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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 OSTI2025

Understanding Peelle’s Pertinent Puzzle bias in generalized least squares regression through eigenspectrum analysis

Certain correlation structures in the data covariance matrix (DCM) used for generalized least squares (GLS) regression can result in biased estimates, commonly known in the field of nuclear data evaluation as Peele’s Pertinent Puzzle (PPP). This article introduces a generative, forward modeling framework within which the PPP bias is characterized through an eigenspectrum analysis of the DCM. This analysis highlights the root cause of the bias, generalizes the problem beyond the nuclear data field, and provides insight to the problem regimes where it can occur. What follows is an understanding that the bias can show up for any experimental neutron time-of-flight data for which systematic uncertainties have been quantified. Lastly, a discussion of the adaptation of cross validation approaches that require pre-whitening to incorporate the known ‘fix’ to the PPP bias in the GLS estimator.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Evaluation of a generalized least squares algorithm for infrasound beamforming with coherent background noise

Infrasonic signals of interest can occur during periods with persistent, coherent, background noise, which may be natural or anthropogenic. For high signal-to-noise (SNR) ratio transient signals, an ‘overprinting’ of the coherent background may occur, and the signal may still be detected. However, this approach fails for low SNR signals of interest, which may be obscured by coherent noise. An infrasound beamforming method based on generalized least squares (GLS) is investigated for detecting transient signals of interest in the presence of coherent and incoherent background noise. This approach relies on an estimate of the noise covariance, captured in a covariance matrix, to effectively null contributions to the array response from noisy directions of arrival. Synthetic array data is used to investigate the performance of the GLS beamformer compared to the Bartlett beamformer when coherent and incoherent backgrounds are present. Additionally, the effects of array element number and relative strength of the interfering signal on the GLS estimates is investigated. GLS empirical area under the curve estimates suggest that the beamformer can recover coherent power for a signal of interest lower in amplitude than the coherent background, but this effectiveness degrades more quickly with SNR for a four element array compared to a six or eight element infrasound array. Finally, infrasound from the Forensic Surface Experiment, a bolide signal observed at IMS array I37NO, and a volcanic signal recorded at the Alaska Volcano Observatory array ADKI are used to evaluate GLS performance on recorded data. A ten minute window was used to capture the background noise, and the coherent background signal was nulled in all three examples.

58 GEOSCIENCES↗
DOE OSTI2020

Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: A Generalized Moving Least-Squares (GMLS) approach

We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime and handle the divergence-free constraints via a generalized vector potential. This provides less coordinate-centric descriptions and enables the development of efficient numerical methods and splitting schemes for the fourth-order governing equations in terms of a system of second-order elliptic operators. Using a Hodge decomposition, we develop methods for manifolds having spherical topology. We show the methods exhibit high-order convergence rates for solving hydrodynamic flows on curved surfaces. The methods also provide general high-order approximations for the metric, curvature, and other geometric quantities of the manifold and associated exterior calculus operators. The approaches also can be utilized to develop high-order solvers for other scalar-valued and vector-valued problems on manifolds.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

First-passage time statistics on surfaces of general shape: Surface PDE solvers using Generalized Moving Least Squares (GMLS)

Here, we develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics d X t = a (X t ) dt + b(X t ) d W t . We formulate descriptions of Brownian motion and general drift-diffusion processes on surfaces. We consider statistics of the form u (x) = E x [$∫^{τ}_{0}$ g (X t ) dt ] + E x [ f (X τ )] for a domain Ω and the exit stopping time τ = inf t { t >0 | X i Ω}, where f , g are general smooth functions. For computing these statistics, we develop high-order Generalized Moving Least Squares (GMLS) solvers for associated surface PDE boundary-value problems based on Backward- Kolmogorov equations. We focus particularly on the mean First Passage Times (FPTs) given by the case f = 0, g = 1 where u (x) = E x [τ]. We perform studies for a variety of shapes showing our methods converge with high-order accuracy both in capturing the geometry and the surface PDE solutions. We then perform studies showing how statistics are influenced by the surface geometry, drift dynamics, and spatially dependent diffusivities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Generalized moving least squares vs. radial basis function finite difference methods for approximating surface derivatives

Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least squares (GMLS) and radial basis function finite differences (RBF-FD) have been shown to be effective for this task as they can give high orders of accuracy at low computational cost, and they can be applied to surfaces defined only by point clouds. However, there have yet to be any studies that perform a direct comparison of these methods for approximating surface differential operators (SDOs). The first purpose of this work is to fill that gap. For this comparison, we focus on an RBF-FD method based on polyharmonic spline kernels and polynomials (PHS+Poly) since they are most closely related to the GMLS method. Additionally, we use a relatively new technique for approximating SDOs with RBF-FD called the tangent plane method since it is simpler than previous techniques and natural to use with PHS+Poly RBF-FD. Further, the second purpose of this work is to relate the tangent plane formulation of SDOs to the local coordinate formulation used in GMLS and to show that they are equivalent when the tangent space to the surface is known exactly. The final purpose is to use ideas from the GMLS SDO formulation to derive a new RBF-FD method for approximating the tangent space for a point cloud surface when it is unknown. For the numerical comparisons of the methods, we examine their convergence rates for approximating the surface gradient, divergence, and Laplacian as the point clouds are refined for various parameter choices. We also compare their efficiency in terms of accuracy per computational cost, both when including and excluding setup costs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids

A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. Here, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5 x improvement in accuracy and allows for taking an 8 x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Selection of a Pair of Experiments to Optimally Reduce Uncertainty in Targeted Nuclear Data

We propose a novel process to select a pair of differential and integral experiments that best reduce uncertainties in targeted 239 ⁢Pu nuclear data while compressing the current nuclear data pipeline from 20 to 3 years. 239⁢ Pu nuclear data are poorly understood for neutrons in the intermediate energy range due to sparsity and uncertainty in historical experiments. New experiments targeting this range will enable better understanding of these nuclear data, but choosing the ideal experiments to conduct is challenging. Beginning with a prior distribution represented by samples of nuclear data generated from theory, generalized least squares adjustments are made to incorporate data from historical experiments. To quantify potential uncertainty reduction obtainable from a pair of candidate experiments, we compute the D-optimality criterion of the posterior covariance of intermediate energy range nuclear data compared to the equivalent covariance after additional adjustment to the pair of candidate experiments. Repeating the process for each of many candidate pairs facilitates the final selection. Results support 63⁢ Cu total cross section measurements for differential experiments and alumina and alumina/graphite configurations for integral experiments. This analysis enables choosing differential and integral experiments to be executed concurrently while shortening decision times relative to the current nuclear data pipeline.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Joint effects of climate, tree size, and year on annual tree growth derived from tree–ring records of ten globally distributed forests

Tree rings provide an invaluable long-term record for understanding how climate and other drivers shape tree growth and forest productivity. However, conventional tree-ring analysis methods were not designed to simultaneously test effects of climate, tree size, and other drivers on individual growth. This has limited the potential to test ecologically relevant hypotheses on tree growth sensitivity to environmental drivers and their interactions with tree size. Here, we develop and apply a new method to simultaneously model nonlinear effects of primary climate drivers, reconstructed tree diameter at breast height (DBH), and calendar year in generalized least squares models that account for the temporal autocorrelation inherent to each individual tree's growth. We analyze data from 3811 trees representing 40 species at 10 globally distributed sites, showing that precipitation, temperature, DBH, and calendar year have additively, and often interactively, influenced annual growth over the past 120 years. Growth responses were predominantly positive to precipitation (usually over ≥3-month seasonal windows) and negative to temperature (usually maximum temperature, over ≤3-month seasonal windows), with concave-down responses in 63% of relationships. Climate sensitivity commonly varied with DBH (45% of cases tested), with larger trees usually more sensitive. Trends in ring width at small DBH were linked to the light environment under which trees established, but basal area or biomass increments consistently reached maxima at intermediate DBH. Accounting for climate and DBH, growth rate declined over time for 92% of species in secondary or disturbed stands, whereas growth trends were mixed in older forests. These trends were largely attributable to stand dynamics as cohorts and stands age, which remain challenging to disentangle from global change drivers. By providing a parsimonious approach for characterizing multiple interacting drivers of tree growth, our method reveals a more complete picture of the factors influencing growth than has previously been possible.

generalized least squares (GLS)↗
DOE OSTI2022

An influence of manufacturing tolerances on Pin-Cell k-infinity of MOX fuel using data from the FUBILA experiment program

An influence of manufacturing tolerances (MTs) was evaluated on the pin-cell k-infinity of MOX fuel through the random sampling of CASMO5 calculations. The data from the FUBILA experiment program was used as the manufacturing parameters. For the uncertainties of element/isotope mass fractions, their covariance matrices were calculated by the generalized least square method. The total k-infinity uncertainty was 120-250 pcm (percent mille). From the breakdown of k-infinity uncertainty per materials, the MTs of fuel pellet had a dominant influence. The individual influences were also evaluated for element/isotope mass fractions, an inner/outer diameter, and a density. Those of element/isotope mass fractions were less than a few dozen pcm. Since the perturbations of fuel pellet diameter and density caused large variations to the total amount of heavy metals and effect of spatial self-shielding, they had a negative correlation with the k-infinity perturbation. On the AG3 (Al-Mg alloy) over-cladding, the inner/outer diameter perturbations had both negative and positive correlations. The negative one was due to decrease in amount of light water and the positive one was due to increase in amount of AG3. Since the effect of neutron slowing-down by light water had a dominant influence, the influence of the former negative correlation was larger than that of the latter positive correlation. It is, therefore, concluded that the consideration of the MTs that had a large influence on the effect of neutron slowing-down is important for precise quantification of the pin-cell k-infinity uncertainty of MOX fuel. (author)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

A semiparametric latent factor model for large scale temporal data with heteroscedasticity

Large scale temporal data have flourished in a vast array of applications, and their sophisticated structures, especially the heteroscedasticity among subjects with inter- and intra-temporal dependence, have fueled a great demand for new statistical models. In this paper, with covariate information, we consider a flexible model for large scale temporal data with subject-specific heteroscedasticity. Formally, the model employs latent semiparametric factors to simultaneously account for the subject-specific heteroscedasticity and the contemporaneous and/or serial correlations. The subject-specific heteroscedasticity is modeled as the product of the unobserved factor process and subject’s covariate effect, which is further characterized via additive models. For estimation, we propose a two-step procedure. First, the latent factor process and nonparametric loading are recovered through projection-based methods, and following, we estimate the regression components by approaches motivated from the generalized least squares. By scrupulously examining the non-asymptotic rates for recovering the factor process and its loading, we show the consistency and efficiency of estimated regression coefficients in the absence of prior knowledge of latent factor process and subject’s covariate effect. Here, the statistical guarantees remain valid even for finite time points that makes our method particularly appealing when the subjects significantly outnumber the observation time points. Using comprehensive simulations, we demonstrate the finite sample performance of our method, which corroborates the theoretical findings. Finally, we apply our method to a data set of air quality and energy consumption collected at 129 monitoring sites in the United States in 2015.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Evaluating 239 Pu(n,f) cross sections via machine learning using experimental data, covariances, and measurement features

In this paper, the neutron-induced 239 Pu fission cross section, 239 Pu(n,f), is evaluated from 1–20 MeV using experimental data and associated covariances while also considering information on the measurement, termed features here. For instance, methods to determine the background, sample backing material, or impurities in the sample, are explicitly taken into account in the evaluation process. To this end, outliers in the experimental data are identified with a modified version of the Hybrid Robust Support Vector Machine. In a second step, two machine learning methods (logistic regression with elastic net regularization and random forest regression with SHAP feature importance metric) are used to highlight measurement features that are common among many of the outlying data points. Based on this analysis, penalty uncertainties are added to the experimental covariances of outlying data points that have outlier measurement features and are put through the generalized-least-squares evaluation. The resulting evaluated mean values and covariances differ distinctly from those data evaluated without the penalty uncertainties. These results highlight that certain measurement features should be more closely examined.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Machine Learning to Select Experiments Driven by Fundamental Science and Applications for Targeted Nuclear Data Improvement

This work describes a blueprint for a process that accelerates progress in science by quantitatively answering the following question: What is the optimal combination of fundamental-science and application-driven experiments to maximally reduce pertinent data uncertainties? Answering this question entails solving a high-dimensional and complex optimization problem that is best solved with advanced statistic techniques often classified as machine learning. We apply this process within the framework of nuclear data with the aim to select an experiment combination that will reduce uncertainties in 239 Pu nuclear data for neutron energies between 1 and 600 keV. In this field, fundamental-physics driven data, called differential, look at one nuclear physics observable at a time. They are contrasted to application-driven, integral, data where one or few resulting values inform a broad set of nuclear data across several nuclides and energies. The candidates for integral experiments are criticality measurements that were refined by a genetic algorithm to be maximally sensitive to 239 Pu fission cross sections in the desired energy range. Twenty-three candidate differential experiments were investigated and span multiple nuclear physics observables (e.g., total, capture cross sections) for isotopes appearing in the integral experiments. The optimal combination among these candidate experiments was investigated via generalized least squares fitting, augmented with Gaussian processes to ameliorate statistical irregularities in data, and the D-optimality criterion. The latter evaluates for each pair of candidates the joint reduction in uncertainties of all 12200 nuclear data appearing in the integral experiments compared to the knowledge we have from 168 past experiments, theory, and nuclear data. We chose as differential measurements those that investigate 63 Cu and 239 Pu total cross sections, based on D-optimality rank and feasibility constraints. Two integral (criticality) experiments were selected: An experiment with Al 2 ⁢O 3 and graphite interleaved with Pu and a thick Cu reflector explores 1–30 keV, while we target the 30–600 keV range with an experiment that swaps boron in place of graphite with a different geometry.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Thermal adaptation of soil microbial growth traits in response to chronic warming

ABSTRACT Adaptation of soil microbes due to warming from climate change has been observed, but it remains unknown what microbial growth traits are adaptive to warming. We studied bacterial isolates from the Harvard Forest Long-Term Ecological Research site, where field soils have been experimentally heated to 5°C above ambient temperature with unheated controls for 30 years. We hypothesized that Alphaproteobacteria from warmed plots have (i) less temperature-sensitive growth rates; (ii) higher optimum growth temperatures; and (iii) higher maximum growth temperatures compared to isolates from control plots. We made high-throughput measurements of bacterial growth in liquid cultures over time and across temperatures from 22°C to 37°C in 2–3°C increments. We estimated growth rates by fitting Gompertz models to the growth data. Temperature sensitivity of growth rate, optimum growth temperature, and maximum growth temperature were estimated by the Ratkowsky 1983 model and a modified Macromolecular Rate Theory (MMRT) model. To determine evidence of adaptation, we ran phylogenetic generalized least squares tests on isolates from warmed and control soils. Our results showed evidence of adaptation of higher optimum growth temperature of bacterial isolates from heated soils. However, we observed no evidence of adaptation of temperature sensitivity of growth and maximum growth temperature. Our project begins to capture the shape of the temperature response curves, but illustrates that the relationship between growth and temperature is complex and cannot be limited to a single point in the biokinetic range. IMPORTANCE Soils are the largest terrestrial carbon sink and the foundation of our food, fiber, and fuel systems. Healthy soils are carbon sinks, storing more carbon than they release. This reduces the amount of carbon dioxide released into the atmosphere and buffers against climate change. Soil microbes drive biogeochemical cycling and contribute to soil health through organic matter breakdown, plant growth promotion, and nutrient distribution. In this study, we determined how soil microbial growth traits respond to long-term soil warming. We found that bacterial isolates from warmed plots showed evidence of adaptation of optimum growth temperature. This suggests that increased microbial biomass and growth in a warming world could result in greater carbon storage. As temperatures increase, greater microbial activity may help reduce the soil carbon feedback loop. Our results provide insight on how atmospheric carbon cycling and soil health may respond in a warming world.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Bayesian Monte Carlo Evaluation Framework for Imperfect Nuclear Data

Bayesian evaluation of resolved resonance region (RRR) nuclear data has historically been carried out using the generalized least squares (GLS) formalism, as implemented in, e.g., SAMMY. We have recently developed a prototype of Bayesian Monte Carlo (BMC) evaluation framework, implemented using a Markov Chain Monte Carlo (MCMC) method with a Metropolis-Hastings (MH) acceptance criterion. This was done in order to remove the approximations underlying the conventional GLS evaluations, namely, the linear approximation, and the approximation that all probability density functions (PDFs) are of the normal kind. Recent works by others have used similar stochastic approaches to quantify cross section uncertainties from ENDF evaluated co-variances, and/or, from integral benchmark data, but those have not been conceived as an evaluation framework like the one presented here.

97 MATHEMATICS AND COMPUTING↗