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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 OSTI2016

Assessing the utility of phase-space-localized basis functions: Exploiting direct product structure and a new basis function selection procedure

In this paper we show that it is possible to use an iterative eigensolver in conjunction with Halverson and Poirier’s symmetrized Gaussian (SG) basis [T. Halverson and B. Poirier, J. Chem. Phys. 137, 224101 (2012)] to compute accurate vibrational energy levels of molecules with as many as five atoms. This is done, without storing and manipulating large matrices, by solving a regular eigenvalue problem that makes it possible to exploit direct-product structure. These ideas are combined with a new procedure for selecting which basis functions to use. The SG basis we work with is orders of magnitude smaller than the basis made by using a classical energy criterion. We find significant convergence errors in previous calculations with SG bases. For sum-of-product Hamiltonians, SG bases large enough to compute accurate levels are orders of magnitude larger than even simple pruned bases composed of products of harmonic oscillator functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Optimization of global model composed of radial basis functions using the term-ranking approach

A term-ranking method is put forward to optimize the global model composed of radial basis functions to improve the predictability of the model. The effectiveness of the proposed method is examined by numerical simulation and experimental data. Numerical simulations indicate that this method can significantly lengthen the prediction time and decrease the Bayesian information criterion of the model. The application to real voice signal shows that the optimized global model can capture more predictable component in chaos-like voice data and simultaneously reduce the predictable component (periodic pitch) in the residual signal.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Adaptive Methods for Radial Basis Functions

Radial basis functions (RBFs) are a powerful tool for constructing high-order accurate reduced representations of scattered data in arbitrary dimension and on manifolds. We present a method of constructing data approximations in which we utilize a functional tail to capture a global background profile and a RBF neural network (NN) to capture the smaller-scale features. In the RBF NN the RBF centers, matrix shape parameters were selected adaptively for each RBF. We also utilized a geodesic notion of distance on the manifold on which the data lies, e.g., the spherical geodesic for data on the sphere. Although each of these ideas have been been investigated separately in previous works, their combination into a single algorithm is novel. We defined a machine learning problem in which these properties are learned to minimize the data reduction error. We demonstrate the algorithm for applications of scattered data reduction in the plane and on the sphere.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The Structural and Functional Basis for Recurring Sulfa Drug Resistance Mutations in Staphylococcus aureus Dihydropteroate Synthase

Staphylococcal species are a leading cause of bacterial drug-resistant infections and associated mortality. One strategy to combat bacterial drug resistance is to revisit compromised targets, and to circumvent resistance mechanisms using structure-assisted drug discovery. The folate pathway is an ideal candidate for this approach. Antifolates target an essential metabolic pathway, and the necessary detailed structural information is now available for most enzymes in this pathway. Dihydropteroate synthase (DHPS) is the target of the sulfonamide class of drugs, and its well characterized mechanism facilitates detailed analyses of how drug resistance has evolved. Here, we surveyed clinical genetic sequencing data in S. aureus to distinguish natural amino acid variations in DHPS from those that are associated with sulfonamide resistance. Five mutations were identified, F17L, S18L, T51M, E208K, and KE257_dup. Their contribution to resistance and their cost to the catalytic properties of DHPS were evaluated using a combination of biochemical, biophysical and microbiological susceptibility studies. These studies show that F17L, S18L, and T51M directly lead to sulfonamide resistance while unexpectedly increasing susceptibility to trimethoprim, which targets the downstream enzyme dihydrofolate reductase. The secondary mutations E208K and KE257_dup restore trimethoprim susceptibility closer to wild-type levels while further increasing sulfonamide resistance. Structural studies reveal that these mutations appear to selectively disfavor the binding of the sulfonamides by sterically blocking an outer ring moiety that is not present in the substrate. This emphasizes that new inhibitors must be designed that strictly stay within the substrate volume in the context of the transition state.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2014

Experimental evaluation and basis function optimization of the spatially variant image-space PSF on the Ingenuity PET/MR scanner

Purpose: The Ingenuity time-of-flight (TF) PET/MR is a recently developed hybrid scanner combining the molecular imaging capabilities of PET with the excellent soft tissue contrast of MRI. It is becoming common practice to characterize the system's point spread function (PSF) and understand its variation under spatial transformations to guide clinical studies and potentially use it within resolution recovery image reconstruction algorithms. Furthermore, due to the system's utilization of overlapping and spherical symmetric Kaiser-Bessel basis functions during image reconstruction, its image space PSF and reconstructed spatial resolution could be affected by the selection of the basis function parameters. Hence, a detailed investigation into the multidimensional basis function parameter space is needed to evaluate the impact of these parameters on spatial resolution. Methods: Using an array of 12 × 7 printed point sources, along with a custom made phantom, and with the MR magnet on, the system's spatially variant image-based PSF was characterized in detail. Moreover, basis function parameters were systematically varied during reconstruction (list-mode TF OSEM) to evaluate their impact on the reconstructed resolution and the image space PSF. Following the spatial resolution optimization, phantom, and clinical studies were subsequently reconstructed using representative basis function parameters. Results: Based on the analysis and under standard basis function parameters, the axial and tangential components of the PSF were found to be almost invariant under spatial transformations (∼4 mm) while the radial component varied modestly from 4 to 6.7 mm. Using a systematic investigation into the basis function parameter space, the spatial resolution was found to degrade for basis functions with a large radius and small shape parameter. However, it was found that optimizing the spatial resolution in the reconstructed PET images, while having a good basis function superposition and keeping the image representation error to a minimum, is feasible, with the parameter combination range depending upon the scanner's intrinsic resolution characteristics. Conclusions: Using the printed point source array as a MR compatible methodology for experimentally measuring the scanner's PSF, the system's spatially variant resolution properties were successfully evaluated in image space. Overall the PET subsystem exhibits excellent resolution characteristics mainly due to the fact that the raw data are not under-sampled/rebinned, enabling the spatial resolution to be dictated by the scanner's intrinsic resolution and the image reconstruction parameters. Due to the impact of these parameters on the resolution properties of the reconstructed images, the image space PSF varies both under spatial transformations and due to basis function parameter selection. Nonetheless, for a range of basis function parameters, the image space PSF remains unaffected, with the range depending on the scanner's intrinsic resolution properties.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2018

Accurate correlation energies in one-dimensional systems from small system-adapted basis functions

We propose a general method for constructing system-dependent basis functions for correlated quantum calculations. Our construction combines features from several traditional approaches: plane waves, localized basis functions, and wavelets. In a one-dimensional mimic of Coulomb systems, it requires only 2–3 basis functions per electron to achieve high accuracy, and reproduces the natural orbitals. We illustrate its effectiveness for molecular energy curves and chains of many one-dimensional atoms. Furthermore, we discuss the promise and challenges for realistic quantum chemical calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

A radial basis function Galerkin method for inhomogeneous nonlocal diffusion

We introduce a discretization for a nonlocal diffusion problem using a localized basis of radial basis functions. The stiffness matrix entries are assembled by a special quadrature routine unique to the localized basis. Combining the quadrature method with the localized basis produces a well-conditioned, sparse, symmetric positive definite stiffness matrix. We demonstrate that both the continuum and discrete problems are well-posed and present numerical results for the convergence behavior of the radial basis function method. As a result, we explore approximating the solution to anisotropic differential equations by solving anisotropic nonlocal integral equations using the radial basis function method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

CONORBIT: constrained optimization by radial basis function interpolation in trust regions

Here, this paper presents CONORBIT (CONstrained Optimization by Radial Basis function Interpolation in Trust regions), a derivative-free algorithm for constrained black-box optimization where the objective and constraint functions are computationally expensive. CONORBIT employs a trust-region framework that uses interpolating radial basis function (RBF) models for the objective and constraint functions, and is an extension of the ORBIT algorithm. It uses a small margin for the RBF constraint models to facilitate the generation of feasible iterates, and extensive numerical tests confirm that such a margin is helpful in improving performance. CONORBIT is compared with other algorithms on 27 test problems, a chemical process optimization problem, and an automotive application. Numerical results show that CONORBIT performs better than COBYLA, a sequential penalty derivative-free method, an augmented Lagrangian method, a direct search method, and another RBF-based algorithm on the test problems and on the automotive application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Satisfiability of logic programming based on radial basis function neural networks

In this paper, we propose a new technique to test the Satisfiability of propositional logic programming and quantified Boolean formula problem in radial basis function neural networks. For this purpose, we built radial basis function neural networks to represent the proportional logic which has exactly three variables in each clause. We used the Prey-predator algorithm to calculate the output weights of the neural networks, while the K-means clustering algorithm is used to determine the hidden parameters (the centers and the widths). Mean of the sum squared error function is used to measure the activity of the two algorithms. We applied the developed technique with the recurrent radial basis function neural networks to represent the quantified Boolean formulas. The new technique can be applied to solve many applications such as electronic circuits and NP-complete problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A computational method for solving stochastic Itô–Volterra integral equations based on stochastic operational matrix for generalized hat basis functions

In this paper, a new computational method based on the generalized hat basis functions is proposed for solving stochastic Itô–Volterra integral equations. In this way, a new stochastic operational matrix for generalized hat functions on the finite interval [0,T] is obtained. By using these basis functions and their stochastic operational matrix, such problems can be transformed into linear lower triangular systems of algebraic equations which can be directly solved by forward substitution. Also, the rate of convergence of the proposed method is considered and it has been shown that it is O(1/(n{sup 2}) ). Further, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient in comparison with the block pule functions method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Determination of many-electron basis functions for a quantum Hall ground state using Schur polynomials

A method for determining the ground state of a planar interacting many-electron system in a magnetic field perpendicular to the plane is described. The ground state wave-function is expressed as a linear combination of a set of basis functions. Given only the flux and the number of electrons describing an incompressible state, we use the combinatorics of partitioning the flux among the electrons to derive the basis wave-functions as linear combinations of Schur polynomials. The procedure ensures that the basis wave-functions form representations of the angular momentum algebra. We exemplify the method by deriving the basis functions for the (5/2) quantum Hall state with a few particles. We find that one of the basis functions is precisely the Moore–Read Pfaffian wave function.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Enhanced Signal Processing of Distributed Brillouin Fiber Sensors using a Decoupled Radial Basis Function Network

A novel decoupled radial basis function network (D-RBFN) is proposed to accelerate signal processing and address the big data challenges associated with ultra-long distance Brillouin optical time-domain analysis (BOTDA) systems. The proposed frame- work is demonstrated on a dataset measured over a 100 km distance using a bi-directional Raman assisted BOTDA system.

Venketeswaran, Abhishek↗
DOE OSTI2024

Relativistic corrections to the correlated basis function effective nuclear Hamiltonian

We discuss the inclusion of relativistic boost corrections into the correlated basis function effective nuclear Hamiltonian, derived from a realistic model of two- and three-nucleon interactions using the formalism of correlated basis functions and the cluster expansion technique. Different procedures to take into account the effects of boost interactions are compared on the basis of the ability to reproduce the nuclear matter equation of state obtained from accurate quantum many-body calculations. Furthermore, the results of our study show that the repulsive contribution of the boost interaction significantly depends on the underlying model of the nonrelativistic potential. On the other hand, the dominant relativistic correction turns out to be the corresponding reduction of the strength of repulsive three-nucleon interactions, leading to a significant softening of the equation of state of nuclear matter at supranuclear densities.

Neutron stars & pulsars↗
DOE OSTI2023

Phase retrieval using Gaussian basis functions

A wavefront map of arbitrary aperture can be represented by a sum of Gaussian basis functions. Its performance is compared here to other representation methods such as orthonormal polynomials and Fourier modes. Gaussian basis functions can be applied to phase retrieval of high-frequency wavefront maps. Experiments show good agreement with direct measurements by a wavefront sensor. Finally, optimum measurement conditions are discussed based on the statistics of wavefront properties.

47 OTHER INSTRUMENTATION↗
DOE OSTI2016

Educating local radial basis functions using the highest gradient of interest in three dimensional geometries: EDUCATING LOCALIZED RBF-SCHEMES

We present a novel methodology to effectively localize radial basis function approximation methods in three dimensions. The local scheme requires shape parameter-dependent functions that can be used to approximate gradients of scattered data and to solve partial differential operators. The optimum shape parameter is obtained from the highest gradient of interest, where a known analytical function, when boundary conditions are not present, or a shape parameter-free global approximation are used to educate the localized scheme. The later option is applicable to problems where the operator needs to be solved multiple times, like in time evolution or stochastic integration. Past shape parameter's optimizations, for two-dimensional domains, based on the condition number of the interpolant matrix, were unable to provide satisfactory approximations. The applicability of our method is illustrated in the context of an analytical expression interpolation and during a Ginzburg-Landau relaxation of a free energy functional. In general, the optimum shape parameter depends on geometry, node distribution, and density, whereas the approximation errors decrease as the node density and the local stencil size increase. The effective localization of radial basis functions motivates its use in moving boundary problems and accelerates solutions through sparse matrix solvers.

free energy functional↗
DOE OSTI2018

Experimental and Numerical Investigation on Vibration of Sandwich Plates with Honeycomb Cores Based on Radial Basis Function

The vibration characteristic of the sandwich plate with a honeycomb core was investigated by experimental measurements and numerical calculation based on radial basis function (RBF). RBF method was used not only in the meshless approach but also in the post-processing of the experimental data. During the experiment, amplitude-fluctuation electronic speckle pattern interferometry was applied to access the resonant frequencies and the corresponding vibration mode shapes simultaneously. Then RBF method was used to improve the quality of patterns and reconstruct the out-of-plane vibration amplitude after fringe analysis. As for numerical calculation, the modal parameters were numerically predicted using the first-order shear deformation theory. The computation approach was based on collocation with multi-quadric radial basis function. To understand the influence of the thickness of face sheet on dynamic behaviors, three types of specimens with different thickness were tested and analyzed. Of particular interest was that the vibration modes show veering due to the thickness increment. Furthermore, the numerical predicted results were compared with the experimental measurements for the first five modes. They are in good agreement with each other for resonant frequencies, mode shapes and relative out-of-plane amplitudes.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Using an iterative eigensolver to compute vibrational energies with phase-spaced localized basis functions

Although phase-space localized Gaussians are themselves poor basis functions, they can be used to effectively contract a discrete variable representation basis [A. Shimshovitz and D. J. Tannor, Phys. Rev. Lett. 109, 070402 (2012)]. This works despite the fact that elements of the Hamiltonian and overlap matrices labelled by discarded Gaussians are not small. By formulating the matrix problem as a regular (i.e., not a generalized) matrix eigenvalue problem, we show that it is possible to use an iterative eigensolver to compute vibrational energy levels in the Gaussian basis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗