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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Computation and illustration of the generalized order restricted criterion (GORIC) for shape constrained spline functions

The selection of a model among alternative models that include inequality constraints is a complex task. The generalized order restricted criterion (GORIC) is a suitable approach to do so. However, the GORIC proves challenging to compute in the general case. This report discusses a number of methods to compute the GORIC and illustrates its use with a didactic example.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Polychromatic sparse image reconstruction and mass attenuation spectrum estimation via B-spline basis function expansion

We develop a sparse image reconstruction method for polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. To obtain a parsimonious measurement model parameterization, we first rewrite the measurement equation using our mass-attenuation parameterization, which has the Laplace integral form. The unknown mass-attenuation spectrum is expanded into basis functions using a B-spline basis of order one. We develop a block coordinate-descent algorithm for constrained minimization of a penalized negative log-likelihood function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and sparsity of the density map image in the wavelet domain. This algorithm alternates between a Nesterov’s proximal-gradient step for estimating the density map image and an active-set step for estimating the incident spectrum parameters. Numerical simulations demonstrate the performance of the proposed scheme.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

SineKAN: Kolmogorov-Arnold Networks using sinusoidal activation functions

Recent work has established an alternative to traditional multi-layer perceptron neural networks in the form of Kolmogorov-Arnold Networks (KAN). The general KAN framework uses learnable activation functions on the edges of the computational graph followed by summation on nodes. The learnable edge activation functions in the original implementation are basis spline functions (B-Spline). Here, we present a model in which learnable grids of B-Spline activation functions are replaced by grids of re-weighted sine functions (SineKAN). We evaluate numerical performance of our model on a benchmark vision task. We show that our model can perform better than or comparable to B-Spline KAN models and an alternative KAN implementation based on periodic cosine and sine functions representing a Fourier Series. Further, we show that SineKAN has numerical accuracy that could scale comparably to dense neural networks (DNNs). Compared to the two baseline KAN models, SineKAN achieves a substantial speed increase at all hidden layer sizes, batch sizes, and depths. Current advantage of DNNs due to hardware and software optimizations are discussed along with theoretical scaling. Additionally, properties of SineKAN compared to other KAN implementations and current limitations are also discussed.

Reinhardt, Eric↗
DOE OSTI2016

Contour interpolated radial basis functions with spline boundary correction for fast 3D reconstruction of the human articular cartilage from MR images

Purpose: The aim of this work is to demonstrate a new image processing technique that can provide a “near real-time” 3D reconstruction of the articular cartilage of the human knee from MR images which is user friendly. This would serve as a point-of-care 3D visualization tool which would benefit a consultant radiologist in the visualization of the human articular cartilage. Methods: The authors introduce a novel fusion of an adaptation of the contour method known as “contour interpolation (CI)” with radial basis functions (RBFs) which they describe as “CI-RBFs.” The authors also present a spline boundary correction which further enhances volume estimation of the method. A subject cohort consisting of 17 right nonpathological knees (ten female and seven male) is assessed to validate the quality of the proposed method. The authors demonstrate how the CI-RBF method dramatically reduces the number of data points required for fitting an implicit surface to the entire cartilage, thus, significantly improving the speed of reconstruction over the comparable RBF reconstruction method of Carr. The authors compare the CI-RBF method volume estimation to a typical commercial package (3D DOCTOR), Carr’s RBF method, and a benchmark manual method for the reconstruction of the femoral, tibial, and patellar cartilages. Results: The authors demonstrate how the CI-RBF method significantly reduces the number of data points (p-value < 0.0001) required for fitting an implicit surface to the cartilage, by 48%, 31%, and 44% for the patellar, tibial, and femoral cartilages, respectively. Thus, significantly improving the speed of reconstruction (p-value < 0.0001) by 39%, 40%, and 44% for the patellar, tibial, and femoral cartilages over the comparable RBF model of Carr providing a near real-time reconstruction of 6.49, 8.88, and 9.43 min for the patellar, tibial, and femoral cartilages, respectively. In addition, it is demonstrated how the CI-RBF method matches the volume estimation of a typical commercial package (3D DOCTOR), Carr’s RBF method, and a benchmark manual method for the reconstruction of the femoral, tibial, and patellar cartilages. Furthermore, the performance of the segmentation method used for the extraction of the femoral, tibial, and patellar cartilages is assessed with a Dice similarity coefficient, sensitivity, and specificity measure providing high agreement to manual segmentation. Conclusions: The CI-RBF method provides a fast, accurate, and robust 3D model reconstruction that matches Carr’s RBF method, 3D DOCTOR, and a manual benchmark method in accuracy and significantly improves upon Carr’s RBF method in data requirement and computational speed. In addition, the visualization tool has been designed to quickly segment MR images requiring only four mouse clicks per MR image slice.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

CALIBRATION OF THE NuSTAR HIGH-ENERGY FOCUSING X-RAY TELESCOPE

We present the calibration of the Nuclear Spectroscopic Telescope Array (NuSTAR) X-ray satellite. We used the Crab as the primary effective area calibrator and constructed a piece-wise linear spline function to modify the vignetting response. The achieved residuals for all off-axis angles and energies, compared to the assumed spectrum, are typically better than ±2% up to 40 keV and 5%–10% above due to limited counting statistics. An empirical adjustment to the theoretical two-dimensional point-spread function (PSF) was found using several strong point sources, and no increase of the PSF half-power diameter has been observed since the beginning of the mission. We report on the detector gain calibration, good to 60 eV for all grades, and discuss the timing capabilities of the observatory, which has an absolute timing of ±3 ms. Finally, we present cross-calibration results from two campaigns between all the major concurrent X-ray observatories (Chandra, Swift, Suzaku, and XMM-Newton), conducted in 2012 and 2013 on the sources 3C 273 and PKS 2155-304, and show that the differences in measured flux is within ∼10% for all instruments with respect to NuSTAR.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2019

Future climate emulations using quantile regressions on large ensembles

The study of climate change and its impacts depends on generating projections of future temperature and other climate variables. For detailed studies, these projections usually require some combination of numerical simulation and observations, given that simulations of even the current climate do not perfectly reproduce local conditions. We present a methodology for generating future climate projections that takes advantage of the emergence of climate model ensembles, whose large amounts of data allow for detailed modeling of the probability distribution of temperature or other climate variables. The procedure gives us estimated changes in model distributions that are then applied to observations to yield projections that preserve the spatiotemporal dependence in the observations. We use quantile regression to estimate a discrete set of quantiles of daily temperature as a function of seasonality and long-term change, with smooth spline functions of season, long-term trends, and their interactions used as basis functions for the quantile regression. A particular innovation is that more extreme quantiles are modeled as exceedances above less extreme quantiles in a nested fashion, so that the complexity of the model for exceedances decreases the further out into the tail of the distribution one goes. We apply this method to two large ensembles of model runs using the same forcing scenario, both based on versions of the Community Earth System Model (CESM), run at different resolutions. The approach generates observation-based future simulations with no processing or modeling of the observed climate needed other than a simple linear rescaling. The resulting quantile maps illuminate substantial differences between the climate model ensembles, including differences in warming in the Pacific Northwest that are particularly large in the lower quantiles during winter. We show how the availability of two ensembles allows the efficacy of the method to be tested with a “perfect model” approach, in which we estimate transformations using the lower-resolution ensemble and then apply the estimated transformations to single runs from the high-resolution ensemble. Finally, we describe and implement a simple method for adjusting a transformation estimated from a large ensemble of one climate model using only a single run of a second, but hopefully more realistic, climate model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

A Global Analysis of Light and Charge Yields in Liquid Xenon

Here, we present an updated model of light and charge yields from nuclear recoils in liquid xenon with a simultaneously constrained parameter set. A global analysis is performed using measurements of electron and photon yields compiled from all available historical data, as well as measurements of the ratio of the two. These data sweep over energies from keV and external applied electric fields from V/cm. The model is constrained by constructing global cost functions and using a simulated annealing algorithm and a Markov Chain Monte Carlo approach to optimize and find confidence intervals on all free parameters in the model. This analysis contrasts with previous work in that we do not unnecessarily exclude datasets nor impose artificially conservative assumptions, do not use spline functions, and reduce the number of parameters used in NEST v 0.98. Here, we report our results and the calculated best-fit charge and light yields. These quantities are crucial to understanding the response of liquid xenon detectors in the energy regime important for rare event searches such as the direct detection of dark matter particles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

TBASS: A Robust Adaptation of Bayesian Adaptive Spline Surfaces

The R package TBASS is an extension of the BASS package created by Francom and Sansó (2019). The package is used to fit a Bayesian multivariate adaptive spline to a dataset that either follows a Student’s t-distribution or has outliers. Much of the framework for TBASS is adapted from the concepts of Bayesian Multivariate Adaptive Regression Splines (BMARS), specifically the work done by Denison, Mallick, and Smith (1998). The spline function is fit using a Reversible-Jump Markov Chain Monte Carlo algorithm,. By including this more robust generalization, a dataset with outliers can be accurately fit using the BMARS model, without the possibility of overfitting or variance inflation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Temporal covariance structure of multi-spectral phenotypes and their predictive ability for end-of-season traits in maize

Vegetation indices (VIs) derived from multi-spectral imaging (MSI) platforms can be used to study properties of crop canopy, providing non-destructive phenotypes that could be used to better understand growth curves throughout the growing season. To investigate the amount of variation present in several VIs and their relationship with important end-of-season traits, genetic and residual (co)variances for VIs, grain yield and moisture were estimated using data collected from maize hybrid trials. The VIs considered were Normalized Difference Vegetation Index (NDVI), Green NDVI, Red Edge NDVI, Soil-Adjusted Vegetation Index, Enhanced Vegetation Index and simple Ratio of Near Infrared to Red (Red) reflectance. Genetic correlations of VIs with grain yield and moisture were used to fit multi-trait models for prediction of end-of-season traits and evaluated using within site/year cross-validation. To explore alternatives to fitting multiple phenotypes from MSI, random regression models with linear splines were fit using data collected in 2016 and 2017. Heritability estimates ranging from (0.10 to 0.82) were observed, indicating that there exists considerable amount of genetic variation in these VIs. Furthermore, strong genetic and residual correlations of the VIs, NDVI and NDRE, with grain yield and moisture were found. Considerable increases in prediction accuracy were observed from the multi-trait model when using NDVI and NDRE as a secondary trait. Finally, random regression with a linear spline function shows potential to be used as an alternative to mixed models to fit VIs from multiple time points.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

2-D seismic wave propagation using the distributional finite-difference method: further developments and potential for global seismology

SUMMARY We present a time-domain distributional finite-difference scheme based on the Lebedev staggered grid for the numerical simulation of wave propagation in acoustic and elastic media. The central aspect of the proposed method is the representation of the stresses and displacements with different sets of B-splines functions organized according to the staggered grid. The distributional finite-difference approach allows domain-decomposition, heterogeneity of the medium, curvilinear mesh, anisotropy, non-conformal interfaces, discontinuous grid and fluid–solid interfaces. Numerical examples show that the proposed scheme is suitable to model wave propagation through the Earth, where sharp interfaces separate large, relatively homogeneous layers. A few domains or elements are sufficient to represent the Earth’s internal structure without relying on advanced meshing techniques. We compare seismograms obtained with the proposed scheme and the spectral element method, and we show that our approach offers superior accuracy, reduced memory usage, and comparable efficiency.

Geochemistry & Geophysics↗
DOE OSTI2015

Interpolating Low Time-Resolution Forecast Data

Methodology that interpolates low time-resolution data (e.g., hourly) to high time-resolution (e.g., minutely) with variability patterns extracted from historical records. Magnitude of the variability inserted into the low time resolution data can be adjusted according to the installed capacity represented by the low time-resolution data compared to that by historical records. This approach enables detailed analysis of the impacts from wind and solar on power system intra-hour operations and balancing reserve requirements even with only hourly data. It also allows convenient creation of high resolution wind or solar generation data with various degree of variability to investigate their operational impacts. The methodology comprises of the following steps: 1. Smooth the historical data (set A) with an appropriate window length l to get its trend (set B); l can be a fraction of an hour (e.g., 15 minutes) or longer than an hour, of which the length of the variability patterns will be; 2. Extract the variable component (set C) of historical data by subtracting the smooth trend from it, i.e. set C = set A - set B 3. For each window length l of the variable component data set, find the average value x (will call it base component) of the corresponding window of the historical data set; 4. Define a series of segments (set D) that the values of data will be grouped into, e.g. (0, 0.1), (0.1, 0.2), ..., (0.9, 1.0) after normalization; Link each variability pattern to a data segment based on its corresponding base component x; after this step, each data segment should be linked to multiple variability patterns after this step; 5. Use spline function to interpolate the low time-resolution forecast data (set E) to become a high time-resolution smooth curve (set F); 6. Based on the window length l , calculate the average value y in each window length of set F; find the data segment that y belongs to; then randomly select one of the variability patterns linked to this data segment; 7. Add the selected variability pattern in each window to set F to get the high time-resolution data (set G) with variability observed from historical data set A; a coefficient k can be multiplied to the selected variability pattern to reflect the potential difference in variability between forecast set E and historical data set A caused by installation capacity and other factors. 8. After set G is constructed, variability statistics can be checked for set A and set G for comparison. Adjust the coefficient k if necessary to achieve desired variability in the reconstructed data.

Lu, Shuai↗
DOE OSTI2020

cabbi-bio/ESM-R-script

This script is intended to provide a starting point for users to implement the equivalent soil mass (ESM) approach for calculating soil organic carbon (SOC) stocks and SOC mass percentages (commonly called “SOC concentration”). The user should read this readme file and understand how the script works before using it. The script contains some basic error checking algorithms, but it cannot catch all data entry mistakes. It is possible to misuse the script and produce invalid results. The script was designed to work on individual soil cores that have been divided into three or more contiguous segments, as the cubic spline function contains four coefficients. The script has not been tested on soil cores containing fewer than three contiguous segments. If only one segment is present, interpolation will necessarily be linear rather than cubic, which is expected to result in higher predictive error (Wendt & Hauser, 2013). Considering the wide range of potential applications, the script should not be expected to function correctly in all situations. The user is encouraged to modify or rewrite the script to meet their specific needs.

von Haden, Adam↗
DOE OSTI2016

A comparison of Redlich-Kister polynomial and cubic spline representations of the chemical potential in phase field computations

Free energies play a central role in many descriptions of equilibrium and non-equilibrium properties of solids. Continuum partial differential equations (PDEs) of atomic transport, phase transformations and mechanics often rely on first and second derivatives of a free energy function. The stability, accuracy and robustness of numerical methods to solve these PDEs are sensitive to the particular functional representations of the free energy. In this communication we investigate the influence of different representations of thermodynamic data on phase field computations of diffusion and two-phase reactions in the solid state. First-principles statistical mechanics methods were used to generate realistic free energy data for HCP titanium with interstitially dissolved oxygen. While Redlich-Kister polynomials have formed the mainstay of thermodynamic descriptions of multi-component solids, they require high order terms to fit oscillations in chemical potentials around phase transitions. Here, we demonstrate that high fidelity fits to rapidly fluctuating free energy functions are obtained with spline functions. As a result, spline functions that are many degrees lower than Redlich-Kister polynomials provide equal or superior fits to chemical potential data and, when used in phase field computations, result in solution times approaching an order of magnitude speed up relative to the use of Redlich-Kister polynomials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

ASP (Adaptive Splines for Prediction) [SWR-22-66]

This software package provides functionality to fit piecewise cubic splines to model the relationship between a univariate X (independent variable) and a univariate Y (dependent variable). The output is akin to linear regression but has higher "capacity" in that it can learn more complicated relationships despite leveraging only a single predictor. It thus can learn very reasonable relationships between X and Y with minimal effort. The canonical intended use case is for predicting electric demand (Y) from temperature (X). There can be complicated, non-linear relationships between these two variables, but these can be reasonably approximated by the sum of: 1) an "aggregate" relationship between daily average temperature and daily average demand, and 2) intra-day patterns represented as hourly offsets from the daily average load. The spline functionality is used for learning a robust "aggregate" relationship without the inconvenience of manual feature engineering while still ensuring robust results. The model fitting workhorse is R's built-in smooth.spline. This package provides a suite of options for controlling how smooth.spline fits a spline to the data. In particular, it is designed to return a model with a single critical point (i.e., a single location along the domain/support where the first derivative is zero). This is to ensure that predicted changes in electric demand are always positive as temperatures become more extreme. This helps to prevent overfitting, particularly when the input data has few observations or has significant uncertainty from other sources.

Murphy, Sinnott↗
DOE OSTI2020

An arbitrarily high-order three-dimensional Cartesian-grid method for reconstructing interfaces from volume fraction fields

Here Tthis work describes a newly developed, arbitrarily high-order Cartesian-grid method for reconstructing material interfaces from a volume fraction field. The method begins by identifying all of the grid cells in the volume fraction field that are intersected by the interface and need to be approximated by the reconstruction scheme. Finite-differences are used to calculate the gradient of the volume fraction field and provide an estimate of the surface normal in all of the interfacial grid cells. Groups of connected grid cells are then identified which all have the same dominant component of the normal vector. This grouping by orientation determines the proper dependent variable to use in the surface reconstruction (e.g. for a 2D curve, this step determines if the surface will be approximated by a function of x or y). A cumulative integral over the surface is constructed and fit using b-splines for two-dimensional problems or tensor-product b-splines for three-dimensional problems. This construction allows for the interface to be recovered through application of the second fundamental theorem of calculus. Fitting the cumulative integral with $\mathscr{N}$ th-order b-splines (or tensor-product b-splines) yields an ($\mathscr{N}$-1) th-order convergence rate of the interface shape. Differentiation of the b-spline interface function(s) allows for the high-order approximation of the normal vector and curvature to be obtained directly anywhere along b-spline. Together, the proposed reconstruction technique can achieve arbitrarily high mesh convergence rates. Validation tests are presented with mesh convergence rates ranging from fourth- to tenth-order.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Quantum Optimal Control Using High Performance Computing

This feasibility study developed numerical methods for the optimal control problem for realizing logical gates in closed quantum systems, where the evolution of the state vector is governed by the time dependent Schrodinger equation. The number of parameters in the control functions is made independent of the number of time steps by expanding them in terms of B-spline basis functions, with and without carrier waves. We use an interior point gradient-based technique from the IPOPT package to minimize the gate infidelity subject to amplitude constraints on the control functions. The symplectic Stromer-Verlet scheme is used to integrate a real-valued formulation of Schrodinger's equation in time and the gradient of the gate infidelity is obtained by solving the corresponding adjoint equation. This allows all components of the gradient to be calculated at the cost of solving three Schrodinger systems, independently of the number of parameters in the control functions. The correctness of the method is verified and applied to Hamiltonians that model the dynamics of coupled super-conducting qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Image reconstruction in higher dimensions: myocardial perfusion imaging of tracer dynamics with cardiac motion due to deformation and respiration

Myocardial perfusion imaging (MPI) using slow rotating large field of view cameras requires spatiotemporal reconstruction of dynamically acquired data to capture the time variation of the radiotracer concentration. In vivo, MPI contains additional degrees of freedom involving unavoidable motion of the heart due to quasiperiodic beating and the effects of respiration, which can severely degrade the quality of the images. This work develops a technique for a single photon emission computed tomography (SPECT) that reconstructs the distribution of the radiotracer concentration in the myocardium using a tensor product of different sets of basis functions that approximately describe the spatiotemporal variation of the radiotracer concentration and the motion of the heart. In this study the temporal B-spline basis functions are chosen to reflect the dynamics of the radiotracer, while the intrinsic deformation and the extrinsic motion of the heart are described by a product of a discrete set of Gaussian basis functions. Reconstruction results are presented showing the dynamics of the tracer in the myocardium as it deforms due to cardiac beating, and is displaced due to respiratory motion. We find these results are compared with the conventional 4D-spatiotemporal reconstruction method that models only the temporal changes of the tracer activity. The higher dimensional reconstruction method proposed here improves bias, yet the signal-to-noise ratio (SNR) decreases slightly due to redistribution of the counts over the cardiac-respiratory gates. Finally, there is a trade-off between the number of gates and the number of projections per gate to achieve high contrast images.

60 APPLIED LIFE SCIENCES↗