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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 OSTI2021

Stochastically estimated covariance matrices for independent and cumulative fission yields in the ENDF/B-VIII.0 and JEFF-3.3 evaluations

A Monte-Carlo method for the generation of correlation and covariance matrices for independent and cumulative fission yields has been developed. The method uses a constrained Monte-Carlo resampling structure in order to vary evaluated fission yield libraries in a way that meets basic conservation principles. This results in the generation of correlation/covariance matrices with limited model bias and uncertainty; the matrices are primarily reflective of the evaluated fission yield uncertainties and correlations that arise from the evaluation process. This method has been applied to generate correlation and covariance matrices for all of the fissioning systems of the ENDF/B-VIII.0 and JEFF-3.3 evaluations, marking the first time such matrices have been generated for all of these systems. These covariance matrices have been published online for immediate public use. These correlation and covariance matrices can be used to improve uncertainty estimation in calculations of reactor antineutrino emission rates, decay heat problems, and nuclear forensics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1987

Errors in plate rotations as described by covariance matrices and their combination in reconstructions

The use of covariance matrices to describe the errors in plate rotations and to combine the contributions of individual plate pairs for plate reconstructions is discussed. Particular attention is given to finite rotations and the combination of covariance matrices for a circuit of successive plate pair rotations. Examples of errors in plate reconstructions in which the position of the Pacific plate relative to North America is reconstructed are presented.

Jurdy, Donna M.↗
DOE OSTI2020

Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space

In this paper, we predict the covariance matrices of both the power spectrum and the bispectrum, including full non-Gaussian contributions, redshift space distortions, linear bias effects, and shot-noise corrections, using perturbation theory (PT). To quantify the redshift-space distortion effect, we focus mainly on the monopole and quadrupole components of both the power and bispectra. We, for the first time, compute the 5- and 6-point spectra to predict the cross-covariance between the power and bispectra, and the autocovariance of the bispectrum in redshift space. Further, we test the validity of our calculations by comparing them with the covariance matrices measured from the MultiDark-Patchy mock catalogues that are designed to reproduce the galaxy clustering measured from the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue that the simple, leading-order PT works because the shot-noise corrections for the Patchy mocks are more dominant than other higher order terms we ignore. In the meantime, we confirm some discrepancies in the comparison, especially of the cross-covariance. We discuss potential sources of such discrepancies. We also show that our PT model reproduces well the cumulative signal-to-noise ratio of the power spectrum and the bispectrum as a function of maximum wavenumber, implying that our PT model captures successfully essential contributions to the covariance matrices.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1975

Computation of transform domain covariance matrices

It is often of interest in applications to compute the covariance matrix of a random process transformed by a fast unitary transform. Here, the recursive definition of fast unitary transforms is used to derive recursive relations for the covariance matrices of the transformed process. These relations lead to fast methods of computation of covariance matrices and to substantial reductions of the number of arithmetic operations required.

Fino, B. J.↗
DOE OSTI2023

Validation of semi-analytical, semi-empirical covariance matrices for two-point correlation function for early DESI data

ABSTRACT We present an extended validation of semi-analytical, semi-empirical covariance matrices for the two-point correlation function (2PCF) on simulated catalogs representative of luminous red galaxies (LRGs) data collected during the initial 2 months of operations of the Stage-IV ground-based Dark Energy Spectroscopic Instrument (DESI). We run the pipeline on multiple effective Zel’dovich (EZ) mock galaxy catalogs with the corresponding cuts applied and compare the results with the mock sample covariance to assess the accuracy and its fluctuations. We propose an extension of the previously developed formalism for catalogs processed with standard reconstruction algorithms. We consider methods for comparing covariance matrices in detail, highlighting their interpretation and statistical properties caused by sample variance, in particular, non-trivial expectation values of certain metrics even when the external covariance estimate is perfect. With improved mocks and validation techniques, we confirm a good agreement between our predictions and sample covariance. This allows one to generate covariance matrices for comparable data sets without the need to create numerous mock galaxy catalogs with matching clustering, only requiring 2PCF measurements from the data itself. The code used in this paper is publicly available at https://github.com/oliverphilcox/RascalC.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Impact of fission yield covariance matrices on decay heat uncertainty quantification with the DARWIN2 package

Although fission yields are strongly correlated, correlations between them are usually not taken into account when performing decay heat uncertainty calculations with the CEA DARWIN2 package due to the lack of reference covariance matrices associated to the JEFF-3.1.1 evaluation. However, covariance matrices for {sup 235}U and {sup 239}Pu thermal fission yields have been produced recently by the subgroup 37 of OECD/NEA Working Party on International Nuclear Data Evaluation Cooperation (WPEC). The study presented in this paper evaluates the effect of those covariances on the decay heat uncertainty calculation, both on fission burst experiments and on integral decay heat measurements that are part of the DARWIN2 experimental validation database. Although some differences are observed, partly due to the variety of models used to produce the matrices, the propagation of fission yield covariances always leads to a reduction of the decay heat uncertainty for cooling time above 10 seconds, indicating that not taking them into account is a conservative hypothesis from a safety point of view. Nevertheless, the strong impact of those covariances on the decay heat uncertainty also highlights the need of documented and consistent fission yield uncertainties and correlation data. On top of that, all the covariance matrices used for this study represent the correlation between the physical model parameters, but none of them includes the experimental correlations. An evaluation of the experimental correlations would also be of strong interest for decay heat uncertainty calculations. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1972

Power series evaluation of transition and covariance matrices.

Reexamination power series solutions to the matrix covariance differential equation and the transition differential equation. Truncation error bounds are derived which are computationally attractive and which extend previous results. Polynomial approximations are obtained by exploiting the functional equations satisfied by the transition and covariance matrices. The series-functional equation propagation technique represents a fast and accurate alternative to the numerical integration of the time-invariant transition and covariance equations.

Bierman, G. J.↗
DOE OSTI2022

Bias on tensor-to-scalar ratio inference with estimated covariance matrices

ABSTRACT We investigate simulation-based bandpower covariance matrices commonly used in cosmological parameter inferences such as the estimation of the tensor-to-scalar ratio r. We find that upper limits on r can be biased low by tens of per cent. The underestimation of the upper limit is most severe when the number of simulation realizations is similar to the number of observables. Convergence of the covariance-matrix estimation can require a number of simulations an order of magnitude larger than the number of observables, which could mean $\mathcal {O}(10\ 000)$ simulations. This is found to be caused by an additional scatter in the posterior probability of r due to Monte Carlo noise in the estimated bandpower covariance matrix, in particular, by spurious non-zero off-diagonal elements. We show that matrix conditioning can be a viable mitigation strategy in the case that legitimate covariance assumptions can be made.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Semi-analytical covariance matrices for two-point correlation function for DESI 2024 data

We present an optimized way of producing the fast semi-analytical covariance matrices for the Legendre moments of the two-point correlation function, taking into account survey geometry and mimicking the non-Gaussian effects. We validate the approach on simulated (mock) catalogs for different galaxy types, representative of the Dark Energy Spectroscopic Instrument (DESI) Data Release 1, used in 2024 analyses. We find only a few percent differences between the mock sample covariance matrix and our results, which can be expected given the approximate nature of the mocks, although we do identify discrepancies between the shot-noise properties of the DESI fiber assignment algorithm and the faster approximation (emulator) used in the mocks. Importantly, we find a close agreement (≤ 8% relative differences) in the projected errorbars for distance scale parameters for the baryon acoustic oscillation measurements. This confirms our method as an attractive alternative to simulation-based covariance matrices, especially for non-standard models or galaxy sample selections, making it particularly relevant to the broad current and future analyses of DESI data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

2D-FFTLog: efficient computation of real-space covariance matrices for galaxy clustering and weak lensing

ABSTRACT Accurate covariance matrices for two-point functions are critical for inferring cosmological parameters in likelihood analyses of large-scale structure surveys. Among various approaches to obtaining the covariance, analytic computation is much faster and less noisy than estimation from data or simulations. However, the transform of covariances from Fourier space to real space involves integrals with two Bessel integrals, which are numerically slow and easily affected by numerical uncertainties. Inaccurate covariances may lead to significant errors in the inference of the cosmological parameters. In this paper, we introduce a 2D-FFTLog algorithm for efficient, accurate, and numerically stable computation of non-Gaussian real-space covariances for both 3D and projected statistics. The 2D-FFTLog algorithm is easily extended to perform real-space bin-averaging. We apply the algorithm to the covariances for galaxy clustering and weak lensing for a Dark Energy Survey Year 3-like and a Rubin Observatory’s Legacy Survey of Space and Time Year 1-like survey, and demonstrate that for both surveys, our algorithm can produce numerically stable angular bin-averaged covariances with the flat sky approximation, which are sufficiently accurate for inferring cosmological parameters. The code CosmoCov for computing the real-space covariances with or without the flat-sky approximation is released along with this paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1997

On the Possibility of Ill-Conditioned Covariance Matrices in the First-Order Two-Step Estimator

The first-order two-step nonlinear estimator, when applied to a problem of orbital navigation, is found to occasionally produce first step covariance matrices with very low eigenvalues at certain trajectory points. This anomaly is the result of the linear approximation to the first step covariance propagation. The study of this anomaly begins with expressing the propagation of the first and second step covariance matrices in terms of a single matrix. This matrix is shown to have a rank equal to the difference between the number of first step states and the number of second step states. Furthermore, under some simplifying assumptions, it is found that the basis of the column space of this matrix remains fixed once the filter has removed the large initial state error. A test matrix containing the basis of this column space and the partial derivative matrix relating first and second step states is derived. This square test matrix, which has dimensions equal to the number of first step states, numerically drops rank at the same locations that the first step covariance does. It is formulated in terms of a set of constant vectors (the basis) and a matrix which can be computed from a reference trajectory (the partial derivative matrix). A simple example problem involving dynamics which are described by two states and a range measurement illustrate the cause of this anomaly and the application of the aforementioned numerical test in more detail.

Garrison, James L.↗
DOE OSTI2022

Covariance matrices for variance-suppressed simulations

ABSTRACT Cosmological N-body simulations provide numerical predictions of the structure of the Universe against which to compare data from ongoing and future surveys, but the growing volume of the Universe mapped by surveys requires correspondingly lower statistical uncertainties in simulations, usually achieved by increasing simulation sizes at the expense of computational power. It was recently proposed to reduce simulation variance without incurring additional computational costs by adopting fixed-amplitude initial conditions. This method has been demonstrated not to introduce bias in various statistics, including the two-point statistics of galaxy samples typically used for extracting cosmological parameters from galaxy redshift survey data, but requires us to revisit current methods for estimating covariance matrices of clustering statistics for simulations. In this work, we find that it is not trivial to construct covariance matrices analytically for fixed-amplitude simulations, but we demonstrate that ezmock (Effective Zel’dovich approximation mock catalogue), the most efficient method for constructing mock catalogues with accurate two- and three-point statistics, provides reasonable covariance matrix estimates for such simulations. We further examine how the variance suppression obtained by amplitude-fixing depends on three-point clustering, small-scale clustering, and galaxy bias, and propose intuitive explanations for the effects we observe based on the ezmock bias model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Analytic Gaussian covariance matrices for galaxy N-point correlation functions

Here, we derive analytic covariance matrices for the N-point correlation functions (NPCFs) of galaxies in the Gaussian limit. Our results are given for arbitrary N and projected onto the isotropic basis functions given by spherical harmonics and Wigner 3j symbols. A numerical implementation of the 4PCF covariance is compared to the sample covariance obtained from a set of lognormal simulations, Quijote dark matter halo catalogues, and MultiDark-Patchy galaxy mocks, with the latter including realistic survey geometry. The analytic formalism gives reasonable predictions for the covariances estimated from mock simulations with a periodic-box geometry. Furthermore, fitting for an effective volume and number density by maximizing a likelihood based on Kullback-Leibler divergence is shown to partially compensate for the effects of a nonuniform window function. Our result is recently shown to facilitate NPCF analysis on a realistic survey data.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1981

Identifiability of unknown noise covariance matrices for some special cases of a linear, time-invariant, discrete-time dynamic system

Two off-line schemes are proposed for the identification of unknown noise covariance matrices Q and R of a discrete-time dynamic system. The first scheme is based on a maximum a posteriori cost function utilizing smoothed state estimates, while the second is based on a maximum likelihood cost function utilizing filtered state estimates. Sensitivity of the cost functions to Q and R is analyzed for the following cases: (1) single-input single-output systems; (2) multiinput single-output systems; and (3) single-input multioutput systems with a diagonal R. Identifiability criteria are presented for the cases considered and demonstrated by examples.

Tsang, W. L.↗
DOE OSTI2023

Calculated covariance matrices for fission product yields using BeoH

Fission product yields (FPY) are important for a variety of applications (reactor neutronics, spent fuel, dosimetry, radiochemistry, etc.) and are currently included in many of the evaluated libraries around the world. The FPYs in the current US evaluation, ENDF/B-VIII.0, are mainly based on the 1994 evaluation of England and Rider and have only had slight updates—such as the inclusion of a 2 MeV point for 239 Pu—since their development. Additionally, only mean values and uncertainties are included in the evaluation, not full correlations. Los Alamos National Laboratory, in collaboration with several other institutes, has been working on an updated evaluation for the FPYs of 239 Pu(n,f), 235 U(n,f), 238 U(n,f), and 252 Cf(sf) using the deterministic, Hauser-Feshbach, fission fragment decay code, BeoH. BeoH calculates the FPYs consistently with many other prompt and delayed fission observables, explicitly taking into account multi-chance fission and ensuring consistency between observables. In addition to providing updated means and uncertainties for the FPYs on a pointwise energy grid from thermal to 20 MeV, we calculate correlations between all FPYs at each incident energy and across incident energies. Here, we discuss the development of these covariance matrices, differences in the correlations between FPYs based on the parameters that are included in the model optimization, and correlations across incident energies for neutron-induced fission.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1990

A numerical algorithm to propagate navigation error covariance matrices associated with generalized strapdown inertial measurement units

The design and operation of a Strapdown Navigation Analysis Program (SNAP) developed to perform covariance analysis on spacecraft inertial-measurement-unit (IMU) navigation errors are described and demonstrated. Consideration is given to the IMU modeling subroutine (with user-specified sensor characteristics), the data input procedures, state updates and the simulation of instrument failures, the determination of the nominal trajectory, the mapping-matrix and Monte Carlo covariance-matrix propagation methods, and aided-navigation simulation. Numerical results are presented in tables for sample applications involving (1) the Galileo/IUS spacecraft from its deployment from the Space Shuttle to a point 10 to the 8th ft from the center of the earth and (2) the TDRS-C/IUS spacecraft from Space Shuttle liftoff to a point about 2 h before IUS deployment. SNAP is shown to give reliable results for both cases, with good general agreement between the mapping-matrix and Monte Carlo predictions.

Weir, Kent A.↗