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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Isotropic N-point basis functions and their properties

Isotropic functions of positions r 1 , r 2 ,..., r N , i.e. functions invariant under simultaneous rotations of all the coordinates, are conveniently formed using spherical harmonics and Clebsch–Gordan coefficients. An orthonormal basis of such functions provides a formalism suitable for analyzing isotropic distributions such as those that arise in cosmology, for instance in the clustering of galaxies as revealed by large-scale structure surveys. The algebraic properties of the basis functions are conveniently expressed in terms of 6-j and 9-j symbols. Finally, the calculation of relations among the basis functions is facilitated by 'Yutsis' diagrams for the addition and recoupling of angular momenta.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1978

A method of weighted residuals with trigonometric basis functions for sound transmission in circular ducts

The method of weighted residuals (MWR) in the form of a modified Galerkin method with trigonometric basis functions is used to compute the transmission of sound in an axisymmetric duct. The method is used to generate the axial wave number for uniform ducts. These are compared with exact solutions generated by a formal eigenvalue routine in the hard-wall case and a Runge-Kutta integration eigenvalue scheme in the soft-wall case. The method is applicable to both flow and no-flow cases.

Vo, P. T.↗
DOE OSTI2024

Constrained curve fitting for semi-parametric models with radial basis function networks

Common to many analysis pipelines in lattice gauge theory and the broader scientific discipline is the need to fit a semi-parametric model to data. We propose a fit method that utilizes a radial basis function network to approximate the non-parametric component of such models. The approximate parametric model is fit to data using the basin hopping global optimization algorithm. Parameter constraints are enforced through Gaussian priors. The viability of our method is tested by examining its use in a finite-size scaling analysis of the $q$-state Potts model and $p$-state clock model with $q=2,3$ and $p=4,\infty$.

Peterson, Curtis T.↗
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↗
NASA NTRS1994

Optimal Space Station solar array gimbal angle determination via radial basis function neural networks

The potential for excessive plume impingement loads on Space Station Freedom solar arrays, caused by jet firings from an approaching Space Shuttle, is addressed. An artificial neural network is designed to determine commanded solar array beta gimbal angle for minimum plume loads. The commanded angle would be determined dynamically. The network design proposed involves radial basis functions as activation functions. Design, development, and simulation of this network design are discussed.

Clancy, Daniel J.↗
DOE OSTI2021

Estimating basis functions in massive fields under the spatial mixed effects model

Abstract Spatial prediction is commonly achieved under the assumption of a Gaussian random field by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For massive datasets, fixed rank kriging using the expectation–maximization algorithm for estimation has been proposed as an alternative to the usual but computationally prohibitive kriging method. The method reduces computation cost of estimation by redefining the spatial process as a linear combination of basis functions and spatial random effects. A disadvantage of this method is that it imposes constraints on the relationship between the observed locations and the knots. We develop an alternative method that utilizes the spatial mixed effects model, but allows for additional flexibility by estimating the range of the spatial dependence between the observations and the knots via an alternating expectation conditional maximization algorithm. Experiments show that our methodology improves estimation without sacrificing prediction accuracy while also minimizing the additional computational burden of extra parameter estimation. The methodology is applied to a temperature dataset archived by the United States National Climate Data Center, with improved results over previous methodology.

Pazdernik, Karl↗
DOE OSTI2022

Time-series forecasting using manifold learning, radial basis function interpolation, and geometric harmonics

We address a three-tier numerical framework based on nonlinear manifold learning for the forecasting of high-dimensional time series, relaxing the “curse of dimensionality” related to the training phase of surrogate/machine learning models. At the first step, we embed the high-dimensional time series into a reduced low-dimensional space using nonlinear manifold learning (local linear embedding and parsimonious diffusion maps). Then, we construct reduced-order surrogate models on the manifold (here, for our illustrations, we used multivariate autoregressive and Gaussian process regression models) to forecast the embedded dynamics. Finally, we solve the pre-image problem, thus lifting the embedded time series back to the original high-dimensional space using radial basis function interpolation and geometric harmonics. The proposed numerical data-driven scheme can also be applied as a reduced-order model procedure for the numerical solution/propagation of the (transient) dynamics of partial differential equations (PDEs). In conclusion, we assess the performance of the proposed scheme via three different families of problems: (a) the forecasting of synthetic time series generated by three simplistic linear and weakly nonlinear stochastic models resembling electroencephalography signals, (b) the prediction/propagation of the solution profiles of a linear parabolic PDE and the Brusselator model (a set of two nonlinear parabolic PDEs), and (c) the forecasting of a real-world data set containing daily time series of ten key foreign exchange rates spanning the time period 3 September 2001–29 October 2020.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1998

Ensembles of radial basis function networks for spectroscopic detection of cervical precancer

The mortality related to cervical cancer can be substantially reduced through early detection and treatment. However, current detection techniques, such as Pap smear and colposcopy, fail to achieve a concurrently high sensitivity and specificity. In vivo fluorescence spectroscopy is a technique which quickly, noninvasively and quantitatively probes the biochemical and morphological changes that occur in precancerous tissue. A multivariate statistical algorithm was used to extract clinically useful information from tissue spectra acquired from 361 cervical sites from 95 patients at 337-, 380-, and 460-nm excitation wavelengths. The multivariate statistical analysis was also employed to reduce the number of fluorescence excitation-emission wavelength pairs required to discriminate healthy tissue samples from precancerous tissue samples. The use of connectionist methods such as multilayered perceptrons, radial basis function (RBF) networks, and ensembles of such networks was investigated. RBF ensemble algorithms based on fluorescence spectra potentially provide automated and near real-time implementation of precancer detection in the hands of nonexperts. The results are more reliable, direct, and accurate than those achieved by either human experts or multivariate statistical algorithms.

Cervix Neoplasms/pathology↗
NASA NTRS1999

Thermal Remote Sensing: A Powerful Tool in the Characterization of Landscapes on a Functional Basis

Thermal remote sensing instruments can function as environmental measuring tools, with capabilities leading toward new directions in functional landscape ecology. Theoretical deduction and phenomenological observation leads us to believe that the second law of thermodynamics requires that all dynamically systems develop in a manner which dissipates gradients as rapidly as possible within the constraints of the system at hand. The ramification of this requirement is that dynamical systems will evolve dissipative structures which grow and complexify over time. This perspective has allowed us to develop a framework for discussing ecosystem development and integrity. In the context of this framework we have developed measures of development and integrity for ecosystems. One set of these measures is based on destruction of the exergy content of incoming solar energy. More developed ecosystems will be more effective at dissipating the solar gradient (destroying its exergy content). This can be measured by the effective surface temperature of the ecosystem on a landscape scale. These surface temperatures are measured using airborne thermal scanners such as the Thermal Infrared Multispectral Scanner (TIMS) and the Airborne Thermal/Visible Land Application Sensor(ATLAS) sensors. An analysis of agriculture and forest ecosystems will be used to illustrate the concept of ecological thermodynamics and the development of ecosystems.

Jeffrey, Luvall C.↗
DOE OSTI2024

A new computational framework for spinor-based relativistic exact two-component calculations using contracted basis functions

Here, a new computational framework for spinor-based relativistic exact two-component (X2C) calculations is developed using contracted basis sets with a spin–orbit contraction scheme. Generally contracted, j-adapted basis sets of p-block elements using primitive functions in the correlation-consistent basis sets are constructed for the X2C Hamiltonian with atomic mean-field spin–orbit integrals (the X2CAMF scheme). The contraction coefficients are taken from atomic X2CAMF Hartree–Fock spinors, thereby following the simple concept of a linear combination of atomic orbitals. Benchmark calculations of spin–orbit splittings, equilibrium bond lengths, and harmonic vibrational frequencies demonstrate the accuracy and efficacy of the j-adapted spin–orbit contraction scheme.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1983

Supplemental basis functions for the second transition row elements

It is noted that for molecular calculations, the basis sets presented by Huzinaga (1977) need to be augmented by (1) 5p functions to describe the 5s - 5p near degeneracy; (2) a diffuse 4d function to provide for a balanced description of the 5s2 4dn, 5s1 4d(n+1), and 4d(n+2) states of the atom; and (3) a set of 4f functions to correlate the 4d functions. Here, the diffuse 4d function is similar in function to the diffuse 3d function for the first transition row elements recommended by Hay (1977). A table is included giving the optimized values for the diffuse 4d, the 5p, and 4f (STO exponent) functions. The diffuse 4d function and the 5p functions are optimized at the SCF level on the basis of the 5s1 4d(n+1) state (except for Pd, which is optimized for the 4d10 state) and the 5s1 5p1 4dn state, respectively. The table also gives the energies and the atomic symmetries for each of the SCF calculations.

Walch, S. P.↗
NASA NTRS2007

Zernike-like Orthogonal Basis Functions for Wavefront Characterization over Sampled, Irregular Apertures

For optical systems with circular apertures, wavefronts are often analyzed using Zernike polynomials, and individual Zernike functions are associated with familiar optical aberrations. For systems with noncircular apertures, or in practical situations in which wavefronts are measured at a limited number of points in the aperture, the Zernike polynomials are no longer an orthogonal basis for the measured data. Although there are an endless number of ways to create a basis for such measured data, a "Zernike-like" basis is useful to connect with our experience with the usual optical aberrations. In this paper, the steps required to identify a Zernike-like basis for wavefronts over sampled, irregular apertures are presented, based on the Gram-Schmidt orthogonalization technique. The benefits of analyzing optical wavefronts using an orthogonal basis specific to an optical system's aperture shape and wavefront sampling, instead of using the traditional Zernike polynomials, are detailed in two examples, from image-based wavefront sensing on a segmented-aperture telescope (the James Webb Space Telescope Testbed Telescope at Ball Aerospace) and from interferometer characterization for surface metrology of a hexagonal mirror segment.

Aronstein, David L.↗
DOE OSTI2021

Time evolution of ML-MCTDH wavefunctions. I. Gauge conditions, basis functions, and singularities

We derive a family of equations-of-motion (EOMs) for evolving multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) wavefunctions that, unlike the standard ML-MCTDH EOMs, never require the evaluation of the inverse of singular matrices. All members of this family of EOMs make use of alternative static gauge conditions than those used for standard ML-MCTDH. These alternative conditions result in an expansion of the wavefunction in terms of a set of potentially arbitrary orthonormal functions, rather than in terms of a set of non-orthonormal and potentially linearly dependent functions, as is the case for standard ML-MCTDH. We show that the EOMs used in the projector splitting integrator (PSI) and the invariant EOM approaches are two special cases of this family obtained from different choices for the dynamic gauge condition, with the invariant EOMs making use of a choice that introduces potentially unbounded operators into the EOMs. As a consequence, all arguments for the existence of parallelizable integration schemes for the invariant EOMs can also be applied to the PSI EOMs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Crystal Diffraction Prediction and Partiality estimation using Gaussian basis functions

A small dataset with good data quality, useful as a benchmark. There exists a two-fold indexing ambiguity, so when processing with CrystFEL you will need to do: ambigator -o disambiguated.stream -y m-3 -w m-3m -j 72 ambiguous.stream Please check the README file for more information about the dataset. ----- Begin unit cell ----- CrystFEL unit cell file version 1.0 lattice_type = cubic centering = I a = 103.40 A b = 103.40 A c = 103.40 A al = 90.00 deg be = 90.00 deg ga = 90.00 deg ; Please note: this is the target unit cell. ; The actual unit cells produced by indexing depend on many other factors. ----- End unit cell -----

Cydia pomonella granulovirus hull protein↗