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At least 91 records · Page 5

Simultaneous inference of equation of state parameters and unknown data errors with uncertainty quantification via hierarchical Bayesian posterior maximization

Equations of state (EOSs) are a key component in running hydrodynamic simulations as they relate the thermodynamic states for the material. The Davis reactants EOS is commonly used for modeling high explosives (HEs), and the EOS model parameters are calibrated using material specific data. The calibrations are often performed with uncertainty quantification via Bayesian inference to account for uncertainty in the data and generate ensembles of likely parameters. However, there are relatively few HE data sets to use for calibration and many are historical and lack error information. In this work, we simultaneously calibrate the Davis reactants EOS model parameters and unknown data error terms for the high explosive PBX 9501. To quantify the uncertainty in the models and the data, we use a Bayesian framework for the calibration and compute the hierarchical Bayesian posterior distribution with both a posteriori maximization approach and Markov Chain Monte Carlo. In general, we find that, given our assumptions, the two approaches result in similar calibrated parameters, posterior covariance matrices, and insights about the parameters but that the posterior maximization requires far less computational resources.

97 MATHEMATICS AND COMPUTING↗

Assimilation of Lidar Planetary Boundary Layer Height Observations

Lidar backscatter and wind retrievals of the planetary boundary layer height (PBLH) are assimilated into 22 hourly forecasts from the NASA Unified - Weather and Research Forecast (NU-WRF) model during the Plains Elevated Convection Convection at Night (PECAN) campaign on July 11, 2015 in Greensburg, Kansas, using error statistics collected from the model profiles to compute the necessary covariance matrices. Two separate forecast runs using different PBL physics schemes were employed, and comparisons with 6 independent radiosonde profiles were made for each run. Both of the forecast runs accurately predicted the PBLH and the state variable profiles within the planetary boundary layer during the early morning, and the assimilation had a small impact during this time. In the late afternoon, the forecast runs showed decreased accuracy as the convective boundary layer developed. However, assimilation of the Doppler lidar PBLH observations were found to improve the temperature and V velocity profiles relative to independent radiosonde profiles. Water vapor was overcorrected, leading to increased differences with independent data. Errors in the U velocity were made slightly larger. The computed forecast error covariances between the PBLH and state variables were found to rise in the late afternoon, leading to the larger improvements in the afternoon. This work represents the first effort to assimilate PBLH into forecast states using ensemble methods.

Andrew Tangborn↗

Remote sensing of earth terrain

A systematic approach for the identification of terrain media such as vegetation canopy, forest, and snow covered fields is developed using the optimum polarimetric classifier. The covariance matrices for the various terrain covers are computed from the theoretical models of random medium by evaluating the full polarimetric scattering matrix elements. The optimal classification scheme makes use of a quadratic distance measure and is applied to classify a vegetation canopy consisting of both trees and grass. Experimentally measured data are used to validate the classification scheme. Theoretical probability of classification error using the full polarimetric matrix are compared with classification based on single features including the phase difference between the VV and HH polarization returns. It is shown that the full polarimetric results are optimal and provide better classification performance than single feature measurements. A systematic approach is presented for obtaining the optimal polarimetric matched filter which produces maximum contrast between two scattering classes, each represented by its respective covariance matrix.

Kong, J. A.↗

Status of the WPEC subgroup 46 - Efficient and effective use of integral experiments for nuclear data validation

The present paper summarizes the current status of the activities of the on-going WPEC subgroup 46 which was the last significant initiative of Massimo before he passed away. The goal of WPEC/SG46 is to define, test and document a methodology to provide unambiguous feedback to the nuclear data evaluator community, based on the joint use of integral experiments and data assimilation techniques. Part of this effort resulted in a renewed analysis of the original Target Accuracy Requirement (TAR) exercise of WPEC/SG26, by adding more diverse nuclear systems and parameters, including reaction channels correlations and a coarser energy group structure; and making use of the progress made in the most recent evaluations in terms of both nuclear data and covariance matrices. The preliminary outcomes of the updated TAR exercise, documented by various groups worldwide are clear already: uncertainty reductions are required for many nuclide-reaction pairs in a variety of energy range if the target uncertainty requirements set by the industry are to be met, especially for k{sub eff}. The inclusion of correlations between the various reaction channels had a major impact on the magnitude of the required uncertainty reduction. Those uncertainty reductions are unlikely to be met by differential measurements alone. However, the selection of relevant integral experiment and a subsequent adjustment procedure may help meet these requirements. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Nuclear data uncertainty propagation applied to the versatile test reactor conceptual design

We report the Versatile Test Reactor (VTR) currently under development is a 300 MWth sodium-cooled fast reactor (SFR) fueled with ternary metal alloy fuel, which aims to accelerate the testing of advanced nuclear fuels, materials, instrumentation, and sensors in high flux environments that are necessary to license the next generation of advanced reactor concepts. To support the VTR design process, uncertainties associated with the nuclear data has been propagated through the reactor core neutronics calculation to global parameters of interest, such as the core multiplication factor, kinetic parameters, and various reactivity feedback coefficients, following the sensitivity based uncertainty propagation approach. By folding the sensitivity coefficients, separately computed by the generalized perturbation theory code PERSENT and Monte Carlo code Serpent 2, with the variance-covariance matrices from COMMARA-2.0, we obtain the reaction-wise, isotope-wise, and overall uncertainties for each response of interest due to nuclear data uncertainty. With Serpent 2, the statistical error of the uncertainty is obtained by propagating the statistical error of the sensitivity coefficients through the same process using a newly developed uncertainty propagation method. From both codes, the overall top uncertainty contributors are found to be the cross section of Fe-56 elastic scattering, Na-23 elastic scattering, and U 238 inelastic scattering. The large contributions of the Fe-56 elastic scattering cross sections to global parameters are due to its relatively large relative uncertainty of 5–10% in nuclear data and the large volume of Fe-containing reflector assemblies in the fairly compact VTR core design. Both codes agreed well for the overall uncertainty estimates of all responses of interest, except the delayed neutron fraction, prompt neutron generation time, and the coolant density feedback coefficient, where Serpent 2 yielded a much larger value than PERSENT due to the large statistical error of sensitivity coefficients. The calculated uncertainties are also compared to those associated with other SFR cores. Another outcome of this study is a variance-covariance matrix of reactivity coefficients, which can be used in the subsequent uncertainty propagation to the system level to investigate the impact of identified uncertainties on system responses in the safety analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Adaptive Error Estimation in Linearized Ocean General Circulation Models

Data assimilation methods are routinely used in oceanography. The statistics of the model and measurement errors need to be specified a priori. This study addresses the problem of estimating model and measurement error statistics from observations. We start by testing innovation based methods of adaptive error estimation with low-dimensional models in the North Pacific (5-60 deg N, 132-252 deg E) to TOPEX/POSEIDON (TIP) sea level anomaly data, acoustic tomography data from the ATOC project, and the MIT General Circulation Model (GCM). A reduced state linear model that describes large scale internal (baroclinic) error dynamics is used. The methods are shown to be sensitive to the initial guess for the error statistics and the type of observations. A new off-line approach is developed, the covariance matching approach (CMA), where covariance matrices of model-data residuals are "matched" to their theoretical expectations using familiar least squares methods. This method uses observations directly instead of the innovations sequence and is shown to be related to the MT method and the method of Fu et al. (1993). Twin experiments using the same linearized MIT GCM suggest that altimetric data are ill-suited to the estimation of internal GCM errors, but that such estimates can in theory be obtained using acoustic data. The CMA is then applied to T/P sea level anomaly data and a linearization of a global GFDL GCM which uses two vertical modes. We show that the CMA method can be used with a global model and a global data set, and that the estimates of the error statistics are robust. We show that the fraction of the GCM-T/P residual variance explained by the model error is larger than that derived in Fukumori et al.(1999) with the method of Fu et al.(1993). Most of the model error is explained by the barotropic mode. However, we find that impact of the change in the error statistics on the data assimilation estimates is very small. This is explained by the large representation error, i.e. the dominance of the mesoscale eddies in the T/P signal, which are not part of the 21 by 1" GCM. Therefore, the impact of the observations on the assimilation is very small even after the adjustment of the error statistics. This work demonstrates that simult&neous estimation of the model and measurement error statistics for data assimilation with global ocean data sets and linearized GCMs is possible. However, the error covariance estimation problem is in general highly underdetermined, much more so than the state estimation problem. In other words there exist a very large number of statistical models that can be made consistent with the available data. Therefore, methods for obtaining quantitative error estimates, powerful though they may be, cannot replace physical insight. Used in the right context, as a tool for guiding the choice of a small number of model error parameters, covariance matching can be a useful addition to the repertory of tools available to oceanographers.

Chechelnitsky, Michael Y.↗

Likelihood Maximization and Moment Matching in Low SNR Gaussian Mixture Models

We derive an asymptotic expansion for the log-likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for parameter estimation: the method of moments and likelihood optimizing algorithms such as Expectation-Maximization (EM). We show that likelihood optimization in the low SNR regime reduces to a sequence of least squares optimization problems that match the moments of the estimate to the ground truth moments one by one. This connection is a stepping stone towards the analysis of EM and maximum likelihood estimation in a wide range of models. A motivating application for the study of low SNR mixture models is cryo-electron microscopy data, which can be modeled as a GMM with algebraic constraints imposed on the mixture centers. We discuss the application of our expansion to algebraically constrained GMMs, among other example models of interest. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.

97 MATHEMATICS AND COMPUTING↗

Gaussian process regression constrained by boundary value problems

We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and boundary conditions, but for which only scattered observations of the source term are available. Scattered observations of the solution may also be used in the regression. The framework combines co-kriging with the linear transformation of a Gaussian process together with the use of kernels given by spectral expansions in eigenfunctions of the boundary value problem. Furthermore, it benefits from a reduced-rank property of covariance matrices. We demonstrate that the resulting framework yields more accurate and stable solution inference as compared to physics-informed Gaussian process regression without boundary condition constraints.

42 ENGINEERING↗

Ab initio calculations of overlap integrals for μ → e conversion in nuclei

The rate for μ → e conversion in nuclei is set to provide the most stringent test of lepton-flavor symmetry and a window into physics beyond the Standard Model. However, to disentangle new lepton-flavor-violating interactions, in combination with information from μ → ey and μ → 3e, it is critical that uncertainties at each step of the analysis be controlled and fully quantified. In this regard, nuclear response functions related to the coupling to neutrons are notoriously problematic, since they are not directly constrained by experiment. We address these shortcomings by combining ab initio calculations with a recently improved determination of charge distributions from electron scattering by exploiting strong correlations among charge, point-proton, and point-neutron radii and densities. We present overlap integrals for 27 Al, 48 Ca, and 48 Ti including full covariance matrices, allowing, for the first time, for a comprehensive consideration of nuclear structure uncertainties in the interpretation of μ → e experiments.

ab initio calculations↗

BEYONDPLANCK X. Planck Low Frequency Instrument frequency maps with sample-based error propagation

We present Planck Low Frequency Instrument (LFI) frequency sky maps derived within the BEYONDPLANCK framework. This framework draws samples from a global posterior distribution that includes instrumental, astrophysical, and cosmological parameters, and the main product is an entire ensemble of frequency sky map samples, each of which corresponds to one possible realization of the various modeled instrumental systematic corrections, including correlated noise, time-variable gain, as well as far sidelobe and bandpass corrections. This ensemble allows for computationally convenient end-to-end propagation of low-level instrumental uncertainties into higher-level science products, including astrophysical component maps, angular power spectra, and cosmological parameters. We show that the two dominant sources of LFI instrumental systematic uncertainties are correlated noise and gain fluctuations, and the products presented here support – for the first time – full Bayesian error propagation for these effects at full angular resolution. We compared our posterior mean maps with traditional frequency maps delivered by the Planck Collaboration, and find generally good agreement. The most important quality improvement is due to significantly lower calibration uncertainties in the new processing, as we find a fractional absolute calibration uncertainty at 70 GHz of Δg 0 /g 0 = 5 x 10 -5 , which is nominally 40 times smaller than that reported by Planck 2018. However, we also note that the original Planck 2018 estimate has a nontrivial statistical interpretation, and this further illustrates the advantage of the new framework in terms of producing self-consistent and well-defined error estimates of all involved quantities without the need of ad hoc uncertainty contributions. We describe how low-resolution data products, including dense pixel-pixel covariance matrices, may be produced from the posterior samples directly, without the need for computationally expensive analytic calculations or simulations. We conclude that posterior-based frequency map sampling provides unique capabilities in terms of low-level systematics modeling and error propagation, and may play an important role for future Cosmic Microwave Background (CMB) B-mode experiments aiming at nanokelvin precision.

79 ASTRONOMY AND ASTROPHYSICS↗

A road map to cosmological parameter analysis with third-order shear statistics: III. Efficient estimation of third-order shear correlation functions and an application to the KiDS-1000 data

Context. Third-order lensing statistics contain a wealth of cosmological information that is not captured by second-order statistics. However, the computational effort it takes to estimate such statistics in forthcoming stage IV surveys is prohibitively expensive. Aims. We derive and validate an efficient estimation procedure for the three-point correlation function (3PCF) of polar fields such as weak lensing shear. We then use our approach to measure the shear 3PCF and the third-order aperture mass statistics on the KiDS-1000 survey. Methods We constructed an efficient estimator for third-order shear statistics that builds on the multipole decomposition of the 3PCF. We then validated our estimator on mock ellipticity catalogs obtained from N -body simulations. Finally, we applied our estimator to the KiDS-1000 data and presented a measurement of the third-order aperture statistics in a tomographic setup. Results. Our estimator provides a speedup of a factor of ∼100–1000 compared to the state-of-the-art estimation procedures. It is also able to provide accurate measurements for squeezed and folded triangle configurations without additional computational effort. We report a significant detection of tomographic third-order aperture mass statistics in the KiDS-1000 data (S/N = 6.69). Conclusions. Our estimator will make it computationally feasible to measure third-order shear statistics in forthcoming stage IV surveys. Furthermore, it can be used to construct empirical covariance matrices for such statistics.

Astronomy & Astrophysics↗

Radiation characterization summary of the NETL beam port 1/5 free-field environment at the 128-inch core centerline adjacent location

The characterization of the neutron, prompt gamma-ray, and delayed gamma-ray radiation fields in the University of Texas at Austin Nuclear Engineering Teaching Laboratory (NETL) TRIGA reactor for the beam port (BP) 1/5 free-field environment at the 128-inch location adjacent to the core centerline has been accomplished. NETL is being explored as an auxiliary neutron test facility for the Sandia National Laboratories radiation effects sciences research and development campaigns. The NETL reactor is a TRIGA Mark-II pulse and steady-state, above-ground pool-type reactor. NETL is intended as a university research reactor typically used to perform irradiation experiments for students and customers, radioisotope production, as well as a training reactor. Initial criticality of the NETL TRIGA reactor was achieved on March 12, 1992, making it one of the newest test reactor facilities in the US. The neutron energy spectra, uncertainties, and covariance matrices are presented as well as a neutron fluence map of the experiment area of the cavity. For an unmoderated condition, the neutron fluence at the center of BP 1/5, at the adjacent core axial centerline, is about 8.2×10 12 n/cm 2 per MJ of reactor energy. About 67% of the neutron fluence is below 1 keV and 22% above 100 keV. The 1-MeV Damage-Equivalent Silicon (DES) fluence is roughly 1.6×10 12 n/cm 2 per MJ of reactor energy.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Uncertainty Quantification of a Light Water Pulsed-Neutron Die-Away Experiment to Thermal Neutron Scattering Laws

Thermal neutron scattering laws are important nuclear data for many nuclear science and engineering applications. Validation helps to ensure that a thermal neutron scattering law has a high quality and often employs critical benchmarks as integral experiments. Recently, pulsed-neutron die-away benchmarks have been used as an experiment to validate thermal neutron scattering laws. Herein, we evidence how this alternative integral experiment has a high sensitivity to these nuclear data by performing an uncertainty quantification analysis. The analysis randomly sampled the nuclear model parameters associated with hydrogen bound in light water thermal neutron scattering law and sampled other nuclear data that influenced the experiment’s integral parameter (e.g., elastic scattering, absorption in hydrogen and oxygen) from their respective covariance matrices. The thermal neutron scattering law caused an uncertainty in the integral parameter that reached 2.67%, which exceeds by an order of magnitude the uncertainties induced in commonly used thermal solution critical benchmarks. The validation performed here, although limited due to a poor description of the historical experiment, indicated that the ENDF/B-VIII.0 thermal neutron scattering law well predicted the integral parameter. These results motivate further benchmark and validation efforts using pulsed-neutron die-away experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Cosmic shear power spectra in practice

Cosmic shear is one of the most powerful probes of Dark Energy, targeted by several current and future galaxy surveys. Lensing shear, however, is only sampled at the positions of galaxies with measured shapes in the catalog, making its associated sky window function one of the most complicated amongst all projected cosmological probes of inhomogeneities, as well as giving rise to inhomogeneous noise. Partly for this reason, cosmic shear analyses have been mostly carried out in real-space, making use of correlation functions, as opposed to Fourier-space power spectra. Since the use of power spectra can yield complementary information and has numerical advantages over real-space pipelines, it is important to develop a complete formalism describing the standard unbiased power spectrum estimators as well as their associated uncertainties. Building on previous work, this paper contains a study of the main complications associated with estimating and interpreting shear power spectra, and presents fast and accurate methods to estimate two key quantities needed for their practical usage: the noise bias and the Gaussian covariance matrix, fully accounting for survey geometry, with some of these results also applicable to other cosmological probes. Here, we demonstrate the performance of these methods by applying them to the latest public data releases of the Hyper Suprime-Cam and the Dark Energy Survey collaborations, quantifying the presence of systematics in our measurements and the validity of the covariance matrix estimate. We make the resulting power spectra, covariance matrices, null tests and all associated data necessary for a full cosmological analysis publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗

DESI 2024 II: sample definitions, characteristics, and two-point clustering statistics

We present the samples of galaxies and quasars used for DESI 2024 cosmological analyses, drawn from the DESI Data Release 1 (DR1). We describe the construction of largescale structure (LSS) catalogs from these samples, which include matched sets of synthetic reference ‘randoms’ and weights that account for variations in the observed density of the samples due to experimental design and varying instrument performance. We detail how we correct for variations in observational completeness, the input ‘target’ densities due to imaging systematics, and the ability to confidently measure redshifts from DESI spectra. We then summarize how remaining uncertainties in the corrections can be translated to systematic uncertainties for particular analyses. We describe the weights added to maximize the signalto-noise of DESI DR1 2-point clustering measurements. We detail measurement pipelines applied to the LSS catalogs that obtain 2-point clustering measurements in configuration and Fourier space. The resulting 2-point measurements depend on window functions and normalization constraints particular to each sample, and we present the corrections required to match models to the data. We compare the configuration- and Fourier-space 2-point clustering of the data samples to that recovered from simulations of DESI DR1 and find they are, generally, in statistical agreement to within 2% in the inferred real-space over-density field. The LSS catalogs, 2-point measurements, and their covariance matrices will be released publicly with DESI DR1.

79 ASTRONOMY AND ASTROPHYSICS↗

An analytic approximation to the covariance between pre- and post-reconstruction galaxy two-point statistics

We present a simple analytic approximation for the covariance between pre-reconstruction galaxy power spectrum measurements and post-reconstruction two-point correlation functions. This cross-covariance is essential for joint analyses that combine full-shape clustering information with baryon acoustic oscillation (BAO) measurements, as commonly performed in modern spectroscopic surveys. Our model builds on the disconnected contribution to the covariance and accounts for the damping of correlations due to the BAO reconstruction process. We validate our analytic prescription against numerical simulations from the Dark Energy Spectroscopic Instrument (DESI), testing both idealized cubic geometries and realistic survey configurations including complex footprints and fiber assignment effects. Despite neglecting survey window functions in the analytic calculation, we find excellent agreement with simulation-based covariances and demonstrate that cosmological parameter constraints are virtually unchanged when using our approximation. Our results show that the pre-post cross-covariance is sufficiently small that even approximate treatments are adequate for cosmological inference, opening a pathway toward fully analytic covariance matrices for next-generation galaxy surveys.

baryon acoustic oscillations↗

Primordial non-Gaussianity from the completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey – I: Catalogue preparation and systematic mitigation

ABSTRACT We investigate the large-scale clustering of the final spectroscopic sample of quasars from the recently completed extended Baryon Oscillation Spectroscopic Survey (eBOSS). The sample contains 343 708 objects in the redshift range 0.8 < z < 2.2 and 72 667 objects with redshifts 2.2 < z < 3.5, covering an effective area of $4699\, {\rm deg}^{2}$. We develop a neural network-based approach to mitigate spurious fluctuations in the density field caused by spatial variations in the quality of the imaging data used to select targets for follow-up spectroscopy. Simulations are used with the same angular and radial distributions as the real data to estimate covariance matrices, perform error analyses, and assess residual systematic uncertainties. We measure the mean density contrast and cross-correlations of the eBOSS quasars against maps of potential sources of imaging systematics to address algorithm effectiveness, finding that the neural network-based approach outperforms standard linear regression. Stellar density is one of the most important sources of spurious fluctuations, and a new template constructed using data from the Gaia spacecraft provides the best match to the observed quasar clustering. The end-product from this work is a new value-added quasar catalogue with the improved weights to correct for non-linear imaging systematic effects, which will be made public. Our quasar catalogue is used to measure the local-type primordial non-Gaussianity in a companion paper.

79 ASTRONOMY AND ASTROPHYSICS↗

Measurements of the z > 5 Lyman-α forest flux autocorrelation functions from the extended XQR-30 data set

We present the first observational measurements of the Lyman-α (Ly α) forest flux autocorrelation functions in ten redshift bins from 5.1 ≤ z ≤ 6.0. We use a sample of 35 quasar sightlines at z > 5.7 from the extended XQR-30 data set; these data have signal-to-noise ratios of >20 per spectral pixel. We carefully account for systematic errors in continuum reconstruction, instrumentation, and contamination by damped Ly α systems. With these measurements, we introduce software tools to generate autocorrelation function measurements from any simulation. Our measurements of the smallest bin of the autocorrelation function increase with redshift when normalizing by the mean flux, $\langle{F}\rangle$. This increase may come from decreasing $\langle{F}\rangle$ or increasing mean free path of hydrogen-ionizing photons, λmfp. Recent work has shown that the autocorrelation function from simulations at z > 5 is sensitive to λmfp, a quantity that contains vital information on the ending of reionization. For an initial comparison, we show our autocorrelation measurements with simulation models for recently measured λmfp values and find good agreements. Further work in modelling and understanding the covariance matrices of the data is necessary to get robust measurements of λmfp from this data.

79 ASTRONOMY AND ASTROPHYSICS↗