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Results for “radial basis function”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration

This article is concerned with the approximation of high-dimensional functions by kernel-based methods. Motivated by uncertainty quantification, which often necessitates the construction of approximations that are accurate with respect to a probability density function of random variables, we aim at minimizing the approximation error with respect to a weighted $L^p$-norm. We present a greedy procedure for designing computer experiments based upon a weighted modification of the pivoted Cholesky factorization. The method successively generates nested samples with the goal of minimizing error in regions of high probability. Numerical experiments validate that this new importance sampling strategy is superior to other sampling approaches, especially when used with non-product probability density functions. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Multivariate Space‐Time Dynamic Model for Characterizing the Atmospheric Impacts Following the Mt. Pinatubo Eruption

The June 1991 Mt. Pinatubo eruption resulted in a massive increase of sulfate aerosols in the atmosphere, absorbing radiation and leading to global changes in surface and stratospheric temperatures. A volcanic eruption of this magnitude serves as a natural analog for stratospheric aerosol injection, a proposed solar radiation modification method to combat a warming climate. The impacts of such an event are multifaceted and region-specific. Our goal is to characterize the multivariate and dynamic nature of the atmospheric impacts following the Mt. Pinatubo eruption. We developed a multivariate space-time dynamic linear model to understand the full extent of the spatially- and temporally-varying impacts. Specifically, spatial variation is modeled using a flexible set of basis functions for which the basis coefficients are allowed to vary in time through a vector autoregressive (VAR) structure. This novel model is cast in a Dynamic Linear Model (DLM) framework and estimated via a customized MCMC approach. We demonstrate how the model quantifies the relationships between key atmospheric parameters prior to and following the Mt. Pinatubo eruption with reanalysis data from MERRA-2 and highlight when such a model is advantageous over univariate models.

Dynamic Linear Model↗
DOE OSTI2025

Kernel Manifolds: Nonlinear‐Augmentation Dimensionality Reduction Using Reproducing Kernel Hilbert Spaces

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections, augment linear dimensionality reduction with a nonlinear correction term in the reconstruction map to overcome approximation accuracy limitations of purely linear approaches. While feature map-based approaches typically learn a least squares optimal polynomial correction term, we generalize this approach by learning an optimal nonlinear correction from a user-defined reproducing kernel Hilbert space. Our approach allows one to impose arbitrary nonlinear structure on the correction term, including polynomial structure, and includes feature map and radial basis function-based corrections as special cases. Furthermore, our method has relatively low training cost and has monotonically decreasing error as the latent space dimension increases. In conclusion, we compare our approach to proper orthogonal decomposition and several recent QM approaches on data from several example problems.

kernel methods↗
DOE OSTI2021

Cholesky-based experimental design for Gaussian process and kernel-based emulation and calibration.

Gaussian processes and other kernel-based methods are used extensively to construct approximations of multivariate data sets. The accuracy of these approximations is dependent on the data used. This paper presents a computationally efficient algorithm to greedily select training samples that minimize the weighted L p error of kernel-based approximations for a given number of data. The method successively generates nested samples, with the goal of minimizing the error in high probability regions of densities specified by users. The algorithm presented is extremely simple and can be implemented using existing pivoted Cholesky factorization methods. Training samples are generated in batches which allows training data to be evaluated (labeled) in parallel. For smooth kernels, the algorithm performs comparably with the greedy integrated variance design but has significantly lower complexity. Numerical experiments demonstrate the efficacy of the approach for bounded, unbounded, multi-modal and non-tensor product densities. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data using Bayesian inference.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1998

Optimization of Turbine Blade Design for Reusable Launch Vehicles

To facilitate design optimization of turbine blade shape for reusable launching vehicles, appropriate techniques need to be developed to process and estimate the characteristics of the design variables and the response of the output with respect to the variations of the design variables. The purpose of this report is to offer insight into developing appropriate techniques for supporting such design and optimization needs. Neural network and polynomial-based techniques are applied to process aerodynamic data obtained from computational simulations for flows around a two-dimensional airfoil and a generic three- dimensional wing/blade. For the two-dimensional airfoil, a two-layered radial-basis network is designed and trained. The performances of two different design functions for radial-basis networks, one based on the accuracy requirement, whereas the other one based on the limit on the network size. While the number of neurons needed to satisfactorily reproduce the information depends on the size of the data, the neural network technique is shown to be more accurate for large data set (up to 765 simulations have been used) than the polynomial-based response surface method. For the three-dimensional wing/blade case, smaller aerodynamic data sets (between 9 to 25 simulations) are considered, and both the neural network and the polynomial-based response surface techniques improve their performance as the data size increases. It is found while the relative performance of two different network types, a radial-basis network and a back-propagation network, depends on the number of input data, the number of iterations required for radial-basis network is less than that for the back-propagation network.

Shyy, Wei↗
NASA NTRS1994

From neural-based object recognition toward microelectronic eyes

Engineering neural network systems are best known for their abilities to adapt to the changing characteristics of the surrounding environment by adjusting system parameter values during the learning process. Rapid advances in analog current-mode design techniques have made possible the implementation of major neural network functions in custom VLSI chips. An electrically programmable analog synapse cell with large dynamic range can be realized in a compact silicon area. New designs of the synapse cells, neurons, and analog processor are presented. A synapse cell based on Gilbert multiplier structure can perform the linear multiplication for back-propagation networks. A double differential-pair synapse cell can perform the Gaussian function for radial-basis network. The synapse cells can be biased in the strong inversion region for high-speed operation or biased in the subthreshold region for low-power operation. The voltage gain of the sigmoid-function neurons is externally adjustable which greatly facilitates the search of optimal solutions in certain networks. Various building blocks can be intelligently connected to form useful industrial applications. Efficient data communication is a key system-level design issue for large-scale networks. We also present analog neural processors based on perceptron architecture and Hopfield network for communication applications. Biologically inspired neural networks have played an important role towards the creation of powerful intelligent machines. Accuracy, limitations, and prospects of analog current-mode design of the biologically inspired vision processing chips and cellular neural network chips are key design issues.

Sheu, Bing J.↗
NASA NTRS1992

Negative-energy states in the Dirac-Hartree-Fock problem - The effect of omission of two-electron integrals involving the small component

The effect of omission of two-electron integrals involving basis functions for the small component of the wavefunction on the eigenvalue spectrum in the Dirac-Hartree-Fock problem is studied. From an analysis of the Fock matrix it is shown that omission of these integrals moves the negative-energy states down, not up. Their complete omission does not give rise to intruder states. The appearance of intruder states occurs when only some of the core integrals are omitted, due to the nature of particular contraction schemes used for the core basis functions. Use of radially localized functions rather than atomic functions alleviates the intruder state problem.

Dyall, Kenneth G.↗
NASA NTRS1986

Eigenfunction methods in magnetospheric radial-diffusion theory

Complete sets of orthonormal basis functions constructed according to a generalization of the quantum-mechanical WKB approximation can be used to generate a nearly-diagonal matrix representation of the radial-transport operator for ring-current ions in the presence of radial diffusion and charge exchange. The resulting eigenfunctions (constructed by weighting the basis functions in proportion to the respective components of the eigenvectors of the matrix representation) and eigenvalues provide a spatial and temporal description of the evolving phase-space density during and following a magnetospheric disturbance (e.g., a magnetic storm). A linear superposition of the basis functions can also be used to eliminate any discrepancy between the steady-state solution of the transport equation and the appropriate WKB approximation of this steady-state solution.

Schulz, Michael↗
NASA NTRS1978

Charge exchange lifetimes for ring current ions

In view of the importance of charge exchange decay as a loss mechanism for magnetospheric ions, the paper summarizes the latest and best measurements of the physical quantities involved in the calculation of the charge exchange lifetime of the mirroring ions. The normalized atomic hydrogen distribution is presented as a function of radial distance on the basis of the Chamberlain model for a range of exobase temperatures and for various combinations of satellite particles. Cross section measurements for various ions in the energy range 1 keV to 200 keV are summarized in the form of normalized charge exchange lifetimes. The equatorial lifetimes can be determined for any of these ions at a specific energy and L-value.

Smith, P. H.↗
NASA NTRS1990

Distributed memory approaches for robotic neural controllers

The suitability is explored of two varieties of distributed memory neutral networks as trainable controllers for a simulated robotics task. The task requires that two cameras observe an arbitrary target point in space. Coordinates of the target on the camera image planes are passed to a neural controller which must learn to solve the inverse kinematics of a manipulator with one revolute and two prismatic joints. Two new network designs are evaluated. The first, radial basis sparse distributed memory (RBSDM), approximates functional mappings as sums of multivariate gaussians centered around previously learned patterns. The second network types involved variations of Adaptive Vector Quantizers or Self Organizing Maps. In these networks, random N dimensional points are given local connectivities. They are then exposed to training patterns and readjust their locations based on a nearest neighbor rule. Both approaches are tested based on their ability to interpolate manipulator joint coordinates for simulated arm movement while simultaneously performing stereo fusion of the camera data. Comparisons are made with classical k-nearest neighbor pattern recognition techniques.

Jorgensen, Charles C.↗
NASA NTRS2016

Application of Interval Predictor Models to Space Radiation Shielding

This paper develops techniques for predicting the uncertainty range of an output variable given input-output data. These models are called Interval Predictor Models (IPM) because they yield an interval valued function of the input. This paper develops IPMs having a radial basis structure. This structure enables the formal description of (i) the uncertainty in the models parameters, (ii) the predicted output interval, and (iii) the probability that a future observation would fall in such an interval. In contrast to other metamodeling techniques, this probabilistic certi cate of correctness does not require making any assumptions on the structure of the mechanism from which data are drawn. Optimization-based strategies for calculating IPMs having minimal spread while containing all the data are developed. Constraints for bounding the minimum interval spread over the continuum of inputs, regulating the IPMs variation/oscillation, and centering its spread about a target point, are used to prevent data over tting. Furthermore, we develop an approach for using expert opinion during extrapolation. This metamodeling technique is illustrated using a radiation shielding application for space exploration. In this application, we use IPMs to describe the error incurred in predicting the ux of particles resulting from the interaction between a high-energy incident beam and a target.

Crespo, Luis G.↗
DOE OSTI2020

PyFLOSIC: Python-based Fermi–Löwdin orbital self-interaction correction

We present pyflosic, an open-source, general-purpose python implementation of the Fermi–Löwdin orbital self-interaction correction (FLO-SIC), which is based on the python simulation of chemistry framework (pyscf) electronic structure and quantum chemistry code. Thanks to pyscf, pyflosic can be used with any kind of Gaussian-type basis set, various kinds of radial and angular quadrature grids, and all exchange-correlation functionals within the local density approximation, generalized-gradient approximation (GGA), and meta-GGA provided in the libxc and xcfun libraries. A central aspect of FLO-SIC is the Fermi-orbital descriptors, which are used to estimate the self-interaction correction. Importantly, they can be initialized automatically within pyflosic; they can also be optimized within pyflosic with an interface to the atomic simulation environment, a python library that provides a variety of powerful gradient-based algorithms for geometry optimization. Although pyflosic has already facilitated applications of FLO-SIC to chemical studies, it offers an excellent starting point for further developments in FLO-SIC approaches, thanks to its use of a high-level programming language and pronounced modularity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Extending the SAGA Survey (xSAGA). I. Satellite Radial Profiles as a Function of Host-galaxy Properties

We present "Extending the Satellites Around Galactic Analogs Survey" (xSAGA), a method for identifying low-z galaxies on the basis of optical imaging and results on the spatial distributions of xSAGA satellites around host galaxies. Using spectroscopic redshift catalogs from the SAGA Survey as a training data set, we have optimized a convolutional neural network (CNN) to identify z < 0.03 galaxies from more-distant objects using image cutouts from the DESI Legacy Imaging Surveys. From the sample of >100,000 CNN-selected low-z galaxies, we identify >20,000 probable satellites located between 36–300 projected kpc from NASA-Sloan Atlas central galaxies in the stellar-mass range $9.5\lt \mathrm{log}({M}_{\star }/{M}_{\odot })\lt 11$. We characterize the incompleteness and contamination for CNN-selected samples and apply corrections in order to estimate the true number of satellites as a function of projected radial distance from their hosts. Satellite richness depends strongly on host stellar mass, such that more-massive host galaxies have more satellites, and on host morphology, such that elliptical hosts have more satellites than disky hosts with comparable stellar masses. We also find a strong inverse correlation between satellite richness and the magnitude gap between a host and its brightest satellite. The normalized satellite radial distribution between 36–300 kpc does not depend on host stellar mass, morphology, or magnitude gap. The satellite abundances and radial distributions we measure are in reasonable agreement with predictions from hydrodynamic simulations. Our results deliver unprecedented statistical power for studying satellite galaxy populations and highlight the promise of using machine-learning for extending galaxy samples of wide-area surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1987

A full simulation of a vortex ring

A three-dimensional spectral method is developed for the solution to the incompressible Navier-Stokes equations in an unbounded domain. The spectral method relies on divergence-free basis functions as proposed by Leonard (1981). The basis functions are formed using vector spherical harmonics and Jacobi polynomials together with a mapping in the radial direction. An axisymmetric code was written and is verified using an exact solution of the Stokes equations. Preliminary results for the evolution of a vortex ring according to the Navier-Stokes equations are presented.

Stanaway, S. K.↗
NASA NTRS1990

Global and radial variations in the efficiency of massive star formation among galaxies

In order to determine the regions within galaxies which give rise to the most efficient star formation and to test the hypothesis that galaxies with high infrared luminosities per unit molecular mass are efficiently producing high mass stars, researchers have undertaken an H alpha imaging survey in galaxies whose CO distributions have been measured as part of the Five College Radio Astronomy Observatory (FCRAO) Extragalactic CO Survey. From these images researchers have derived global H alpha fluxes and distributions for comparison with far infrared radiation (FIR) fluxes and CO fluxes and distributions. Here, researchers present results on the global massive star formation efficiency (SFE = L sub H sub alpha/M(H2)) as a function of morphological type and environment, and on the radial distribution of the SFE within both peculiar and isolated galaxies. On the basis of comparison of the global L sub H sub alpha/M(H2) and L sub FIR/M(H2) for 111 galaxies, researchers conclude that environment rather than morphological type has the strongest effect on the global efficiency of massive star formation. Based on their study of a small sample, they find that the largest radial gradients are observed in the interacting/peculiar galaxies, indicating that environment affects the star formation efficiency within galaxies as well.

Allen, Lori E.↗