Search NASA⌕ Search

SEARCH · Search NASA

Results for “Kernel density estimator”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Monte Carlo estimates of sensitivities to geometric perturbations for shielding problems using kernel density estimators - 25605

A Monte Carlo method to estimate the sensitivity of reaction rates like dose and flux spectra to geometric perturbations using kernel density estimators is demonstrated for shielding problems. The method is used to estimate the sensitivity of the spectrum emitted from a Cf-252 source at the center of an iron sphere as well as the sensitivity of the dose due to Cf-252 neutrons shielded using various materials. Results are compared against reference solutions obtained using Monte Carlo direct perturbations with central differences, with agreement within 5% and 3σ for the majority of results. The results indicate that a bandwidth that is 10-20% of the shielding thickness produces accurate results with statistically insignificant bias for the chosen test problems. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2021

Nonparametric, data-based kernel interpolation for particle-tracking simulations and kernel density estimation

Traditional interpolation techniques for particle tracking include binning and convolutional formulas that use pre-determined (i.e., closed-form, parameteric) kernels. In many instances, the particles are introduced as point sources in time and space, so the cloud of particles (either in space or time) is a discrete representation of the Green’s function of an underlying PDE. As such, each particle is a sample from the Green’s function; therefore, each particle should be distributed according to the Green’s function. In short, the kernel of a convolutional interpolation of the particle sample “cloud” should be a replica of the cloud itself. This idea gives rise to an iterative method by which the form of the kernel may be discerned in the process of interpolating the Green’s function. When the Green’s function is a density, this method is broadly applicable to interpolating a kernel density estimate based on random data drawn from a single distribution. We formulate and construct the algorithm and demonstrate its ability to perform kernel density estimation of skewed and/or heavy-tailed data including breakthrough curves.

42 ENGINEERING↗
DOE OSTI2025

The effective number of parameters in kernel density estimation

We devise a new formula for measuring the effective degrees of freedom (EDoF) in kernel density estimation (KDE). Starting from the orthogonal polynomial sequence (OPS) expansion for the ratio of the empirical to the oracle density, we show how convolution with the kernel leads to a new OPS with respect to which one may express the resulting KDE. The expansion coefficients of the two OPS systems can then be related via a kernel sensitivity matrix, which leads to a natural oracle definition of EDoF through the trace operator. Asymptotic properties of the (empirical) plug-in EDoF are worked out through influence functions, and connections with other empirical EDoFs are established. Minimization of Kullback-Leibler divergence is investigated as an alternative to integrated squared error based bandwidth selection rules, yielding a new normal scale rule. The methodology, which arises from a proper oracle formulation and is not restricted to convolution kernels, suggests the possibility of a new bandwidth selection rule based on an information criterion such as AIC.

bandwidth selection↗
DOE OSTI2019

Kernel Density Estimators for SAMPLER Analyses [Slides]

This presentation discusses Sampler, specifically in terms of uncertainty quantification and states that for many simulation tasks nominal input parameters have complicated influence on the uncertainty in the final result. Sampler provides a convenient means to perform stochastic uncertainty quantification, brute force sampling parameter space and tallying changes in outputs, and it can be coupled with any SCALE modules. Perturbed responses can be collected and analyzed with standard statistical measures; however, two problems have been identified. The first problem is that for Monte Carlo simulations the individual response uncertainties are ignored, and the second problem is that features of distributions are easily hidden in histograms. They found that the solution is to add Kernel Density Estimator (KDE) analysis to the Sampler output. In conclusion, Sampler is a unique tool for stochastic uncertainty propagation, and it can be coupled with any module in SCALE. Current functionality is limited to histograms, and it may not adequately account for sample uncertainties and/or not adequately display underlying distribution features. Work is in progress to implement KDE in the Sampler module and no additional flagging is needed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Next-Cycle Optimal Dilute Combustion Control via Online Learning of Cycle-to-Cycle Variability Using Kernel Density Estimators

Dilute combustion using exhaust gas recirculation (EGR) presents a cost-effective method for increasing the efficiency of spark-ignition (SI) engines. However, the maximum amount of EGR that can be used at a given condition is limited by a rapid increment of cycle-to-cycle variability (CCV). This study describes a methodology to design a model-based stochastic optimal controller to adjust the cycle-to-cycle fuel injection quantity in order to reduce CCV and further extend the dilute limit. Given the complexity and chaotic nature of combustion events, the controller was enhanced with online learning in order to identify the statistical properties of combustion efficiency, which are needed to generate predictions for next-cycle events. This study showed that a kernel density estimator (KDE) can be used to learn the combustion properties in real time and can be incorporated into the feedback policy in order to calculate the optimal control command. Experimental results suggested that the dilute limit can be extended from 18.5% to 21% EGR fraction at an operating condition relevant for highway cruising. Additionally, the proposed controller can achieve a large CCV reduction with less fuel enrichment compared to previous methods, overall contributing to an increase in 0.2% indicated fuel conversion efficiency.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2018

A Non-Parametric Density Estimation Approach to Measuring Beam Cooling in MICE

The goal of the international Muon Ionization Cooling Experiment (MICE) is to demonstrate muon beam ionization cooling for the first time. It constitutes a key part of the R&D towards a future neutrino factory or muon collider. The intended MICE precision requires the development of analysis tools that can account for any effects (e.g., optical aberrations) which may lead to inaccurate cooling measurements. Non-parametric density estimation techniques, in particular, kernel density estimation (KDE), allow very precise calculations of the muon beam phase-space density and its increase as a result of cooling. In this study, kernel density estimation technique and its application to measuring the reduction in MICE muon beam phase-space volume is investigated.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Efficient screening of rare large pit anomalies on polished surfaces using a minimalist sampling scheme

Lawrence Livermore National Laboratory (LLNL) has made significant strides in generating clean energy through its inertial confinement fusion (ICF) experiments. These experiments rely on high-density carbon (HDC) coated shells to encapsulate the fusion fuel. The success of these experiments is heavily dependent on the surface quality of these shells, as even minor imperfections, such as deep pits, can negatively impact fusion yield. Ensuring the required smoothness involves an extensive surface-finishing process that spans approximately 20 stages, making it both time-intensive and resource-demanding. A critical challenge in this process is the need for high-resolution scans to detect rare deep pits, which can be costly and impractical if performed on every shell. This highlights the necessity of developing more efficient scanning methods to optimize time and cost without compromising accuracy. To address these challenges, we introduce a novel approach that employs the multivariate Dvoretzky–Kiefer–Wolfowitz (DKW) inequality to provide a probabilistic upper bound on the error in estimating pit distribution characteristics via a Kernel Density Estimator (KDE). This error bound enables efficient and reliable estimation of pit distribution characteristics at a specified statistical confidence level using a minimal number of surface scans. The integrated DKW-KDE approach was validated through surface-finishing experiments across two batches of HDC-coated shells, demonstrating consistent and robust performance across multiple stages of the surface-finishing experiments. The validation studies suggest that the integrated DKW-KDE approach achieves comparable accuracy in estimating the risk of deleterious large pits with six scans, thus conserving time and resources. Further evaluations show that performance remains consistent across batches and over multiple polishing stages. In conclusion, based on these findings, one can leverage the minimal-scan insights to strategically improve the bottleneck inspection process, thus enhancing the productivity and quality of shell polishing and similar challenging manufacturing processes.

Inertial confinement fusion↗
DOE OSTI2021

Next-Cycle Optimal Fuel Control for Cycle-to-Cycle Variability Reduction in EGR-Diluted Combustion

In this simulation study, cycle-to-cycle fuel control was used to reduce CCV by injecting additional fuel in operating conditions with sporadic misfires and partial burns. An optimal control policy was proposed that utilizes 1) a physics-based model that tracks in-cylinder gas composition and 2) a one-step-ahead prediction of the combustion efficiency based on a kernel density estimator. The optimal solution, however, presents a tradeoff between the reduction in combustion CCV and the increase in fuel injection quantity required to stabilize the charge. Such a tradeoff can be ad- just by a single parameter embedded in the cost function.

Maldonado, BryanP. [Oak Ridge National Lab. (ORNL)↗
DOE OSTI2023

A Multi-Fidelity Gaussian Process Regression Method for Probabilistic Wind Farm Power Curve Estimation

Accurate estimation of the power curve for wind turbines or wind farms is crucial to ensure their efficient operation and management. However, conventional methods for power curve estimation rely either on expensive and infrequent measurements or on low-quality numerical simulations. Moreover, the majority of previous studies on power curve estimation for wind turbines or wind farms focused on deterministic estimation, which provides a point estimate of the relationship between wind speed and power generation. Nevertheless, the deterministic approach fails to consider the inherent uncertainty associated with wind energy production resulting from varying turbine characteristics. This can lead to inaccurate power generation estimation and suboptimal decisions regarding energy management. In this paper, a kernel density estimation (KDE) based Multi-Fidelity Gaussian Process Regression (MFGPR) model is proposed to fuse theoretical power curve data and the ground true measurements to create a mapping of wind speed and wind power. By conducting a case study on an actual wind farm in China, the efficacy of the proposed MFGPR model was demonstrated in characterizing the variability of wind power. The probabilistic MFGPR model was also able to generate confidence intervals that encompassed the measured power, thereby improving the accuracy and confidence in wind power estimation or wind resource assessment. Overall, the proposed MFGPR model offers a reliable approach to integrate high-fidelity ground measurements and theoretical power curve data, resulting in precise wind resource assessment and power estimation.

Gaussian process regression↗
DOE OSTI2021

Noise and error analysis and optimization in particle-based kinetic plasma simulations

In this paper we analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We begin by describing kernel density estimation for continuous values of the spatial variable x, expressing the kernel in a form in which its shape and width are represented separately. The covariance matrix of the noise in the density is computed, first for uniform true density. The bandwidth of the covariance matrix C(x,y) is related to the width of the kernel. A feature that stands out is the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step; they also lead to the property ∫C(x,y)dy = 0. We investigate the effect of these negative correlations on the electric field computed by Gauss's law, finding that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge, leading to a covariance matrix of the electric field with variance significantly reduced relative to that of a Brownian process. For non-constant density, p(x), still with continuous x, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length l, determined by the density and its second derivative, and kernel width h, having too few particles within h leads to too much variance; for h that is large relative to l, there is too much smoothing of the density. The optimum between these two limits is found by BVO. For kernels of the same width, it is shown that this optimum (minimum) is weakly sensitive to the kernel shape. Next, we repeat the analysis for x discretized on a grid. In this case the charge deposition rule is determined by a particle shape. An important property to be respected in the discrete system is the exact preservation of total charge on the grid; this property is necessary to ensure that the electric field is equal at both ends, consistent with periodic boundary conditions. We find that if the particle shapes satisfy a partition of unity property, the particle charge deposited on the grid is conserved exactly. Further, if the particle shape is expressed as the convolution of a kernel with another kernel that satisfies the partition of unity, then the particle shape obeys the partition of unity. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. Furthermore, we show results relaxing the approximations used to do BVO optimization analytically, by doing numerical computations of the total error as a function of the kernel width, on a grid in x. The comparison between numerical and analytical results shows good agreement over a range of particle shapes. We discuss the practical implications of our results, including the criteria for design and implementation of computationally efficient particle shapes that take advantage of the developed theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Density estimation techniques for multiscale coupling of kinetic models of the plasma material interface

In this work we analyze two classes of Density-Estimation techniques which can be used to consistently couple different kinetic models of the plasma-material interface, intended as the region of plasma immediately interacting with the first surface layers of a material wall. In particular, we handle the general problem of interfacing a continuum multi-species Vlasov-Poisson-BGK plasma model to discrete surface erosion models. The continuum model solves for the energy-angle distributions of the particles striking the surface, which are then driving the surface response. A modification to the classical Binary-Collision Approximation (BCA) method is here utilized as a prototype discrete model of the surface, to provide boundary conditions and impurity distributions representative of the material behavior during plasma irradiation. The numerical tests revealed the superior convergence properties of Gaussian Mixture Models over Kernel Density Estimation methods, with Gaussian Mixtures and Epanechnikov-KDEs both being up to two orders of magnitude faster than Gaussian-KDEs. The methodology here presented allows a self-consistent treatment of the plasma-material interface in magnetic fusion devices, including both the near-surface plasma (plasma sheath and presheath) in magnetized conditions, and surface effects such as sputtering, back-scattering, and ion implantation. The same coupling techniques can also be utilized for other discrete material models such as Molecular Dynamics.

42 ENGINEERING↗
DOE OSTI2022

A functional global sensitivity measure and efficient reliability sensitivity analysis with respect to statistical parameters

Sensitivity analysis and reliability assessment are two important aspects of structural and system safety. Epistemic uncertainty with respect to probabilistic model of input parameters due to lack of knowledge is present in many scarce-data applications and complicates the characterization of uncertainty in model response. In this article, we present two importance measures to evaluate the impact of distribution parameters on the probability distribution function (PDF) of the output and the failure probability. The epistemic uncertainty associated with the distribution parameters is modeled as random variables. Additionally, a modified extended polynomial chaos expansion (MEPCE) approach is introduced in which aleatory and epistemic random variables are modeled and propagated simultaneously while allowing the separate assessment for any single epistemic variable. A MEPCE-based kernel density estimation (KDE) construction provides a composite map from each epistemic variable to the response PDF. The functional global sensitivity index of the PDF with respect to the distribution parameters is thus derived, as a function of output, which is both more informative and more efficient than standard scalar sensitivity measures. Reliability sensitivity indices can be readily evaluated by integrating the global sensitivity index function over the failure zone. Three illustrative examples are used to demonstrate the proposed methodology.

42 ENGINEERING↗
DOE OSTI2022

Improved Data Interpretation through Identification of Time Series Periodicity Changes

Analysis and interpretation of time series data is easiest when the data values occur at uniform intervals in time, but actual data may have differing data sampling frequencies, such as monthly and daily readings. Applying data analysis techniques, such as smoothing, to such a data set may not give a representative result between time segments. The ability to automatically distinguish time segments of differing data frequency would provide a means for applying data analysis independently to each segment, though a suitable blending at segment boundaries would be required. A method for detecting frequency changes was developed and applied to Gaussian and median smoothing of hydraulic head data from groundwater wells at the U.S. Department of Energy Hanford Site in southeastern Washington state. The process identifies time segments of high-frequency (daily) or low-frequency (greater than daily) data using adjusted-bandwidth Gaussian kernel density estimation and a threshold value, which are further refined to address small blocks of low-frequency data within larger blocks of high-frequency data. User-selectable levels of smoothing are then applied independently to the time segments prior to combining the segment results for a single smoothed data set. This time segment identification approach provides effective low- and high-frequency data separation, which provides a method to apply data analysis independently to each time segment.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Novel Data-based Stochastic Distribution Control for Non-Gaussian Stochastic Systems

In this note, we present a novel data-based approach to investigate the non-Gaussian stochastic distribution control problem. As the motivation of this note, the existing methods have been summarised regarding to the drawbacks, for example, neural network weights training for unknown stochastic distribution and so on. To overcome these disadvantages, a new transformation for dynamic probability density function is given by kernel density estimation using interpolation. Based upon this transformation, a representative model has been developed while the stochastic distribution control problem has been transformed into an optimisation problem. Then, data-based direct optimisation and identification-based indirect optimisation have been proposed. In addition, the convergences of the presented algorithms are analysed and the effectiveness of these algorithms has been evaluated by numerical examples. In summary, the contributions of this note are as follows: 1) a new data-based probability density function transformation is given; 2) the optimisation algorithms are given based on the presented model; and 3) a new research framework is demonstrated as the potential extensions to the existing stochastic distribution control.

42 ENGINEERING↗
DOE OSTI2020

eFESTA: Ensemble Feature Exploration with Surface Density Estimates

We propose surface density estimate (SDE) to model the spatial distribution of surface features-isosurfaces, ridge surfaces, and streamsurfaces-in 3D ensemble simulation data. The inputs of SDE computation are surface features represented as polygon meshes, and no field datasets are required (e.g., scalar fields or vector fields). The SDE is defined as the kernel density estimate of the infinite set of points on the input surfaces and is approximated by accumulating the surface densities of triangular patches. We also propose an algorithm to guide the selection of a proper kernel bandwidth for SDE computation. An ensemble Feature Exploration method based on Surface densiTy EstimAtes (eFESTA) is then proposed to extract and visualize the major trends of ensemble surface features. For an ensemble of surface features, each surface is first transformed into a density field based on its contribution to the SDE, and the resulting density fields are organized into a hierarchical representation based on the pairwise distances between them. The hierarchical representation is then used to guide visual exploration of the density fields as well as the underlying surface features. We demonstrate the application of our method using isosurface in ensemble scalar fields, Lagrangian coherent structures in uncertain unsteady flows, and streamsurfaces in ensemble fluid flows.

Computational modeling↗
DOE OSTI2022

Quasar Identification Using Multivariate Probability Density Estimated from Nonparametric Conditional Probabilities

Nonparametric estimation for a probability density function that describes multivariate data has typically been addressed by kernel density estimation (KDE). A novel density estimator recently developed by Farmer and Jacobs offers an alternative high-throughput automated approach to univariate nonparametric density estimation based on maximum entropy and order statistics, improving accuracy over univariate KDE. This article presents an extension of the single variable case to multiple variables. The univariate estimator is used to recursively calculate a product array of one-dimensional conditional probabilities. In combination with interpolation methods, a complete joint probability density estimate is generated for multiple variables. Good accuracy and speed performance in synthetic data are demonstrated by a numerical study using known distributions over a range of sample sizes from 100 to 10 6 for two to six variables. Performance in terms of speed and accuracy is compared to KDE. The multivariate density estimate developed here tends to perform better as the number of samples and/or variables increases. As an example application, measurements are analyzed over five filters of photometric data from the Sloan Digital Sky Survey Data Release 17. The multivariate estimation is used to form the basis for a binary classifier that distinguishes quasars from galaxies and stars with up to 94% accuracy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

GalaxyFlow: upsampling hydrodynamical simulations for realistic mock stellar catalogues

ABSTRACT Cosmological N-body simulations of galaxies operate at the level of ‘star particles’ with a mass resolution on the scale of thousands of solar masses. Turning these simulations into stellar mock catalogues requires ‘upsampling’ the star particles into individual stars following the same phase-space density. In this paper, we introduce two new upsampling methods. First, we describe GalaxyFlow, a sophisticated upsampling method that utilizes normalizing flows to both estimate the stellar phase-space density and sample from it. Secondly, we improve on existing upsamplers based on adaptive kernel density estimation (KDE), using maximum likelihood estimation to fine-tune the bandwidth for such algorithms in a way that improves both the density estimation accuracy and upsampling results. We demonstrate our upsampling techniques on a neighbourhood of the Solar location in two simulated galaxies: Auriga 6 and h277. Both yield smooth stellar distributions that closely resemble the stellar densities seen in the Gaia DR3 catalogue. Furthermore, we introduce a novel multimodel classifier test to compare the accuracy of different upsampling methods quantitatively. This test confirms that GalaxyFlow more accurately estimates the density of the underlying star particles than methods based on KDE, at the cost of being more computationally intensive.

Lim, Sung Hak (ORCID:0000000330981092)↗
DOE OSTI2024

Experimental and Computational Evaluation of Lipidomic In-Source Fragmentation as a Result of Postionization with Matrix-Assisted Laser Desorption/Ionization

Matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI-MSI) can provide spatially resolved molecular information about a sample. Recently, a postionization approach (MALDI-2) has been commercially integrated with MALDI-MSI, allowing for bettered sensitivity and consequent improved spatial resolution. While advantages of MALDI-2 have previously been established, we demonstrate here statistically increased in-source fragmentation (ISF) results from postionization with a commercial instrument. Via lipid standard analyses, known MALDI ISF pathways (e.g., loss of trimethylamine) were statistically increased in MALDI-2 compared to MALDI-1 (65–172% increase in fragmentation). Gas phase molecular modeling with density functional theory estimated that the most-weighted virtual orbitals to excite within lipids involve ester and phosphate bonds. Protonated lipid excitation energies are furthermore red-shifted compared to those of other adduct types [e.g., 254 nm for protonated PC(16:0/18:1)] and approach the MALDI-2 laser energy (266 nm). Analysis of rat brain homogenate detected statistically more positive-ion mode peaks with MALDI-2 (1090) than that with MALDI-1 (719), where Kernel density estimations showed that the majority of this enhancement occurs with low m/z ions (i.e., m/z 75–500). Taken together with the lipid standard data, these observations may indicate ISF due to postionization. Finally, while artifact contributions from matrix blanks were also noted, both experimental and computational data sets suggest that the overall extent of ISF is statistically increased in MALDI-2 compared to MALDI-1.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗