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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS2021

Monte Carlo Tree Search Methods for the Earth-Observing Satellite Scheduling Problem

This work explores on-board planning for the single spacecraft, multiple ground station Earth-observing satellite scheduling problem through artificial neural network function approximation of state–action value estimates generated by Monte Carlo tree search (MCTS). An extensive hyperparameter search is conducted for MCTS on the basis of performance, safety, and downlink opportunity utilization to determine the best hyperparameter combination for data generation. A hyperparameter search is also conducted on neural network architectures. The learned behavior of each network is explored, and each network architecture’s robustness to orbits and epochs outside of the training distributions is investigated. Furthermore, each algorithm is compared with a genetic algorithm, which serves to provide a baseline for optimality. MCTS is shown to compute near-optimal solutions in comparison to the genetic algorithm. The state–action value networks are shown to match or exceed the performance of MCTS in six orders of magnitude less execution time, showing promise for execution on board spacecraft.

Adam P. Herrmann↗
NASA NTRSDate not supplied

Comparison of Multivariate Time Series Prediction Techniques for Emulating Noah-LSM Soil Moisture Outputs

Land surface models are crucial tools for many earth science applications including numerical weather prediction, water resource and crop monitoring, and climatological analysis. Given a set of atmospheric forcings, seasonal data, and static parameters, models like Noah-LSM solve for land surface quantities including skin temperature, sensible heat flux, and soil moisture. While these calculations are theoretically robust, they are often computationally expensive. Since artificial neural networks (ANNs) are universal function approximators, they can learn to emulate the output of a deterministic numerical model given a time series of input forcings, with the learned ANN having substantially shorter execution time. The ANN could efficiently parameterize other models, generate ensembles, and provide first-guess inputs for retrievals. As such, with the goal of developing a model that efficiently mimics the output of Noah-LSM given NLDAS2 forcings on a region covering much of the central US, we examine and compare several neural network architectures for the multi-horizon multivariate time series forecasting problem. Recent literature includes a diverse set of approaches including autoregressive architectures like LSTM and GRU, parametric and non-parametric statistical predictors (ForecastNet and MQRNN), self-attention (LSTM-attention-LSTM), and temporal convovlution (DeepTCN). We implement several of these models for the Noah-LSM prediction task, highlighting the features and challenges for each and providing practical insight on the training process.

Mitchell Dodson↗
NASA NTRS1995

Kravchuk functions for the finite oscillator approximation

Kravchuk orthogonal functions - Kravchuk polynomials multiplied by the square root of the weight function - simplify the inversion algorithm for the analysis of discrete, finite signals in harmonic oscillator components. They can be regarded as the best approximation set. As the number of sampling points increases, the Kravchuk expansion becomes the standard oscillator expansion.

Atakishiyev, Natig M.↗
DOE OSTI2025

Anti-symmetric barron functions and their approximation with sums of determinants

A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The architecture of neural network models for the electron wave function typically comprises an equivariant component followed by a summation of determinants. The recently introduced Generic Antisymmetric (GA) block is designed to enhance the expressivity of such neural wave functions, and it was found that the 2-layer GA block achieved more accurate energies than the corresponding single-determinant FermiNet architecure, suggesting its promise as a way to improve the expressivity of neural wave functions. In this paper we show how the function expressed by the 2-layer GA block can be decomposed into a sum of determinants. We formalize this result by defining the antisymmetric Barron space as a generalized version of the 2-layer GA block and providing an appromation theorem for this function class. This result can be viewed as a negative result showing that the 2-layer GA block is not more expressive than using multiple determinants.

Abrahamsen, Nilin↗
NASA NTRS1995

Combining Comparison Functions and Finite Element Approximations in CFD

In a variety of potential flow applications, the modal element method has been shown to significantly reduce the numerical grid, employ a more precise grid termination boundary condition, and give theoretical insight to the flow physics. The method employs eigenfunctions to replace the numerical grid over significant portions of the flow field. Generally, a numerical grid is employed around obstacles with complex geometry while eigenfunctions are applied to regions in the flow field where the boundary conditions can easily be satisfied. To handle a wider class of computational fluid dynamics (CFD) problems, the present paper extends the modal element to include function approximations which do not satisfy the governing differential equation. To accomplish this task, a double modal series approximation and weighted residual constraints are developed to force the comparison functions to satisfy the governing differential equation and to interface properly with the finite element solution. As an example, the method is applied to the problem of potential flow in a channel with two-dimensional cylindrical like obstacles. The calculated flow fields are in excellent agreement with exact analytical solutions.

Baumeister, Kenneth J.↗
NASA NTRS1972

Constrained Chebyshev approximations to some elementary functions suitable for evaluation with floating point arithmetic

Approximations which can be evaluated with precision using floating-point arithmetic are presented. The particular set of approximations thus far developed are for the function TAN and the functions of USASI FORTRAN excepting SQRT and EXPONENTIATION. These approximations are, furthermore, specialized to particular forms which are especially suited to a computer with a small memory, in that all of the approximations can share one general purpose subroutine for the evaluation of a polynomial in the square of the working argument.

Manos, P.↗
NASA NTRS1993

Approximate Green's function methods for HZE transport in multilayered materials

A nonperturbative analytic solution of the high charge and energy (HZE) Green's function is used to implement a computer code for laboratory ion beam transport in multilayered materials. The code is established to operate on the Langley nuclear fragmentation model used in engineering applications. Computational procedures are established to generate linear energy transfer (LET) distributions for a specified ion beam and target for comparison with experimental measurements. The code was found to be highly efficient and compared well with the perturbation approximation.

Wilson, John W.↗
NASA NTRS1985

A physically realistic approximate form for the redistribution function R(II-A)

An approximation is proposed to the redistribution function R(II-A) (coherent, isotropic scattering in the rest frame of the atom) which is fast to compute and attains much higher accuracy than previous approximations for the astrophysically important case of small Voigt parameters. Further, the new approximation permits the diffusion in frequency of wing photons ('Doppler drifting') which is lost in one of the widely-used versions of the R(II-A) approximation schemes: Kneer's normalization of the Jefferies-White formulation.

Ayres, T. R.↗
DOE OSTI2026

Multiscale Neural Networks for Approximating Green’s Functions

Neural networks (NNs) have been widely used to solve partial differential equations (PDEs) in the applications of physics, biology, and engineering. One effective approach for solving PDEs with a fixed differential operator is learning Green’s functions. However, Green’s functions are notoriously difficult to learn due to their poor regularity, which typically requires larger NNs and longer training times. In this work, we address these challenges by leveraging multiscale NNs to learn Green’s functions. Through theoretical analysis using multiscale Barron space methods and experimental validation, we show that the multiscale approach significantly reduces the necessary NN size and accelerates training.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1978

The determination of gravity anomalies from geoid heights using the inverse Stokes' formula, Fourier transforms, and least squares collocation

A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite.

Rummel, R.↗
NASA NTRS1983

Spline approximation of quantile functions

The study reported here explored the development and utility of a spline representation of the sample quantile function of a continuous probability distribution in providing a functional description of a random sample and a method of generating random variables. With a spline representation, the random samples are generated by transforming a sample of uniform random variables to the interval of interest. This is useful, for example, in simulation studies in which a random sample represents the only known information about the distribution. The spline formulation considered here consists of a linear combination of cubic basis splines (B-splines) fit in a least squares sense to the sample quantile function using equally spaced knots. The following discussion is presented in five parts. The first section highlights major results realized from the study. The second section further details the results obtained. The methodology used is described in the third section, followed by a brief discussion of previous research on quantile functions. Finally, the results of the study are evaluated.

Schiess, J. R.↗
NASA NTRS1990

Neural computation of arithmetic functions

An area of application of neural networks is considered. A neuron is modeled as a linear threshold gate, and the network architecture considered is the layered feedforward network. It is shown how common arithmetic functions such as multiplication and sorting can be efficiently computed in a shallow neural network. Some known results are improved by showing that the product of two n-bit numbers and sorting of n n-bit numbers can be computed by a polynomial-size neural network using only four and five unit delays, respectively. Moreover, the weights of each threshold element in the neural networks require O(log n)-bit (instead of n-bit) accuracy. These results can be extended to more complicated functions such as multiple products, division, rational functions, and approximation of analytic functions.

Siu, Kai-Yeung↗