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Large Scale Neuromorphic Computing at Sandia National Labs from Algorithms to Architectures
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Advances in Image-Domain Multi-Resolution and Super-Resolution Algorithms for Industrial X-Ray Computed Tomography: A Literature Survey and New Insights
Industrial X-ray Computed Tomography (XCT) is a nondestructive method for inspection and character ization of materials and parts. XCT captures images of a part from various angles, and these images are then used to construct Three-Dimensional (3D) representations of that part. This method enables assessing the quality of the parts, identifying defects and understanding their physical properties without damaging them.
Novel Algorithms for Beyond-von-Neumann Computing
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The application of generalized, cyclic, and modified numerical integration algorithms to problems of satellite orbit computation
Generalized, cyclic, and modified multistep numerical integration methods are developed and evaluated for application to problems of satellite orbit computation. Generalized methods are compared with the presently utilized Cowell methods; new cyclic methods are developed for special second-order differential equations; and several modified methods are developed and applied to orbit computation problems. Special computer programs were written to generate coefficients for these methods, and subroutines were written which allow use of these methods with NASA's GEOSTAR computer program.
Spectral analysis of GEOS-3 altimeter data and frequency domain collocation
The mathematical background in spectral analysis as applied to geodetic applications is summarized. The resolution (cut-off frequency) of the GEOS 3 altimeter data is examined by determining the shortest wavelength (corresponding to the cut-off frequency) recoverable. The data from some 18 profiles are used. The total power (variance) in the sea surface topography with respect to the reference ellipsoid as well as with respect to the GEM-9 surface is computed. A fast inversion algorithm for matrices of simple and block Toeplitz matrices and its application to least squares collocation is explained. This algorithm yields a considerable gain in computer time and storage in comparison with conventional least squares collocation. Frequency domain least squares collocation techniques are also introduced and applied to estimating gravity anomalies from GEOS 3 altimeter data. These techniques substantially reduce the computer time and requirements in storage associated with the conventional least squares collocation. Numerical examples given demonstrate the efficiency and speed of these techniques.
Apparatus for using a time interval counter to measure frequency stability
An apparatus for measuring the relative stability of two signals is disclosed comprising a means for mixing the two signals down to a beat note sine wave and for producing a beat note square wave whose upcrossings are the same as the sine wave. A source of reference frequency is supplied to a clock divider and interval counter to synchronize them and to generate a picket fence for providing a time reference grid of period shorter than the beat period. An interval counter is employed to make a preliminary measurement between successive upcrossings of the beat note square wave for providing an approximate time interval therebetween as a reference. The beat note square wave and the picket fence are then provided to the interval counter to provide an output consisting of the time difference between the upcrossing of each beat note square wave cycle and the next picket fence pulse such that the counter is ready for each upcrossing and dead time is avoided. A computer containing an algorithm for calculating the exact times of the beat note upcrossings then computes the upcrossing times.
Research in computational fluid dynamics and analysis of algorithms
Recently, higher-order compact schemes have seen increasing use in the DNS (Direct Numerical Simulations) of the Navier-Stokes equations. Although they do not have the spatial resolution of spectral methods, they offer significant increases in accuracy over conventional second order methods. They can be used on any smooth grid, and do not have an overly restrictive CFL dependence as compared with the O(N(exp -2)) CFL dependence observed in Chebyshev spectral methods on finite domains. In addition, they are generally more robust and less costly than spectral methods. The issue of the relative cost of higher-order schemes (accuracy weighted against physical and numerical cost) is a far more complex issue, depending ultimately on what features of the solution are sought and how accurately they must be resolved. In any event, the further development of the underlying stability theory of these schemes is important. The approach of devising suitable boundary clusters and then testing them with various stability techniques (such as finding the norm) is entirely the wrong approach when dealing with high-order methods. Very seldom are high-order boundary closures stable, making them difficult to isolate. An alternative approach is to begin with a norm which satisfies all the stability criteria for the hyperbolic system, and look for the boundary closure forms which will match the norm exactly. This method was used recently by Strand to isolate stable boundary closure schemes for the explicit central fourth- and sixth-order schemes. The norm used was an energy norm mimicking the norm for the differential equations. Further research should be devoted to BC for high order schemes in order to make sure that the results obtained are reliable. The compact fourth order and sixth order finite difference scheme had been incorporated into a code to simulate flow past circular cylinders. This code will serve as a verification of the full spectral codes. A detailed stability analysis by Carpenter (from the fluid Mechanics Division) and Gottlieb gave analytic conditions for stability as well as asymptotic stability. This had been incorporated in the code in form of stable boundary conditions. Effects of the cylinder rotations had been studied. The results differ from the known theoretical results. We are in the middle of analyzing the results. A detailed analysis of the effects of the heating of the cylinder on the shedding frequency had been studied using the above schemes. It has been found that the shedding frequency decreases when the wire was heated. Experimental work is being carried out to affirm this result.
Controlling under-actuated robot arms using a high speed dynamics process
The invention controls an under-actuated manipulator by first obtaining predetermined active joint accelerations of the active joints and the passive joint friction forces of the passive joints, then computing articulated body qualities for each of the joints from the current positions of the links, and finally computing from the articulated body qualities and from the active joint accelerations and the passive joint forces, active joint forces of the active joints. Ultimately, the invention transmits servo commands to the active joint forces thus computed to the respective ones of the joint servos. The computation of the active joint forces is accomplished using a recursive dynamics algorithm. In this computation, an inward recursion is first carried out for each link, beginning with the outermost link in order to compute the residual link force of each link from the active joint acceleration if the corresponding joint is active, or from the known passive joint force if the corresponding joint is passive. Then, an outward recursion is carried out for each link in which the active joint force is computed from the residual link force if the corresponding joint is active or the passive joint acceleration is computed from the residual link force if the corresponding joint is passive.
Reliability enhancement of Navier-Stokes codes through convergence acceleration
Methods for enhancing the reliability of Navier-Stokes computer codes through improving convergence characteristics are presented. The improving of these characteristics decreases the likelihood of code unreliability and user interventions in a design environment. The problem referred to as a 'stiffness' in the governing equations for propulsion-related flowfields is investigated, particularly in regard to common sources of equation stiffness that lead to convergence degradation of CFD algorithms. Von Neumann stability theory is employed as a tool to study the convergence difficulties involved. Based on the stability results, improved algorithms are devised to ensure efficient convergence in different situations. A number of test cases are considered to confirm a correlation between stability theory and numerical convergence. The examples of turbulent and reacting flow are presented, and a generalized form of the preconditioning matrix is derived to handle these problems, i.e., the problems involving additional differential equations for describing the transport of turbulent kinetic energy, dissipation rate and chemical species. Algorithms for unsteady computations are considered. The extension of the preconditioning techniques and algorithms derived for Navier-Stokes computations to three-dimensional flow problems is discussed. New methods to accelerate the convergence of iterative schemes for the numerical integration of systems of partial differential equtions are developed, with a special emphasis on the acceleration of convergence on highly clustered grids.
Machine-Vision Aids for Improved Flight Operations
The development of machine vision based pilot aids to help reduce night approach and landing accidents is explored. The techniques developed are motivated by the desire to use the available information sources for navigation such as the airport lighting layout, attitude sensors and Global Positioning System to derive more precise aircraft position and orientation information. The fact that airport lighting geometry is known and that images of airport lighting can be acquired by the camera, has lead to the synthesis of machine vision based algorithms for runway relative aircraft position and orientation estimation. The main contribution of this research is the synthesis of seven navigation algorithms based on two broad families of solutions. The first family of solution methods consists of techniques that reconstruct the airport lighting layout from the camera image and then estimate the aircraft position components by comparing the reconstructed lighting layout geometry with the known model of the airport lighting layout geometry. The second family of methods comprises techniques that synthesize the image of the airport lighting layout using a camera model and estimate the aircraft position and orientation by comparing this image with the actual image of the airport lighting acquired by the camera. Algorithms 1 through 4 belong to the first family of solutions while Algorithms 5 through 7 belong to the second family of solutions. Algorithms 1 and 2 are parameter optimization methods, Algorithms 3 and 4 are feature correspondence methods and Algorithms 5 through 7 are Kalman filter centered algorithms. Results of computer simulation are presented to demonstrate the performance of all the seven algorithms developed.
Self-consistent modeling of inner magnetospheric convection
The initial results of a model of inner magnetospheric convection are presented. The model employs the Rice convection model with a magnetic field computed with the constraint of magnetostatic equilibrium. The approach computes equilibria from a magnetofriction code which is a modified version of the Hesse-Birn equilibrium code adopted for use in the inner magnetosphere. The code uses the pressure distribution computed from the Rice convection model to update the magnetic field. The algorithm used to compute the inner magnetospheric equilibria is outlined, and the coupling of the equilibrium code with the convection model is described.
Early events in the folding of an amphipathic peptide: A multinanosecond molecular dynamics study
Folding of the capped LQQLLQQLLQL peptide is investigated at the water-hexane interface by molecular dynamics simulations for 161.5 ns. Initially placed in the aqueous phase as a beta-strand, the peptide rapidly adsorbs to the interface, where it adopts an amphipathic conformation. The marginal presence of nonamphipathic structures throughout the complete trajectory indicates that the corresponding conformations are strongly disfavored at the interface. It is further suggestive that folding in an interfacial environment proceeds through a pathway of successive amphipathic intermediates. The energetic and entropic penalties involved in the conformational changes along this pathway markedly increase the folding time scales of LQQLLQQLLQL, explaining why the alpha-helix, the hypothesized lowest free energy structure for a sequence with a hydrophobic periodicity of 3.6, has not been reached yet. The formation of a type I beta-turn at the end of the simulation confirms the importance of such motifs as initiation sites allowing the peptide to coalesce towards a secondary structure. Proteins 1999;36:383-399. Copyright 1999 Wiley-Liss, Inc.
Computational Sciences and Math at Sandia -- Algorithms Software and Applications.
Abstract not provided.
Theory and Computation of Optimal Low- and Medium- Thrust Orbit Transfers
This report presents new theoretical results which lead to new algorithms for the computation of fuel-optimal multiple-burn orbit transfers of low and medium thrust. Theoretical results introduced herein show how to add burns to an optimal trajectory and show that the traditional set of necessary conditions may be replaced with a much simpler set of equations. Numerical results are presented to demonstrate the utility of the theoretical results and the new algorithms. Two indirect methods from the literature are shown to be effective for the optimal orbit transfer problem with relatively small numbers of burns. These methods are the Minimizing Boundary Condition Method (MBCM) and BOUNDSCO. Both of these methods make use of the first-order necessary conditions exactly as derived by optimal control theory. Perturbations due to Earth's oblateness and atmospheric drag are considered. These perturbations are of greatest interest for transfers that take place between low Earth orbit altitudes and geosynchronous orbit altitudes. Example extremal solutions including these effects and computed by the aforementioned methods are presented. An investigation is also made into a suboptimal multiple-burn guidance scheme. The FORTRAN code developed for this study has been collected together in a package named ORBPACK. ORBPACK's user manual is provided as an appendix to this report.
A grid-embedding transonic flow analysis computer program for wing/nacelle configurations
An efficient grid-interfacing zonal algorithm was developed for computing the three-dimensional transonic flow field about wing/nacelle configurations. the algorithm uses the full-potential formulation and the AF2 approximate factorization scheme. The flow field solution is computed using a component-adaptive grid approach in which separate grids are employed for the individual components in the multi-component configuration, where each component grid is optimized for a particular geometry such as the wing or nacelle. The wing and nacelle component grids are allowed to overlap, and flow field information is transmitted from one grid to another through the overlap region using trivariate interpolation. This report represents a discussion of the computational methods used to generate both the wing and nacelle component grids, the technique used to interface the component grids, and the method used to obtain the inviscid flow solution. Computed results and correlations with experiment are presented. also presented are discussions on the organization of the wing grid generation (GRGEN3) and nacelle grid generation (NGRIDA) computer programs, the grid interface (LK) computer program, and the wing/nacelle flow solution (TWN) computer program. Descriptions of the respective subroutines, definitions of the required input parameters, a discussion on interpretation of the output, and the sample cases illustrating application of the analysis are provided for each of the four computer programs.
True Load Balancing for Matricized Tensor Times Khatri-Rao Product
MTTKRP is the bottleneck operation in algorithms used to compute the CP tensor decomposition. For sparse tensors, utilizing the compressed sparse fibers (CSF) storage format and the CSF-oriented MTTKRP algorithms is important for both memory and computational efficiency on distributed-memory architectures. Existing intelligent tensor partitioning models assume the computational cost of MTTKRP to be proportional to the total number of nonzeros in the tensor. However, this is not the case for the CSF-oriented MTTKRP on distributed-memory architectures. We outline two deficiencies of nonzero-based intelligent partitioning models when CSF-oriented MTTKRP operations are performed locally: failure to encode processors' computational loads and increase in total computation due to fiber fragmentation. We focus on existing fine-grain hypergraph model and propose a novel vertex weighting scheme that enables this model encode correct computational loads of processors. We also propose to augment the fine-grain model by fiber nets for reducing the increase in total computational load via minimizing fiber fragmentation. In this way, the proposed model encodes minimizing the load of the bottleneck processor. In conclusion, parallel experiments with real-world sparse tensors on up to 1024 processors prove the validity of the outlined deficiencies and demonstrate the merit of our proposed improvements in terms of parallel runtimes.
On the Computational Capabilities of Physical Systems: The Impossibility of Infallible Computation - Part 1
In this first of two papers, strong limits on the accuracy of physical computation are established. First it is proven that there cannot be a physical computer C to which one can pose any and all computational tasks concerning the physical universe. Next it is proven that no physical computer C can correctly carry out any computational task in the subset of such tasks that can be posed to C. This result holds whether the computational tasks concern a system that is physically isolated from C, or instead concern a system that is coupled to C. As a particular example, this result means that there cannot be a physical computer that can, for any physical system external to that computer, take the specification of that external system's state as input and then correctly predict its future state before that future state actually occurs; one cannot build a physical computer that can be assured of correctly 'processing information faster than the universe does'. The results also mean that there cannot exist an infallible, general-purpose observation apparatus, and that there cannot be an infallible, general-purpose control apparatus. These results do not rely on systems that are infinite, and/or non-classical, and/or obey chaotic dynamics. They also hold even if one uses an infinitely fast, infinitely dense computer, with computational powers greater than that of a Turing Machine. This generality is a direct consequence of the fact that a novel definition of computation - a definition of 'physical computation' - is needed to address the issues considered in these papers. While this definition does not fit into the traditional Chomsky hierarchy, the mathematical structure and impossibility results associated with it have parallels in the mathematics of the Chomsky hierarchy. The second in this pair of papers presents a preliminary exploration of some of this mathematical structure, including in particular that of prediction complexity, which is a 'physical computation analogue' of algorithmic information complexity. It is proven in that second paper that either the Hamiltonian of our universe proscribes a certain type of computation, or prediction complexity is unique (unlike algorithmic information complexity), in that there is one and only version of it that can be applicable throughout our universe.