Search NASA⌕ Search

SEARCH · Search NASA

Results for “function mapping”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Learning to Predict Physical Properties Using Sums of Separable Functions

We present an algorithm for learning the function that maps a material structure to its value on some property, given the value of this function on several structures. We pose this problem as one of learning (regressing) a function of many variables from scattered data. Each structure is first converted to a weighted set of points by a process that removes irrelevant translations and rotations but otherwise retains full information about the structure. Then, incorporating a weighted average for each structure, we construct the multivariate regression function as a sum of separable functions, following the paradigm of separated representations. The algorithm can treat all finite and periodic structures within a common framework, and in particular does not require all structures to lie on a common lattice. We show how the algorithm simplifies when the structures do lie on a common lattice, and we present numerical results for that case.

36 MATERIALS SCIENCE↗
NASA NTRS1982

A grid spacing control technique for algebraic grid generation methods

A technique which controls the spacing of grid points in algebraically defined coordinate transformations is described. The technique is based on the generation of control functions which map a uniformly distributed computational grid onto parametric variables defining the physical grid. The control functions are smoothed cubic splines. Sets of control points are input for each coordinate directions to outline the control functions. Smoothed cubic spline functions are then generated to approximate the input data. The technique works best in an interactive graphics environment where control inputs and grid displays are nearly instantaneous. The technique is illustrated with the two-boundary grid generation algorithm.

Smith, R. E.↗
DOE OSTI2011

Regular zeros of quadratic maps and their application

Sufficient conditions for the existence of regular zeros of quadratic maps are obtained. Their applications are indicated to certain problems of analysis related to the inverse function theorem in a neighbourhood of an abnormal point. Bibliography: 13 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Exact solitary solution of Schamel equation in plasmas with negative ions

A theoretical investigation is carried out for understanding the properties of the solitary solution in plasmas with negative ions. Schamel equation for a plasma consisting of electron, positive ions and negative ions has been derived by using the reductive perturbation method. The effects of negative ions and the density on the properties of the solitary solution is discussed. We make use of the extended mapping method and auxiliary equation to obtain the solution of Schamel equation. This solution includes the Jacobi elliptic function solutions, hyperbolic function solutions, rational solutions, and periodic wave solutions. Furthermore, we show that the incorporate negative ion effects in the nonlinear propagation of ion acoustic waves that are controlled by trapped electrons and the results of the solitary solution in plasmas with negative ions model are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

A comprehensive and fair comparison of two neural operators (with practical extensions) based on $\mathrm{FAIR}$ data

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and engineering. Herein, we investigate the performance of two neural operators, which have shown promising results so far, and we develop new practical extensions that will make them more accurate and robust and importantly more suitable for industrial-complexity applications. The first neural operator, DeepONet, was published in 2019 (Lu et al., 2019), and its original architecture was based on the universal approximation theorem of Chen & Chen (1995). The second one, named Fourier Neural Operator or FNO, was published in 2020, and it is based on parameterizing the integral kernel in the Fourier space. DeepONet is represented by a summation of products of neural networks (NNs), corresponding to the branch NN for the input function and the trunk NN for the output function; both NNs are general architectures, e.g., the branch NN can be replaced with a CNN or a ResNet. According to Kovachki et al. (2021), FNO in its continuous form can be viewed conceptually as a DeepONet with a specific architecture of the branch NN and a trunk NN represented by a trigonometric basis. In order to compare FNO with DeepONet computationally for realistic setups, we develop several extensions of FNO that can deal with complex geometric domains as well as mappings where the input and output function spaces are of different dimensions. We also develop an extended DeepONet with special features that provide inductive bias and accelerate training, and we present a faster implementation of DeepONet with cost comparable to the computational cost of FNO, which is based on the Fast Fourier Transform. Here we consider 16 different benchmarks to demonstrate the relative performance of the two neural operators, including instability wave analysis in hypersonic boundary layers, prediction of the vorticity field of a flapping airfoil, porous media simulations in complex-geometry domains, etc. We follow the guiding principles of FAIR (Findability, Accessibility, Interoperability, and Reusability) for scientific data management and stewardship. The performance of DeepONet and FNO is comparable for relatively simple settings, but for complex geometries the performance of FNO deteriorates greatly. We also compare theoretically the two neural operators and obtain similar error estimates for DeepONet and FNO under the same regularity assumptions.

42 ENGINEERING↗
DOE OSTI2021

Artificial Neural Networks as Mappings between Proton Potentials, Wave Functions, Densities, and Energy Levels

We report artificial neural networks (ANNs) have become important in quantum chemistry. Herein, applications to nuclear quantum effects, such as zero-point energy, vibrationally excited states, and hydrogen tunneling, are explored. ANNs are used to solve the time-independent Schrödinger equation for single- and double-well potentials representing hydrogen-bonded molecular systems capable of proton transfer. ANN mappings are trained to predict the lowest five proton vibrational energies, wave functions, and densities from the proton potentials and to predict the excited state proton vibrational energies and densities from the proton ground state density. For the inverse problem, ANN mappings are trained to predict the proton potential from the proton vibrational energy levels or the proton ground state density. This latter mapping is theoretically justified by the first Hohenberg-Kohn theorem establishing a one-to-one correspondence between the external potential and the ground state density. ANNs for two- and three-dimensional systems are also presented to illustrate the straightforward extension to higher dimensions.

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

Multifidelity multiobjective optimization for wake-steering strategies

Abstract. Wake steering is an emerging wind power plant control strategy where upstream turbines are intentionally yawed out of perpendicular alignment with the incoming wind, thereby “steering” wakes away from downstream turbines. However, trade-offs between the gains in power production and fatigue loads induced by this control strategy are the subject of continuing investigation. In this study, we present a multifidelity multiobjective optimization approach for exploring the Pareto front of trade-offs between power and loading during wake steering. A large eddy simulation is used as the high-fidelity model, where an actuator line representation is used to model wind turbine blades and a rainflow-counting algorithm is used to compute damage equivalent loads. A coarser simulation with a simpler loads model is employed as a supplementary low-fidelity model. Multifidelity Bayesian optimization is performed to iteratively learn both a surrogate of the low-fidelity model and an additive discrepancy function, which maps the low-fidelity model to the high-fidelity model. Each optimization uses the expected hypervolume improvement acquisition function, weighted by the total cost of a proposed model evaluation in the multifidelity case. The multifidelity approach is able to capture the logit function shape of the Pareto frontier at a computational cost only 30 % that of the single-fidelity approach. Additionally, we provide physical insights into the vortical structures in the wake that contribute to the Pareto front shape.

17 WIND ENERGY↗
DOE OSTI2012

ISOTROPY IN THE TWO-POINT ANGULAR CORRELATION FUNCTION OF THE COSMIC MICROWAVE BACKGROUND

We study the directional dependence of the angular two-point correlation function in maps of the cosmic microwave background (CMB). We propose two new statistics: one which measures the correlation of each point in the sky with a ring of points separated an angle {theta} away, and a second one that measures the missing angular correlation above 60 deg as a function of direction. Using these statistics, we find that most of the low power in cut-sky maps measured by the Wilkinson Microwave Anisotropy Probe experiment comes from unusually low contributions from the directions of the lobes of the quadrupole and the octupole. These findings may aid a future explanation of why the CMB exhibits low power at large angular scales.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

1 × 1 km maps of abundances of eight enzyme functional classes for soil C, N, and P cycling across the CONUS

This dataset includes eight 1 × 1 km maps of the abundances of eight enzyme functional classes (EFC) for soil C, N, and P cycling across the CONUS. These mappings are predicted by the machine learning model trained using metagenomics and the corresponding environmental data. This item corresponds to our article: Fan, C., Song, Y., Mishra, U., Gautam, S., & Mayes, M. A. (2025). Harnessing the Power of Machine Learning and Omics to Identify Environmental Regulation on Microbial Functional Composition for Soil C, N, and P Cycling. Journal of Geophysical Research: Biogeosciences, 130(10).

1 × 1 km↗
NASA NTRS2003

Improved Fine Sun Sensor Field of View Calibration

The fine Sun sensor used on many spacecraft consists of two independent single-axis sensor heads, nominally mounted perpendicularly. These detect the Sun angle over a field of view typically of +32 deg. (There is a trade-off between accuracy and size of the field of view that allows for much latitude in any numbers quoted.) The nonlinear "transfer" function that maps the telemetered counts into observed angles consists of 9 adjustable parameters for each axis (1 8 total). An augmented transfer function has previously been reported that achieves a significant accuracy improvement across the entire field of view. That function expands the parameter set to 12 coefficients per axis (24 total) and includes cross terms combining counts from both axes. To make the best use of the Sun sensor for attitude determination, it must be calibrated after launch. However, the large number of parameters and the nonlinearity of the problem make this a challenging task. The purpose of this paper is to examine ways to improve convergence of the parameter search algorithm. In particular, experience has shown that the problem should be broken down into several steps, solving for a selected subset of the parameters at each step. This approach has now been incorporated as an option in the calibration utility.

Sedlak, J.↗
DOE OSTI2018

Formation of Supported Graphene Oxide: Evidence for Enolate Species

Graphene oxides are promising materials for novel electronic devices or anchoring of the active sites for catalytic applications. Here we focus on understanding the oxygen binding on different regions of graphene (Gr) on Ru(0001). Differences in the Gr/Ru lattices result in the superstructure, which offers an array of distinct adsorption sites. We employ scanning tunneling microscopy and density functional theory to map out the chemical identity and stability of prepared oxygen functionalities in different Gr regions. We demonstrate that in the regions that are close to the metal substrate, the terminally-bonded enolate groups are strongly preferred over bridge-bonded epoxy configurations. No oxygen species are observed on the graphene regions that are far from the underlying Ru, indicating their low relative stability. This study provides a clear fundamental basis for understanding the structural and electronic factors that affect the stability of enolate and epoxy species as a function of Gr/Ru interactions.

Supported Graphene, Graphene Functionalization, Gr↗
NASA NTRS1978

Global color variations on the Martian surface

Spectral reflectance data from the Viking-II Orbiter vidicon cameras have provided a means of mapping and classifying Martian surface materials over about 65% of the planet. The imagery, acquired at three wavelengths, was processed to remove an average Martian photometric function; albedo maps at the three wavelengths were created. Analysis of the imagery showed that the dark region between the equator and about 30 deg S in the Martian highlands consists of ancient ridges, crater rims and rugged plateaus which are very red, and younger intercrater volcanic plains exhibiting mare ridges which are much less red. In addition probable eolian deposits were found in the intermediate and high albedo regions.

Soderblom, L. A.↗
NASA NTRS1988

The Use of Efficient Broadcast Protocols in Asynchronous Distributed Systems

Reliable broadcast protocols are important tools in distributed and fault-tolerant programming. They are useful for sharing information and for maintaining replicated data in a distributed system. However, a wide range of such protocols has been proposed. These protocols differ in their fault tolerance and delivery ordering characteristics. There is a tradeoff between the cost of a broadcast protocol and how much ordering it provides. It is, therefore, desirable to employ protocols that support only a low degree of ordering whenever possible. This dissertation presents techniques for deciding how strongly ordered a protocol is necessary to solve a given application problem. It is shown that there are two distinct classes of application problems: problems that can be solved with efficient, asynchronous protocols, and problems that require global ordering. The concept of a linearization function that maps partially ordered sets of events to totally ordered histories is introduced. How to construct an asynchronous implementation that solves a given problem if a linearization function for it can be found is shown. It is proved that in general the question of whether a problem has an asynchronous solution is undecidable. Hence there exists no general algorithm that would automatically construct a suitable linearization function for a given problem. Therefore, an important subclass of problems that have certain commutativity properties are considered. Techniques for constructing asynchronous implementations for this class are presented. These techniques are useful for constructing efficient asynchronous implementations for a broad range of practical problems.

Schmuck, Frank Bernhard↗
NASA NTRS2011

Temporal mapping and analysis

A compositing process for selecting spatial data collected over a period of time, creating temporal data cubes from the spatial data, and processing and/or analyzing the data using temporal mapping algebra functions. In some embodiments, the temporal data cube is creating a masked cube using the data cubes, and computing a composite from the masked cube by using temporal mapping algebra.

O'Hara, Charles G.↗
DOE OSTI2017

Electron tomography and fractal aspects of MoS 2 and MoS 2 /Co spheres

A study was made by a combination of 3D electron tomography reconstruction methods and N 2 adsorption for determining the fractal dimension for nanometric MoS 2 and MoS 2 /Co catalyst particles. DFT methods including Neimarke-Kiselev’s method allowed to determine the particle porosity and fractal arrays at the atomic scale for the S-Mo-S(Co) 2D- layers that conform the spherically shaped catalyst particles. A structural and textural correlation was sought by further characterization performed by x-ray Rietveld refinement and Radial Distribution Function (RDF) methods, electron density maps, computational density functional theory methods and nitrogen adsorption methods altogether, for studying the structural and textural features of spherical MoS 2 and MoS 2 /Co particles. Neimark-Kiselev’s equations afforded the evaluation of a pore volume variation from 10 to 110 cm 3 /g by cobalt insertion in the MoS 2 crystallographic lattice, which induces the formation of cavities and throats in between of less than 29 nm, with a curvature radius r k < 14.4 nm; typical large needle-like arrays having 20 2D layers units correspond to a model consisting of smooth surfaces within these cavities. Decreasing D P , D B , D I and D M values occur when Co atoms are present in the MoS 2 laminates, which promote the formation of smoother edges and denser surfaces that have an influence on the catalytic properties of the S-Mo-S(Co) system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1993

Functional approximation using artificial neural networks in structural mechanics

The artificial neural networks (ANN) methodology is an outgrowth of research in artificial intelligence. In this study, the feed-forward network model that was proposed by Rumelhart, Hinton, and Williams was applied to the mapping of functions that are encountered in structural mechanics problems. Several different network configurations were chosen to train the available data for problems in materials characterization and structural analysis of plates and shells. By using the recall process, the accuracy of these trained networks was assessed.

Alam, Javed↗
DOE OSTI2021

High Throughput Mapping of Single Molecules’ Redox Potentials on Electrode

By synchronizing electrochemical potential scanning with a single-molecule localization super-resolution fluorescence microscope, kinetic fluorescence changes of hundreds of single molecular redox events were tracked simultaneously with high throughput, and subsequent cross-correlation function analysis mapped single molecules’ redox potentials (times) out on the imaging area from site to site in unprecedented detail by extracting electrochemically induced fluorescence change from apparently random fluorescence on/off blinking. This work paves the way toward mapping redox states at single-molecule levels in high throughput in chemical and biological systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗