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Results for “Randomized methods”

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
NASA NTRS1982

Generation of pseudo-random numbers

Practical methods for generating acceptable random numbers from a variety of probability distributions which are frequently encountered in engineering applications are described. The speed, accuracy, and guarantee of statistical randomness of the various methods are discussed.

Howell, L. W.↗
DOE OSTI2025

Randomized Algorithms for Symmetric Nonnegative Matrix Factorization

Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a matrix with a product of a nonnegative, low-rank matrix and it transpose. To design faster and more scalable algorithms for SymNMF we develop two randomized algorithms for its computation. The first method uses randomized matrix sketching to compute an initial low-rank approximation to the input matrix and proceeds to uses this as a low-rank input to rapidly compute a SymNMF. The second methods uses randomized leverage score sampling to approximately solve constrained least squares problems. Many successful methods for SymNMF rely on (approximately) solving sequences of constrained least squares problems. Here, we prove theoretically that leverage score sampling can approximately solve constrained least squares problems to e-accuracy. Finally we demonstrate both methods work in practice by applying them to graph clustering tasks on large real world data sets. These experiments show that our methods approximately maintain solution quality and achieve significant speed ups for both large dense and large sparse problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Time and Frequency Domain Methods for Basis Selection in Random Linear Dynamical Systems

Polynomial chaos methods have been extensively used to analyze systems in uncertainty quantification. Furthermore, several approaches exist to determine a low-dimensional approximation (or sparse approximation) for some quantity of interest in a model, where just a few orthogonal basis polynomials are required. In this work, we consider linear dynamical systems consisting of ordinary differential equations with random variables. The aim of this paper is to explore methods for producing low-dimensional approximations of the quantity of interest further. We investigate two numerical techniques to compute a low-dimensional representation, which both fit the approximation to a set of samples in the time domain. On the one hand, a frequency domain analysis of a stochastic Galerkin system yields the selection of the basis polynomials. It follows a linear least squares problem. On the other hand, a sparse minimization yields the choice of the basis polynomials by information from the time domain only. An orthogonal matching pursuit produces an approximate solution of the minimization problem. Finally, we compare the two approaches using a test example from a mechanical application.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1978

A method for determining the weak statistical stationarity of a random process

A method for determining the weak statistical stationarity of a random process is presented. The core of this testing procedure consists of generating an equivalent ensemble which approximates a true ensemble. Formation of an equivalent ensemble is accomplished through segmenting a sufficiently long time history of a random process into equal, finite, and statistically independent sample records. The weak statistical stationarity is ascertained based on the time invariance of the equivalent-ensemble averages. Comparison of these averages with their corresponding time averages over a single sample record leads to a heuristic estimate of the ergodicity of a random process. Specific variance tests are introduced for evaluating the statistical independence of the sample records, the time invariance of the equivalent-ensemble autocorrelations, and the ergodicity. Examination and substantiation of these procedures were conducted utilizing turbulent velocity signals.

Sadeh, W. Z.↗
NASA NTRS2026

Methods for Validation of Random Uncertainty Estimates and Their Applications to Ozone Profiles From Limb-Viewing Satellite Instruments

For satellite measurements of atmospheric composition, the random uncertainty estimates provided by retrieval algorithms might be imperfect due to various approximations used in the retrievals or the presence of unknown error sources. This paper presents an overview of the methods used for the validation of random uncertainty estimates. All methods discussed in this study are categorized, and assumptions and limitations of each method are discussed. This overview evaluates these methods in application to ozone profile measurements from limb and occultation satellite instruments and provides practical illustrations of random uncertainty validation.

Viktoria F Sofieva↗
DOE OSTI2021

Application of the locally self-consistent embedding approach to the Anderson model with non-uniform random distributions

Highlights: • Typical Medium Theory (TMT) for the Anderson Localization. • Locally Self-Consistent Multiple Scattering Method (LSMS) for Random Disordered Systems. • Linear Scaling Computational Method for Random Disordered Systems. We apply the recently developed embedding scheme for the locally self-consistent method to random disorder electrons systems. The method is based on the locally self-consistent multiple scattering theory and the typical medium theory. The locally self-consistent multiple scattering theory divides a system into many small designated local interaction zones. The subsystem within each local interaction zone is embedded in a self-consistent field from the typical medium theory. This approximation allows the study of random systems with large numbers of sites. We present results for the three dimensional Anderson model with different random disorder potential distributions. Using the typical density of states as an indicator of Anderson localization, we find that the method can capture the localization for commonly studied disorder potentials. These include the uniform distribution, the Gaussian distribution, and even the unbounded Cauchy distribution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings

In this paper we develop a set of stochastic numerical schemes for hyperbolic and transport equations with diffusive scalings and subject to random inputs. The schemes are asymptotic preserving (AP), in the sense that they preserve the diffusive limits of the equations in discrete setting, without requiring excessive refinement of the discretization. Our stochastic AP schemes are extensions of the well-developed deterministic AP schemes. To handle the random inputs, we employ generalized polynomial chaos (gPC) expansion and combine it with stochastic Galerkin procedure. We apply the gPC Galerkin scheme to a set of representative hyperbolic and transport equations and establish the AP property in the stochastic setting. We then provide several numerical examples to illustrate the accuracy and effectiveness of the stochastic AP schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Devices and methods for increasing the speed and efficiency at which a computer is capable of modeling a plurality of random walkers using a particle method

A method for increasing a speed or energy efficiency at which a computer is capable of modeling a plurality of random walkers. The method includes defining a virtual space in which a plurality of virtual random walkers will move among different locations in the virtual space. The method also includes either assigning a corresponding set of ringed neurons in a spiking neural network to a corresponding virtual random walker, or assigning a corresponding set of ringed neurons to a point in the virtual space. Movement of a given virtual random walker is tracked by decoding differences between states of individual neurons in a corresponding given set of ringed neurons. A virtual random walk of the plurality of virtual random walkers is executed using the spiking neural network.

Aimone, James Bradley↗
DOE OSTI2014

New MOF based on lithium tetrahydrofuran-2,3,4,5-tetracarboxylate: Its structure and conductivity behavior

A novel metal–organic framework, [Li{sub 6}(HTFTA){sub 2}(H{sub 2}O){sub 3}]·3H{sub 2}O (LiTFTA, H{sub 4}TFTA is tetrahydrofuran-2,3,4,5-tetracarboxylic acid), has been synthesized under solvothermal conditions and its structure was determined by single-crystal X-ray diffraction studies. It has six different LiO{sub 4} tetrahedra which forms two kinds of tetranuclear clusters that are coordinated to the ligands and form an overall three-dimensional structure with channels running along the crystallographic a axis. Some of the carboxylate groups of the ligand moiety jut out into the channels and the channels are occupied by water molecules. The proton conductivity behavior of LiTFTA with respect to temperature and relative humidity was analyzed by our newly developed impedance data analysis method called a random-walk approach. The results were compared with the data obtained by an analysis using an equivalent electric circuit model. Based on the physical parameters obtained by the random-walk method and the known structure we suggested the mechanism of the proton conductivity in this material. The proton conduction proceeds most probably by a vehicle conduction mechanism which employs mainly water molecules of crystallization present in the channels of LiTFTA. The value of the diffusion coefficient increases with temperature whereas the number of charge carriers remains constant. On the other hand, both the number of charge carriers and diffusion coefficient increase with increasing relative humidity. - Graphical abstract: Structure of a new metal organic framework was determined and its ionic conductivity was evaluated using a random-walk approach. - Highlights: • Lithium tetrahydrofuran-2,3,4,5-tetracarboxylate is a MOF with water-filled pores. • The impedance spectra indicate that this material is ion conductive. • Conductivity was evaluated using a random walk approach. • The number of charge carriers and diffusion coefficient was determined.

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

Devices and methods for increasing the speed and efficiency at which a computer is capable of modeling a plurality of random walkers using a density method

A method for increasing a speed or energy efficiency at which a computer is capable of modeling a plurality of random walkers. The method includes defining a virtual space in which a plurality of virtual random walkers will move among different locations in the virtual space, wherein the virtual space comprises a plurality of vertices and wherein the different locations are ones of the plurality of vertices. A corresponding set of neurons in a spiking neural network is assigned to a corresponding vertex such that there is a correspondence between sets of neurons and the plurality of vertices, wherein a spiking neural network comprising a plurality of sets of spiking neurons is established. A virtual random walk of the plurality of virtual random walkers is executed using the spiking neural network, wherein executing includes tracking how many virtual random walkers are at each vertex at a given time increment.

Aimone, James Bradley↗
NASA NTRS1987

Natural fracture systems on planetary surfaces: Genetic classification and pattern randomness

One method for classifying natural fracture systems is by fracture genesis. This approach involves the physics of the formation process, and it has been used most frequently in attempts to predict subsurface fractures and petroleum reservoir productivity. This classification system can also be applied to larger fracture systems on any planetary surface. One problem in applying this classification system to planetary surfaces is that it was developed for ralatively small-scale fractures that would influence porosity, particularly as observed in a core sample. Planetary studies also require consideration of large-scale fractures. Nevertheless, this system offers some valuable perspectives on fracture systems of any size.

Rossbacher, Lisa A.↗
NASA NTRS1990

Wave propagation through random media: A local method of small perturbations based on the Helmholtz equation

Propagation of sound through the turbulent atmosphere is a statistical problem. The randomness of the refractive index field causes sound pressure fluctuations. Although no general theory to predict sound pressure statistics from given refractive index statistics exists, there are several approximate solutions to the problem. The most common approximation is the parabolic equation method. Results obtained by this method are restricted to small refractive index fluctuations and to small wave lengths. While the first condition is generally met in the atmosphere, it is desirable to overcome the second. A generalization of the parabolic equation method with respect to the small wave length restriction is presented.

Grosse, Ralf↗
NASA NTRS2017

Treatment of Overlapping Gaseous Absorption with the Correlated-k Method in Hot Jupiter and Brown Dwarf Atmosphere Models

The correlated-k method is frequently used to speed up radiation calculations in both one-dimensional and three-dimensional atmosphere models. An inherent difficulty with this method is how to treat overlapping absorption, i.e. absorption by more than one gas in a given spectral region. We have evaluated the applicability of three different methods in hot Jupiter and brown dwarf atmosphere models, all of which have been previously applied within models in the literature: (i) Random overlap, both with and without resorting and rebinning, (ii) equivalent extinction and (iii) pre-mixing of opacities, where (i) and (ii) combine k-coefficients for different gases to obtain k-coefficients for a mixture of gases, while (iii) calculates k-coefficients for a given mixture from the corresponding mixed line-by-line opacities. We find that the random overlap method is the most accurate and flexible of these treatments, and is fast enough to be used in one-dimensional models with resorting and rebinning. In three-dimensional models such as GCMs it is too slow, however, and equivalent extinction can provide a speed-up of at least a factor of three with only a minor loss of accuracy while at the same time retaining the flexibility gained by combining k-coefficients computed for each gas individually. Pre-mixed opacities are significantly less flexible, and we also find that particular care must be taken when using this method in order to to adequately resolve steep variations in composition at important chemical equilibrium boundaries. We use the random overlap method with resorting and rebinning in our one-dimensional atmosphere model and equivalent extinction in our GCM, which allows us to e.g. consistently treat the feedback of non-equilibrium chemistry on the total opacity and therefore the calculated P-T profiles in our models.

atmospheres↗
NASA NTRS2004

Multi-Agent Methods for the Configuration of Random Nanocomputers

As computational devices continue to shrink, the cost of manufacturing such devices is expected to grow exponentially. One alternative to the costly, detailed design and assembly of conventional computers is to place the nano-electronic components randomly on a chip. The price for such a trivial assembly process is that the resulting chip would not be programmable by conventional means. In this work, we show that such random nanocomputers can be adaptively programmed using multi-agent methods. This is accomplished through the optimization of an associated high dimensional error function. By representing each of the independent variables as a reinforcement learning agent, we are able to achieve convergence must faster than with other methods, including simulated annealing. Standard combinational logic circuits such as adders and multipliers are implemented in a straightforward manner. In addition, we show that the intrinsic flexibility of these adaptive methods allows the random computers to be reconfigured easily, making them reusable. Recovery from faults is also demonstrated.

Lawson, John W.↗