a sensor is measuring a car's velocity, steering wheel angle, braking and acceleration, TICC can determine when the car was stopped, beginning/exiting a turn, slowing or accelerating at an intersection, or driving on straight or curved roads. TICC can be applied to measure multiple quantities at known times. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525

Dalbey, Keith↗
NASA NTRS1999

Measuring Greenland Ice Mass Variation With Gravity Recovery and the Climate Experiment Gravity and GPS

The response of the Greenland ice sheet to climate change could significantly alter sea level. The ice sheet was much thicker at the last glacial maximum. To gain insight into the global change process and the future trend, it is important to evaluate the ice mass variation as a function of time and space. The Gravity Recovery and Climate Experiment (GRACE) mission to fly in 2001 for 5 years will measure gravity changes associated with the current ice variation and the solid earth's response to past variations. Our objective is to assess the separability of different change sources, accuracy and resolution in the mass variation determination by the new gravity data and possible Global Positioning System (GPS) bedrock uplift measurements. We use a reference parameter state that follows a dynamic ice model for current mass variation and a variant of the Tushingham and Peltier ICE-3G deglaciation model for historical deglaciation. The current linear trend is also assumed to have started 5 kyr ago. The Earth model is fixed as preliminary reference Earth model (PREM) with four viscoelastic layers. A discrete Bayesian inverse algorithm is developed employing an isotropic Gaussian a priori covariance function over the ice sheet and time. We use data noise predicted by the University of Texas and JPL for major GRACE error sources. A 2 mm/yr uplift uncertainty is assumed for GPS occupation time of 5 years. We then carry out covariance analysis and inverse simulation using GRACE geoid coefficients up to degree 180 in conjunction with a number of GPS uplift rates. Present-day ice mass variation and historical deglaciation are solved simultaneously over 146 grids of roughly 110 km x 110 km and with 6 time increments of 3 kyr each, along with a common starting epoch of the current trend. For present-day ice thickness change, the covariance analysis using GRACE geoid data alone results in a root mean square (RMS) posterior root variance of 2.6 cm/yr, with fairly large a priori uncertainties in the parameters and a Gaussian correlation length of 350 km. Simulated inverse can successfully recover most features in the reference present-day change. The RMS difference between them over the grids is 2.8 cm/yr. The RMS difference becomes 1.1 cm/yr when both are averaged with a half Gaussian wavelength of 150 km. With a fixed Earth model, GRACE alone can separate the geoid signals due to past and current load fairly well. Shown are the reference geoid signatures of direct and elastic effects of the current trend, the viscoelastic effect of the same trend starting from 5 kyr ago, the Post Glacial Rebound (PGR), and the predicted GRACE geoid error. The difference between the reference and inverse modeled total viscoelastic signatures is also shown. Although past and current ice mass variations are allowed the same spatial scale, their geoid signals have different spatial patterns. GPS data can contribute to the ice mass determination as well. Additional information is contained in the original.

Wu, Xiao-Ping↗
DOE OSTI2021

Pre-conditioned BFGS-based uncertainty quantification in elastic full-waveform inversion

SUMMARY Full-waveform inversion has become an essential technique for mapping geophysical subsurface structures. However, proper uncertainty quantification is often lacking in current applications. In theory, uncertainty quantification is related to the inverse Hessian (or the posterior covariance matrix). Even for common geophysical inverse problems its calculation is beyond the computational and storage capacities of the largest high-performance computing systems. In this study, we amend the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to perform uncertainty quantification for large-scale applications. For seismic inverse problems, the limited-memory BFGS (L-BFGS) method prevails as the most efficient quasi-Newton method. We aim to augment it further to obtain an approximate inverse Hessian for uncertainty quantification in FWI. To facilitate retrieval of the inverse Hessian, we combine BFGS (essentially a full-history L-BFGS) with randomized singular value decomposition to determine a low-rank approximation of the inverse Hessian. Setting the rank number equal to the number of iterations makes this solution efficient and memory-affordable even for large-scale problems. Furthermore, based on the Gauss–Newton method, we formulate different initial, diagonal Hessian matrices as pre-conditioners for the inverse scheme and compare their performances in elastic FWI applications. We highlight our approach with the elastic Marmousi benchmark model, demonstrating the applicability of pre-conditioned BFGS for large-scale FWI and uncertainty quantification.

58 GEOSCIENCES↗
NASA NTRS1972

On estimating the Venus spin vector

The improvement in spin vector and probe position estimates one may reasonably expect from the processing of such data is indicated. This was done by duplicating the ensemble calculations associated with a weighed least squares with a priori estimation technique applied to range rate data that were assumed to be unbiased and uncorrelated. The weighting matrix was assumed to be the inverse of the covariance matrix of the noise on the data. Attention is focused primarily on the spin vector estimation.

Argentiero, P. D.↗
DOE OSTI2020

Fast matrix algebra for Bayesian model calibration

In Bayesian model calibration, evaluation of the likelihood function usually involves finding the inverse and determinant of a covariance matrix. When Markov Chain Monte Carlo (MCMC) methods are used to sample from the posterior, hundreds of thousands of likelihood evaluations may be required. In this paper, we demonstrate that the structure of the covariance matrix can be exploited, leading to substantial time savings in practice. Here, we also derive two simple equations for approximating the inverse of the covariance matrix in this setting, which can be computed in near-quadratic time. The practical implications of these strategies are demonstrated using a simple numerical case study and the "quack" R package. For a covariance matrix with 1000 rows, application of these strategies for a million likelihood evaluations leads to a speedup of roughly 4000 compared to the naive implementation

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

The updated statistical inversion technique to the evaluation of Umkehr observations

In the present study the standard retrieval Umkehr method to estimate the vertical distribution of ozone was updated using a statistical approach to the mathematical inversion scheme. The vertical ozone profile covariance matrix was used as a priori information for the inverse problem. A new method of the ozonesonde data organization according to air mass types helped to improve the covariance matrix quality. A retrieval method was developed using eigenvector technique. An optimal vertical ozone profile resolution was determined from the mathematical inversion scheme analysis based on the same technique. The sun radiation transfer was accounted for multiple scattering and atmospheric sphericity in this calculation. The retrievals using actual Umkehr Dobson spectrophotometer observations were also performed to provide the comparison of the standard and updated methods with concurrent ozone sound data at Boulder U.S. The comparison has revealed that the present method has some advantages in both resolution and accuracy, as compared to the standard one, especially for the atmospheric layers below ozone maximum.

Frolov, Alexander D.↗