Results for “Vectorized algorithm” — Page 38

NASA NTRS1989

Multigrid solution of the Navier-Stokes equations on triangular meshes

A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.

Mavriplis, Dimitri J.↗

NASA NTRS1990

Multigrid solution of the Navier-Stokes equations on triangular meshes

A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.

Mavriplis, D. J.↗

NASA NTRS1992

Fast temporal neural learning using teacher forcing

A neural network is trained to output a time dependent target vector defined over a predetermined time interval in response to a time dependent input vector defined over the same time interval by applying corresponding elements of the error vector, or difference between the target vector and the actual neuron output vector, to the inputs of corresponding output neurons of the network as corrective feedback. This feedback decreases the error and quickens the learning process, so that a much smaller number of training cycles are required to complete the learning process. A conventional gradient descent algorithm is employed to update the neural network parameters at the end of the predetermined time interval. The foregoing process is repeated in repetitive cycles until the actual output vector corresponds to the target vector. In the preferred embodiment, as the overall error of the neural network output decreasing during successive training cycles, the portion of the error fed back to the output neurons is decreased accordingly, allowing the network to learn with greater freedom from teacher forcing as the network parameters converge to their optimum values. The invention may also be used to train a neural network with stationary training and target vectors.

Toomarian, Nikzad↗

NASA NTRS1995

Fast temporal neural learning using teacher forcing

A neural network is trained to output a time dependent target vector defined over a predetermined time interval in response to a time dependent input vector defined over the same time interval by applying corresponding elements of the error vector, or difference between the target vector and the actual neuron output vector, to the inputs of corresponding output neurons of the network as corrective feedback. This feedback decreases the error and quickens the learning process, so that a much smaller number of training cycles are required to complete the learning process. A conventional gradient descent algorithm is employed to update the neural network parameters at the end of the predetermined time interval. The foregoing process is repeated in repetitive cycles until the actual output vector corresponds to the target vector. In the preferred embodiment, as the overall error of the neural network output decreasing during successive training cycles, the portion of the error fed back to the output neurons is decreased accordingly, allowing the network to learn with greater freedom from teacher forcing as the network parameters converge to their optimum values. The invention may also be used to train a neural network with stationary training and target vectors.

Toomarian, Nikzad↗

NASA NTRS1996

Visualizing Time-Varying Phenomena In Numerical Simulations Of Unsteady Flows

Streamlines, contour lines, vector plots, and volume slices (cutting planes) are commonly used for flow visualization. These techniques are sometimes referred to as instantaneous flow visualization techniques because calculations are based on an instant of the flowfield in time. Although instantaneous flow visualization techniques are effective for depicting phenomena in steady flows,they sometimes do not adequately depict time-varying phenomena in unsteady flows. Streaklines and timelines are effective visualization techniques for depicting vortex shedding, vortex breakdown, and shock waves in unsteady flows. These techniques are examples of time-dependent flow visualization techniques, which are based on many instants of the flowfields in time. This paper describes the algorithms for computing streaklines and timelines. Using numerically simulated unsteady flows, streaklines and timelines are compared with streamlines, contour lines, and vector plots. It is shown that streaklines and timelines reveal vortex shedding and vortex breakdown more clearly than instantaneous flow visualization techniques.

Lane, David A.↗

DOE OSTI2024

Taylor-Expansion-Based Robust Power Flow in Unbalanced Distribution Systems: A Hybrid Data-Aided Method

Traditional power flow methods often adopt certain assumptions designed for passive balanced distribution systems, thus lacking practicality for unbalanced operation. moreover, their computation accuracy and efficiency are heavily subject to unknown errors and bad data in measurements or prediction data of distributed energy resources (ders). to address these issues, this paper proposes a hybrid data-aided robust power flow algorithm in unbalanced distribution systems, which combines taylor series expansion knowledge with a data-driven regression technique. the proposed method initiates a linearization power flow model to derive an explicitly analytical solution by modified taylor expansion. to mitigate the approximation loss that surges due to the der integration and bad data, we further develop a data-aided robust support vector regression approach to estimate the errors efficiently. comparative analysis in the 13-bus and 123-bus ieee unbalanced feeders shows that the proposed hybrid algorithm achieves superior computational efficiency, with guaranteed accuracy and robustness against outliers.

data-driven↗

NASA NTRS1977

Minimax decoding of cyclic block codes

A minimax decoding algorithm utilizing soft bit detection of an (n,k) cyclic block code is described which will permit the correction of up to n-k bit errors interspersed at random locations throughout the block. The decoding solution consists of: (1) identifying the ordered soft bit set and, (2) finding the minimum order solution to the resulting syndrome equations where the nonzero error vector components are constrained to be a subset of the soft bit set. An efficient implementation of the decoding operation is described. In essence, this algorithm focuses the correction capability of the code on those bit positions which have the lowest a posteriori probabilities of correct detection.

Greene, E. P.↗

NASA NTRS2015

Use of a Closed-Loop Tracking Algorithm for Orientation Bias Determination of an S-Band Ground Station

The Space Communications and Navigation (SCaN) Testbed project completed installation and checkout testing of a new S-Band ground station at the NASA Glenn Research Center in Cleveland, Ohio in 2015. As with all ground stations, a key alignment process must be conducted to obtain offset angles in azimuth (AZ) and elevation (EL). In telescopes with AZ-EL gimbals, this is normally done with a two-star alignment process, where telescope-based pointing vectors are derived from catalogued locations with the AZ-EL bias angles derived from the pointing vector difference. For an antenna, the process is complicated without an optical asset. For the present study, the solution was to utilize the gimbal control algorithms closed-loop tracking capability to acquire the peak received power signal automatically from two distinct NASA Tracking and Data Relay Satellite (TDRS) spacecraft, without a human making the pointing adjustments. Briefly, the TDRS satellite acts as a simulated optical source and the alignment process proceeds exactly the same way as a one-star alignment. The data reduction process, which will be discussed in the paper, results in two bias angles which are retained for future pointing determination. Finally, the paper compares the test results and provides lessons learned from the activity.

ground station↗

NASA NTRS2015

Use of a Closed-Loop Tracking Algorithm for Orientation Bias Determination of an S-Band Ground Station

The Space Communications and Navigation (SCaN) Testbed project completed installation and checkout testing of a new S-Band ground station at the NASA Glenn Research Center in Cleveland, Ohio in 2015. As with all ground stations, a key alignment process must be conducted to obtain offset angles in azimuth (AZ) and elevation (EL). In telescopes with AZ-EL gimbals, this is normally done with a two-star alignment process, where telescope-based pointing vectors are derived from catalogued locations with the AZ-EL bias angles derived from the pointing vector difference. For an antenna, the process is complicated without an optical asset. For the present study, the solution was to utilize the gimbal control algorithms closed-loop tracking capability to acquire the peak received power signal automatically from two distinct NASA Tracking and Data Relay Satellite (TDRS) spacecraft, without a human making the pointing adjustments. Briefly, the TDRS satellite acts as a simulated optical source and the alignment process proceeds exactly the same way as a one-star alignment. The data reduction process, which will be discussed in the paper, results in two bias angles which are retained for future pointing determination. Finally, the paper compares the test results and provides lessons learned from the activity.

reflector antenna↗

NASA NTRS1980

Short-interval SMS wind vector determinations for a severe local storms area

Short-interval SMS-2 visible digital image data are used to derive wind vectors from cloud tracking on time-lapsed sequences of geosynchronous satellite images. The cloud tracking areas are located in the Central Plains, where on May 6, 1975 hail-producing thunderstorms occurred ahead of a well defined dry line. Cloud tracking is performed on the Goddard Space Flight Center Atmospheric and Oceanographic Information Processing System. Lower tropospheric cumulus tracers are selected with the assistance of a cloud-top height algorithm. Divergence is derived from the cloud motions using a modified Cressman (1959) objective analysis technique which is designed to organize irregularly spaced wind vectors into uniformly gridded wind fields. The results demonstrate the feasibility of using satellite-derived wind vectors and their associated divergence fields in describing the conditions preceding severe local storm development. For this case, an area of convergence appeared ahead of the dry line and coincided with the developing area of severe weather. The magnitude of the maximum convergence varied between -10 to the -5th and -10 to the -14th per sec. The number of satellite-derived wind vectors which were required to describe conditions of the low-level atmosphere was adequate before numerous cumulonimbus cells formed. This technique is limited in areas of advanced convection.

Peslen, C. A.↗

DOE OSTI2026

Accelerating multigrid with streaming chiral SVD for Wilson fermions in lattice QCD

A modification to the setup algorithm for the multigrid preconditioner of Wilson fermions in lattice QCD is presented. A larger basis of test vectors than that used in regular multigrid is calculated by the smoother and truncated by singular value decomposition on the chiral components of the test vectors. The truncated basis is used to form the prolongation and restriction matrices of the multigrid hierarchy. This modification of the setup method is demonstrated to increase the convergence of linear solvers on an anisotropic lattice with m π ≈ 239 MeV from the Hadron Spectrum Collaboration and an isotropic lattice with m π ≈ 220 MeV from the MILC Collaboration. The lattice volume dependence of the method is also examined. Increasing the number of test vectors improves speedup up to a point, but storing these vectors becomes impossible in limited memory resources such as GPUs. To address storage cost, we implement a streaming singular value decomposition of the basis of test vectors on the chiral components and demonstrate a decrease in the number of fine level iterations by a factor of 1.7 for m q ≈ m crit

Iterative methods↗

DOE OSTI2024

Short-Term Probabilistic Solar Forecasting via Reinforcement Learning over ECMWF

In this paper, we present an innovative reinforcement learning approach for short-term solar forecasting, leveraging data from the European Centre for Medium-Range Weather Forecasts (ECMWF). The methodology begins with the application of the System Advisor Model (SAM) to transform various ECMWF numerical weather prediction members into predictive photovoltaic power generation. To enhance the precision of deterministic forecasting, we introduce a dynamic model selection algorithm based on Q-learning. This algorithm dynamically identifies and utilizes the most accurate ensemble member for forecasting purposes. Furthermore, we employ a support vector regression surrogate model with a Gaussian distribution to generate probabilistic forecasts, providing a holistic view of solar energy generation uncertainty. To expedite the training process and make it more practical for real-world applications, we integrate a rolling update workflow. This innovative workflow reduces the training period from months to a mere 19 days, making our method highly efficient. Numerical results of the case study show that in comparison to benchmark models, the proposed method improves the deterministic and probabilistic solar forecasting accuracy by up to 40.84% and 48.42%, respectively.

ensemble forecasting↗

NASA NTRS1975

Algorithms

The implementation of the algorithms used in the flight program to approximate elementary functions and mathematical procedures was checked. This was done by verifying that at least one, and in most cases, more than one function computed through the use of the algorithms was calculated properly. The following algorithms were checked: sine-cosine, arctangent, natural logarithm, square root, inverse square root, as well as the vector dot and cross products.

Source record↗

NASA NTRS1976

Singularity-free extraction of a quaternion from a direction-cosine matrix

A computer algorithm for extracting a quaternion from a direction-cosine matrix (DCM) is described. The quaternion provides a four-parameter representation of rotation, as against the nine-parameter representation afforded by a DCM. Commanded attitude in space shuttle steering is conveniently computed by DCM, while actual attitude is computed most compactly as a quaternion, as is attitude error. The unit length of the rotation quaternion, and interchangeable of a quaternion and its negative, are used to advantage in the extraction algorithm. Protection of the algorithm against square root failure and division overflow are considered. Necessary and sufficient conditions for handling the rotation vector element of largest magnitude are discussed

Klumpp, A. R.↗

NASA NTRS1982

Equivalent source modeling of the main field using MAGSAT data

An iterative least squares estimation algorithm with the capability for including a priori statistical information was implemented to recover multiple magnetic dipole models of the Earth's main magnetic field. The dipoles are fixed to a specified radius at or below the core-mantle boundary and centered on equal area blocks. The algorithm can solve for dipole magnitudes only (fixed orientations), or allow full freedom of orientation and solve for vector components. External field parameters and observatory anomaly biases can also be estimated simultaneously. Time dependence is modeled using first time derivatives for dipole vector components. Single-epoch and time dependent dipole models are derived using MAGSAT and observatory annul means data. Equivalent spherical harmonic representation are computed in closed form from the dipole models and compared with truncated spherical harmonic models estimated in the standard way from the same data sets. In particular, a 21 deg spatial resolution model based on 93 dipoles was computed based on observatory annual means data and a selected MAGSAT data set and was compared with candidate IGRF 1975 models and their 1980 secular variation.

Mayhew, M. A.↗

NASA NTRS1986

Results in least-square estimation algorithms with systolic array architectures

It is proposed that the derivation of least-square algorithms for systolic array processing is best accomplished via a geometrical approach. This approach generates a set of vector equations from which a large number of new and previously known systolic arrays can be obtained in a unified manner. The paper presents and qualitatively describes these vector equations and shows how one such systolic array follows.

Kalson, S.↗

NASA NTRS1987

Variational four-dimensional analysis using quasi-geostrophic constraints

A variational four-dimensional analysis technique using quasi-geostrophic models as constraints is examined using gridded fields as data. The analysis method uses a standard iterative nonlinear minimization technique to find the solution to the constraining forecast model which best fits the data as measured by a predefined functional. The minimization algorithm uses the derivative of the functional with respect to each of the initial condition values. This derivative vector is found by inserting the weighted differences between the model solution and the inserted data into a backwards integrating adjoint model. The four-dimensional analysis system was examined by applying it to fields created from a primitive equations model forecast and to fields created from satellite retrievals. The results show that the technique has several interesting characteristics not found in more traditional four-dimensional assimilation techniques. These features include a close fit of the model solution to the observations throughout the analysis interval and an insensitivity to the frequency of data insertion or the amount of data. The four-dimensional analysis technique is very versatile and can be extended to more complex problems with little theoretical difficulty.

Derber, John C.↗

NASA NTRS1991

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices

The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. An implementation is presented of a look-ahead version of the Lanczos algorithm that, except for the very special situation of an incurable breakdown, overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products as the standard Lanczos process without look-ahead.

Freund, Roland W.↗