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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

On the Lebesgue constant of weighted Leja points for Lagrange interpolation on unbounded domains

Here, this work focuses on weighted Lagrange interpolation on an unbounded domain and analyzes the Lebesgue constant for a sequence of weighted Leja points. The standard Leja points are a nested sequence of points defined on a compact subset of the real line and can be extended to unbounded domains with the introduction of a weight function w:R → [0,1]. Due to a simple recursive formulation in one dimension, such abscissas provide a foundation for high-dimensional approximation methods such as sparse grid collocation, deterministic least squares and compressed sensing. Just as in the unweighted case of interpolation on a compact domain, we use results from potential theory to prove that the Lebesgue constant for the Leja points grows subexponentially with the number of interpolation nodes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Tungsten anode spectral model using interpolating cubic splines: Unfiltered x-ray spectra from 20 kV to 640 kV

Purpose: Monte Carlo methods were used to generate lightly filtered high resolution x-ray spectra spanning from 20 kV to 640 kV. Methods: X-ray spectra were simulated for a conventional tungsten anode. The Monte Carlo N-Particle eXtended radiation transport code (MCNPX 2.6.0) was used to produce 35 spectra over the tube potential range from 20 kV to 640 kV, and cubic spline interpolation procedures were used to create piecewise polynomials characterizing the photon fluence per energy bin as a function of x-ray tube potential. Using these basis spectra and the cubic spline interpolation, 621 spectra were generated at 1 kV intervals from 20 to 640 kV. The tungsten anode spectral model using interpolating cubic splines (TASMICS) produces minimally filtered (0.8 mm Be) x-ray spectra with 1 keV energy resolution. The TASMICS spectra were compared mathematically with other, previously reported spectra. Results: Using pairedt-test analyses, no statistically significant difference (i.e., p > 0.05) was observed between compared spectra over energy bins above 1% of peak bremsstrahlung fluence. For all energy bins, the correlation of determination (R{sup 2}) demonstrated good correlation for all spectral comparisons. The mean overall difference (MOD) and mean absolute difference (MAD) were computed over energy bins (above 1% of peak bremsstrahlung fluence) and over all the kV permutations compared. MOD and MAD comparisons with previously reported spectra were 2.7% and 9.7%, respectively (TASMIP), 0.1% and 12.0%, respectively [R. Birch and M. Marshall, “Computation of bremsstrahlung x-ray spectra and comparison with spectra measured with a Ge(Li) detector,” Phys. Med. Biol. 24, 505–517 (1979)], 0.4% and 8.1%, respectively (Poludniowski), and 0.4% and 8.1%, respectively (AAPM TG 195). The effective energy of TASMICS spectra with 2.5 mm of added Al filtration ranged from 17 keV (at 20 kV) to 138 keV (at 640 kV); with 0.2 mm of added Cu filtration the effective energy was 9 keV at 20 kV and 169 keV at 640 kV. Conclusions: Ranging from 20 kV to 640 kV, 621 x-ray spectra were produced and are available at 1 kV tube potential intervals. The spectra are tabulated at 1 keV intervals. TASMICS spectra were shown to be largely equivalent to published spectral models and are available in spreadsheet format for interested users by emailing the corresponding author (JMB)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Improved method for temporally interpolating radiosonde profiles in the convective boundary layer

A significantly improved technique for temporally interpolating radiosonde (RS) profiles of potential temperature and water vapor mixing ratio in the planetary boundary layer during daytime is introduced. The key innovation of this technique is its operation on a height grid normalized with the planetary boundary layer height. This study utilized a three-month dataset of three-hourly soundings from the Atmospheric Radiation Measurement Facility's Southern Great Plains site. The technique was evaluated for convective boundary layer cases, with the necessary boundary layer height data obtained from a ground-based infrared spectrometer. A total of 79 comparisons were conducted between reference soundings and interpolated profiles that did and did not employ height normalization. The results demonstrated a substantial improvement in the representation of interpolated profiles using the new technique, characterized by enhanced correlation, improved amplitude representation, and reduced bias for potential temperature, as well as improved correlation and reduced bias for water vapor mixing ratio.

convective boundary layer↗
NASA NTRS2019

Optical Flow for Intermediate Frame Interpolation of Multispectral Geostationary Satellite Data

Applications in areas such as weather tracking and modeling, ecosystem monitoring, wildfire detection, and land-cover change are heavily dependent on spatial and temporal resolutions of satellite observations. However, there are typically trade-offs between spatial and temporal resolutions in dataset selection. For instance, geostationary weather tracking satellites are designed to take snapshots many times throughout the day but sensor hardware limits data collection. In this work we tackle this limitation, developing a method for temporal upsampling of multi-spectral satellite imagery using optical flow video interpolation deep convolutional neural networks. The presented model, extends Super SloMo (SSM) from single optical flow estimates to multichannel where flows are computed per band. We apply this technique on 8 multi-spectral bands of NOAA/NASA's GOES-16 mesoscale dataset to temporally enhance full disk hemispheric snapshots from 15 minutes to 1 minute. Through extensive experimentation, we show SSM vastly outperforms the linear interpolation baseline and that multichannel optical flows improves performance on GOES-16. A visual analysis of optical flow vectors clearly identifies hurricanes and large-scale atmospheric dynamics. Furthermore, we discuss challenges and open questions related to optical flow and temporal interpolation of multispectral geostationary satellite imagery.

Optical Flow↗
DOE OSTI2016

On-the-fly Doppler Broadening with Probability Table Interpolation for Unresolved Resonance Region in RMC

With the rapid development of computational power and parallel algorithms, Monte Carlo method has been widely investigated and used in neutron transport simulations due to its advantages in geometry modelling and usage of continuous energy point-wise cross sections. Nowadays the road has been paved to couple Monte Carlo codes with thermal-hydraulics codes to make multi-physics calculations. One of the most important aspects of thermal-hydraulics feedback is the detailed temperature distribution, which demands temperature dependent cross sections in neutron transport simulations. The conventional pre-generated cross section libraries at each temperature point are no longer feasible for detailed temperature distributions because of tremendous memory footprint. Hence, different on-the-fly Doppler broadening methods have been proposed for resolved resonance energy region and thermal energy region, such as the interpolation, regress model fitting, multipole representation (MPR), target motion sampling (TMS) and different integration algorithms based on Doppler broadening equation. Compared to resolved resonance energy region and thermal energy region, the representation of cross sections in unresolved resonance region is slightly different. As a result of the limitation of experiment measurements, the overlapped resonances cannot be distinguished from each other and the statistic average resonance parameters are given in the evaluated nuclear data file. In early applications, infinite-dilute pointwise cross sections were obtained from average parameters and were directly used in neutron simulations. However, it was proven that these infinite-dilute pointwise cross sections cannot capture the energy self-shielding effect, thus leading to an overestimate of reaction rates and usually an underestimate of k{sub eff} owing to the increased absorption rates and increased scattering probability to energy below unresolved resonance region where the capture-to-fission ratio is typically higher. This phenomenon is of great importance especially for problems where there is a considerable flux in unresolved resonance region. Then the probability table method was put forward by Levitt to take energy self-shielding effect into account, which provides probability distribution function of cross sections in unresolved resonance region instead of specific cross section values. The probability distribution function is presented in the form of tables and the mean values are equal to the infinite dilution cross sections. To obtain the temperature dependent cross sections in unresolved energy region, there are two different methods. One is to calculate cross sections directly from average resonance parameters and their statistical distributions , which is effective and precise but time-consuming. The other is to interpolate between pre-generated probability table files, which is much more efficient. In this paper, on-the-fly Doppler broadening of cross sections in unresolved resonance regions based on probability tables interpolation was implemented in RMC codes as a supplement to on-the-fly Doppler broadening for resolved resonance energy region and thermal region, which is based on the integration of Doppler broadening equation. The results of criticality calculation and depletion calculation show that on-the-fly Doppler broadening for the whole energy region is accurate and efficient. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Direct interpolative construction of the discrete Fourier transform as a matrix product operator

The quantum Fourier transform (QFT), which can be viewed as a reindexing of the discrete Fourier transform (DFT), has been shown to be compressible as a low-rank matrix product operator (MPO) or quantized tensor train (QTT) operator. However, the original proof of this fact does not furnish a construction of the MPO with a guaranteed error bound. Meanwhile, the existing practical construction of this MPO, based on the compression of a quantum circuit, is not as efficient as possible. We present a simple closed-form construction of the QFT MPO using the interpolative decomposition, with guaranteed near-optimal compression error for a given rank. This construction can speed up the application of the QFT and the DFT, respectively, in quantum circuit simulations and QTT applications. We also connect our interpolative construction to the approximate quantum Fourier transform (AQFT) by demonstrating that the AQFT can be viewed as an MPO constructed using a different interpolation scheme.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Modified multi-dimensional q-deformed Newton oscillators: Algebra, interpolating statistics and thermodynamics

Highlights: • A new quasi-particle algebra is proposed. • The invariance group of the algebra constructed is shown. • The algebra constructed leads to the interpolating statistics. • Anyonic behavior is studied in two dimensions. - Abstract: In this work, we present a new algebraic modelby constructing the modified multi-dimensional q-deformed bosonic and fermionic Newton oscillator algebras. This construction leads effectively to describe interpolating statistics, which can be used to approach the properties of quasi-particle excitations occurring in many-body interacting quantum systems. It is shown that the model algebras are endowed with the SU{sub φ}(d)- and SU{sub θ}(d)-symmetries, where φ and θ are real parameters describing the special phase shifts between two different modes of the models. Particular emphasis is given to the two-dimensional case, which reveals a suitable framework for analyzing anyonic behavior of the models. Furthermore, we discuss the effects of deformation on the general thermodynamical and statistical properties of gas models of these interpolating statistics particles such as the q-deformed statistical distribution function and the equation of state in two and three dimensions. Finally, we concisely point out other possible physical applications of the present deformed (quasi)particle models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

The effects of introducing elasticity using different interpolation schemes to the grand potential phase field model

Introducing elastic energy in the phase field method has been shown to influence interfacial energy, depending on the elastic interpolation scheme. This study investigates the impact of the elastic energy when using a grand potential-based phase field method, comparing the result of Khachaturyan’s strain interpolation scheme (KHS) and Voight-Taylor’s elastic energy interpolation scheme (VTS). The KHS model leads to a decrease in the interfacial energy, while the VTS model leads to an increase. The change in interfacial energy is greater with the VTS model than the KHS model, which suggests that the KHS model is more appropriate to limit the artificial impact of the elastic energy on the interfacial energy. When the contribution at the interface is not negligible, it is shown that both the microstructure evolution kinetics and the equilibrium microstructure can be influenced by the choice of the elastic scheme being used. In addition, this paper shows that the grand potential model might not be appropriate when the system requires the introduction of a composition-dependent term in the elastic energy contribution. This limitation is due to the need for an explicit and invertible relation between the total potential and the composition.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Stabilized bases for high-order, interpolation semi-Lagrangian, element-based tracer transport

In a computational fluid model of the atmosphere, the advective transport of trace species, or tracers, can be computationally expensive. For efficiency, models often use semi-Lagrangian advection methods. High-order interpolation semi-Lagrangian (ISL) methods, in particular, can be extremely efficient, if the problem of property preservation specific to them can be addressed. Atmosphere models often use geometrically and logically nonuniform grids for efficiency and, as a result, element-based discretizations. Such grids and discretizations make stability a particular problem for ISL methods. Generally, high-order, element-based ISL methods that use the natural polynomial interpolant associated with a nodal finite-element discretization are unstable. Here, we derive new bases having order of accuracy up to nine, with positive nodal weights, that stabilize the element-based ISL method. We use these bases to construct the linear advection operator in the property-preserving Interpolation Semi-Lagrangian Element-based Transport (Islet) method. Then we discuss key software implementation details. Finally, we show performance results for the Energy Exascale Earth System Model's atmosphere dynamical core, comparing the original and new transport methods. These simulations used up to 27,600 Graphical Processing Units (GPU) on the Oak Ridge Leadership Computing Facility's Summit supercomputer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Dimensional interpolation for metallic hydrogen

In this work, we employ a simple and mostly accurate dimensional interpolation formula using dimensional limits D = 1 and D = ∞ to obtain D = 3 ground-state energy of metallic hydrogen. We also present results describing the phase transitions for different symmetries of three-dimensional structure lattices. The interpolation formula not only predicts fairly accurate energies but also predicts a correct functional form of the energy as a function of the lattice parameters. That allows us to calculate different physical quantities such as the bulk modulus, Debye temperature, and critical transition temperature, from the gradient and the curvature of the energy curve as a function of the lattice parameters. These theoretical calculations suggest that metallic hydrogen is a likely candidate for high temperature superconductivity. The dimensional interpolation formula is robust and might be useful to obtain the energies of complex many-body systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Interpolating individual line-of-sight neutron spectrometer measurements onto the “sky” at the National Ignition Facility (NIF)

Nuclear diagnostics provide measurements of inertial confinement fusion implosions used as metrics of performance for the shot. The interpretation of these measurements for shots with low mode asymmetries requires a way of combining the data to produce a “sky map” where the individual line-of-sight values are used to interpolate to other positions in the sky. These interpolations can provide information regarding the orientation of the low mode asymmetries. We describe the interpolation method, associated uncertainties, and correlations between different metrics, e.g., Tion, down scatter ratio, and hot-spot velocity direction. This work is also related to recently reported studies [H. G. Rinderknecht et al., Phys. Rev. Lett. 124, 145002 (2020) and K. M. Woo et al., Phys. Plasmas 27, 062702 (2020)] of low mode asymmetries. We report an analysis that makes use of a newly commissioned line of sight, a scheme for incorporating multiple neutron spectrum measurement types, and recent work on the sources of implosion asymmetry to provide a more complete picture of implosion performance.

Hartouni, E. P. (ORCID:0000000198694351)↗
DOE OSTI2025

Least H 2 norm updating of quadratic interpolation models for derivative-free trust-region algorithms

One particular class of derivative-free optimization algorithms is trust-region algorithms based on quadratic models given by the under-determined interpolation. Different techniques in updating the quadratic model from iteration to iteration will give different interpolation models. We propose a new way to update the quadratic model by minimizing the $H^{2}$ norm of the difference between neighboring quadratic models. The motivation for applying the $H^{2}$ norm is given. The theoretical properties of our new updating technique are also presented. We propose the projection in the sense of $H^{2}$ norm and the interpolation error analysis of our model function. We obtain the coefficients of the quadratic model function using the Karush–Kuhn–Tucker (KKT) conditions. Numerical results show the advantages of our model on the test set considered, and the derivative-free algorithms based on our least $H^{2}$ norm updating quadratic model functions can solve test problems with fewer function evaluations than the algorithm based on the least Frobenius norm updating model and the other compared methods.

derivative-free optimization↗
DOE OSTI2022

Interpolating between small- and large-$\mathscr{g}$ expansions using Bayesian model mixing

Bayesian model mixing (BMM) is a statistical technique that can be used to combine models that are predictive in different input domains into a composite distribution that has improved predictive power over the entire input space. We explore the application of BMM to the mixing of two expansions of a function of a coupling constant $\mathscr{g}$ that are valid at small and large values of $\mathscr{g}$ respectively. This type of problem is quite common in nuclear physics, where physical properties are straightforwardly calculable in strong and weak interaction limits or at low and high densities or momentum transfers, but difficult to calculate in between. Interpolation between these limits is often accomplished by a suitable interpolating function, e.g., Padé approximants, but it is then unclear how to quantify the uncertainty of the interpolant. We address this problem in the simple context of the partition function of zero-dimensional Φ 4 theory, for which the (asymptotic) expansion at small $\mathscr{g}$ and the (convergent) expansion at large $\mathscr{g}$ are both known. We consider three mixing methods: linear mixture BMM, localized bivariate BMM, and localized multivariate BMM with Gaussian processes. Here, we find that employing a Gaussian process in the intermediate region between the two predictive models leads to the best results of the three methods. The methods and validation strategies we present here should be generalizable to other nuclear physics settings.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning

This repository contains python scripts and numerical data accompanying the paper: "Leveraging Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning," Tyler Chang, Andrew Gillette, Romit Maulik, 2024. The following subdirectories are included: - "interpolants" contains our interpolation scripts used for all studies - "experiments" contains scripts demonstrating our experiments with synthetic data - "airfoil" contains scripts demonstrating our experiments with the publicly available UIUC airfoil dataset. Further instructions are provided in READMEs within the sub-directories.

Gillette, Andrew↗
DOE OSTI2021

Algebraic Multigrid with Optimal Interpolation and Adaptive Smoothers (Final Report)

The project team continued with work on developing new bootstrap AMG techniques for solving symmetric and non-symmetric PDE systems. The focus of this work is to derive more reliable measures of the quality of the coarse space set than the convergence rate of the standard F-relaxation form of CR and a more robust form of interpolation than the so-called ideal form. We have successfully derived a sharp variant of CR that gives the precise convergence rate of the two-grid method using this optimal interpolation and, in addition, we derived a new Generalized Bootstrap AMG setup algorithm that uses as its main tool a multilevel eigensolver for the generalized eigenvalue problem involving the system matrix and the symmetrized smoother. In addition, the approach allows for general block smoothers with overlap. We have applied the method to scalar diffusion problems, linear elasticity, and Maxwell’s and the method shows marked improvements over existing AMG methods for these problems. In addition, the team worked with CASC members on new forms of ideal AMG interpolation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Scalable Interpolation on GPUs for Thermal Fluids Applications

The need for efficient interpolation arises in many use cases for spectral element simulations. Towards this end, we present a fast and robust GPU-enable interpolation utility for NekRS, a spectral-element, Navier-Stokes solver. This utility is based on the findpts and findpts eval routines from the gslib library. To demonstrate the functionality, we added support for particle tracking. The GPU implementation of the interpolation allows for tracking 100 times more particles for the same computational cost.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1973

Curvilinear bicubic spline fit interpolation scheme

Modification of the rectangular bicubic spline fit interpolation scheme so as to make it suitable for use with a polar grid pattern. In the proposed modified scheme the interpolation function is expressed in terms of the radial length and the arc length, and the shape of the patch, which is a wedge or a truncated wedge, is taken into account implicitly. Examples are presented in which the proposed interpolation scheme was used to reproduce the equations of a hemisphere.

Chi, C.↗
NASA NTRS1974

Error in interpolation and choice of the range of discreteness in measurements in a hydrophysical field

Errors in interpolation and the choosing of the range of discreteness when making measurements in a hydrophysical field are discussed. Equations for optimum interpolating based on the theory of linear interpolation of stationary random sequences are presented; analogous equations are derived for the case of data collected at stations located at the apices of a right triangle.

Zudin, O. F.↗