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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 55 records · Page 3

Projection techniques for iterative solution of A(bar x) equals (bar b) with successive right-hand sides

Two projection techniques for computing approximate solutions to linear systems of the form A(bar x)(sup n) = (bar b)(sup n), for a sequence n = 1, 2, ..., e.g., such as arises from time discretization of a partial differential equation, are presented. The inexpensive approximate solutions can be used as initial guesses for iterative solution of the system, resulting in significantly reduced computational expense. Examples of two- and three-dimensional incompressible Navier-Stokes calculations are presented in which x represents the pressure, and A is a discrete Poisson operator. In flows containing significant dynamic activity, these projection techniques lead to as much as a two-fold reduction in solution time.

Fischer, Paul F.↗

The second-generation Shifted Boundary Method and its numerical analysis

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.

42 ENGINEERING↗

Ball bearing heat analysis program (BABHAP)

The Ball Bearing Heat Analysis Program (BABHAP) is an attempt to assemble a series of equations, some of which are non-linear algebraic systems, in a logical order, which when solved, provide a complex analysis of load distribution among the balls, ball velocities, heat generation resulting from friction, applied load, and ball spinning, minimum lubricant film thickness, and many additional characteristics of ball bearing systems. Although initial design requirements for BABHAP were dictated by the core limitations of the PDP 11/45 computer, (approximately 8K of real words with limited number of instructions) the program dimensions can easily be expanded for large core computers such as the UNIVAC 1108. The PDP version of BABHAP is also operational on the UNIVAC system with the exception that the PDP uses 029 punch and the UNIVAC uses 026. A conversion program was written to allow transfer between machines.

Source record↗

Probabilistic resource allocation system with self-adaptive capability

A probabilistic resource allocation system is disclosed containing a low capacity computational module (Short Term Memory or STM) and a self-organizing associative network (Long Term Memory or LTM) where nodes represent elementary resources, terminal end nodes represent goals, and weighted links represent the order of resource association in different allocation episodes. Goals and their priorities are indicated by the user, and allocation decisions are made in the STM, while candidate associations of resources are supplied by the LTM based on the association strength (reliability). Weights are automatically assigned to the network links based on the frequency and relative success of exercising those links in the previous allocation decisions. Accumulation of allocation history in the form of an associative network in the LTM reduces computational demands on subsequent allocations. For this purpose, the network automatically partitions itself into strongly associated high reliability packets, allowing fast approximate computation and display of allocation solutions satisfying the overall reliability and other user-imposed constraints. System performance improves in time due to modification of network parameters and partitioning criteria based on the performance feedback.

Yufik, Yan M.↗

Probabilistic resource allocation system with self-adaptive capability

A probabilistic resource allocation system is disclosed containing a low capacity computational module (Short Term Memory or STM) and a self-organizing associative network (Long Term Memory or LTM) where nodes represent elementary resources, terminal end nodes represent goals, and directed links represent the order of resource association in different allocation episodes. Goals and their priorities are indicated by the user, and allocation decisions are made in the STM, while candidate associations of resources are supplied by the LTM based on the association strength (reliability). Reliability values are automatically assigned to the network links based on the frequency and relative success of exercising those links in the previous allocation decisions. Accumulation of allocation history in the form of an associative network in the LTM reduces computational demands on subsequent allocations. For this purpose, the network automatically partitions itself into strongly associated high reliability packets, allowing fast approximate computation and display of allocation solutions satisfying the overall reliability and other user-imposed constraints. System performance improves in time due to modification of network parameters and partitioning criteria based on the performance feedback.

Yufik, Yan M.↗

Randomized Sketching Algorithms for Low-Memory Dynamic Optimization

This paper develops a novel limited-memory method to solve dynamic optimization problems. The memory requirements for such problems often present a major obstacle, particularly for problems with PDE constraints such as optimal flow control, full waveform inversion, and optical tomography. In these problems, PDE constraints uniquely determine the state of a physical system for a given control; the goal is to find the value of the control that minimizes an objective. While the control is often low dimensional, the state is typically more expensive to store. This paper suggests using randomized matrix approximation to compress the state as it is generated and shows how to use the compressed state to reliably solve the original dynamic optimization problem. Concretely, the compressed state is used to compute approximate gradients and to apply the Hessian to vectors. The approximation error in these quantities is controlled by the target rank of the sketch. This approximate first- and second-order information can readily be used in any optimization algorithm. As an example, we develop a sketched trust-region method that adaptively chooses the target rank using a posteriori error information and provably converges to a stationary point of the original problem. Numerical experiments with the sketched trust-region method show promising performance on challenging problems such as the optimal control of an advection-reaction-diffusion equation and the optimal control of fluid flow past a cylinder.

97 MATHEMATICS AND COMPUTING↗

HD-Bind: Encoding of Molecular Structure with Low Precision, Hyperdimensional Binary Representations

Publicly available collections of drug-like molecules have grown to comprise tens of billions of compounds due to advances in combinatorial chemistry. Traditional methods for identifying "hit" molecules from a large collection of potential drug-like candidates have relied on biophysical theory to compute approximations to the Gibbs free energy of the binding interaction between the drug and its protein target. These approaches have the major drawback that they require exceptional computing capabilities for even relatively small collections of molecules. Hyperdimensional Computing (HDC) is a recently-proposed learning paradigm that represents data with high-dimension binary vectors; this allows the use of low-precision binary vector arithmetic to create models of the data that can be learned without the need for the gradient-based optimization required in many conventional machine learning and deep learning methods. This algorithmic simplicity allows for acceleration in hardware that has been previously demonstrated in a range of application areas. We consider existing HDC approaches for molecular property classification and introduce two novel encodings of a commonly-used molecular representation, the extended connectivity fingerprint (ECFP). We show that HDC-based inference methods are as much as 91 times more efficient than traditional machine learning methods, and achieve an acceleration of nearly nine orders of magnitude compared to molecular docking. Our results show that HDC accelerated methods retain competitive accuracy on a number of well-studied tasks such as molecular property predictions using the MoleculeNet dataset, and bind/no-bind activity classification using the DUD-E and LIT-PCBA datasets. Our work thus motivates further investigation into molecular representation learning to develop ultraefficient pre-screening tools.

Jones, William↗

Verification of floating-point software

Floating point computation presents a number of problems for formal verification. Should one treat the actual details of floating point operations, or accept them as imprecisely defined, or should one ignore round-off error altogether and behave as if floating point operations are perfectly accurate. There is the further problem that a numerical algorithm usually only approximately computes some mathematical function, and we often do not know just how good the approximation is, even in the absence of round-off error. ORA has developed a theory of asymptotic correctness which allows one to verify floating point software with a minimum entanglement in these problems. This theory and its implementation in the Ariel C verification system are described. The theory is illustrated using a simple program which finds a zero of a given function by bisection. This paper is presented in viewgraph form.

Hoover, Doug N.↗

HDBind: encoding of molecular structure with hyperdimensional binary representations

Traditional methods for identifying “hit” molecules from a large collection of potential drug-like candidates rely on biophysical theory to compute approximations to the Gibbs free energy of the binding interaction between the drug and its protein target. These approaches have a significant limitation in that they require exceptional computing capabilities for even relatively small collections of molecules. Increasingly large and complex state-of-the-art deep learning approaches have gained popularity with the promise to improve the productivity of drug design, notorious for its numerous failures. However, as deep learning models increase in their size and complexity, their acceleration at the hardware level becomes more challenging. Hyperdimensional Computing (HDC) has recently gained attention in the computer hardware community due to its algorithmic simplicity relative to deep learning approaches. The HDC learning paradigm, which represents data with high-dimension binary vectors, allows the use of low-precision binary vector arithmetic to create models of the data that can be learned without the need for the gradient-based optimization required in many conventional machine learning and deep learning methods. This algorithmic simplicity allows for acceleration in hardware that has been previously demonstrated in a range of application areas (computer vision, bioinformatics, mass spectrometery, remote sensing, edge devices, etc.). To the best of our knowledge, our work is the first to consider HDC for the task of fast and efficient screening of modern drug-like compound libraries. We also propose the first HDC graph-based encoding methods for molecular data, demonstrating consistent and substantial improvement over previous work. We compare our approaches to alternative approaches on the well-studied MoleculeNet dataset and the recently proposed LIT-PCBA dataset derived from high quality PubChem assays. We demonstrate our methods on multiple target hardware platforms, including Graphics Processing Units (GPUs) and Field Programmable Gate Arrays (FPGAs), showing at least an order of magnitude improvement in energy efficiency versus even our smallest neural network baseline model with a single hidden layer. Our work thus motivates further investigation into molecular representation learning to develop ultra-efficient pre-screening tools. We make our code publicly available at https://github.com/LLNL/hdbind.

59 BASIC BIOLOGICAL SCIENCES↗

The role of fracture mechanics in the design of fuel tanks in space vehicles

With special reference to design of fuel tanks in space vehicles, the principles of fracture mechanics are reviewed. An approximate but extremely simple relationship is derived among the operating stress level, the length of crack, and the number of cycles of failure. Any one of the variables can be computed approximately from the knowledge of the other two, if the loading schedule (mission of the tank) is not greatly altered. Two sample examples illustrating the procedures of determining the allowable safe operating stress corresponding to a set of assumed loading schedule are included. The selection of sample examples is limited by the relatively meager available data on the candidate material for various stress ratios in the cycling.

Denton, S. J.↗

Modelling Equilibrium and Fractional Crystallization in the System MgO-FeO-CaO-Al2O3-SiO2

A mathematical modelling technique for use in petrogenesis calculations in the system MgO-FeO-CaO-Al2O3-SiO2 is reported. Semiempirical phase boundary and elemental distribution information was combined with mass balance to compute approximate equilibrium crystallization paths for arbitrary system compositions. The calculation is applicable to a range of system compositions and fractionation calculations are possible. The goal of the calculation is the computation of the composition and quantity of each phase present as a function of the degree of solidification. The degree of solidification is parameterized by the heat released by the solidifying phases. The mathematical requirement for the solution of this problem is: (1) An equation constraining the composition of the magma for each solid phase in equilibrium with the liquidus phase, and (2) an equation for each solid phase and each component giving the distribution of that element between that phase and the magma.

Herbert, F.↗

Scalable implementation of polynomial filtering for density functional theory calculation in PARSEC

In this work, we present an efficient implementation of polynomial filtering methods in PARSEC, a real-space pseudopotential based Kohn–Sham density functional theory solver. The implementation described here improves upon a Chebyshev-filtered subspace iteration algorithm used in the previous version of PARSEC. We present a hybrid polynomial filtering scheme that combines Chebyshev-filtered subspace iteration and a spectrum slicing method that partitions the spectrum into several spectral slices and uses bandpass-filtered subspace iteration to compute approximate eigenpairs within each interior slice simultaneously. We describe a procedure to partition a spectrum and construct polynomial filters. We also discuss a number of practical issues such as the use of appropriate data layouts for carrying out the computation on a two-dimensional process grid and how to achieve good load balance by allocating an appropriate number of process groups to each spectral slice. Numerical examples are presented to demonstrate the effectiveness of the hybrid polynomial filtering method as well as the superior parallel scalability of spectrum slicing in comparison to that of Chebyshev-filtered subspace iteration.

97 MATHEMATICS AND COMPUTING↗

Proceedings of the Third International Workshop on Neural Networks and Fuzzy Logic, volume 2

Papers presented at the Neural Networks and Fuzzy Logic Workshop sponsored by the National Aeronautics and Space Administration and cosponsored by the University of Houston, Clear Lake, held 1-3 Jun. 1992 at the Lyndon B. Johnson Space Center in Houston, Texas are included. During the three days approximately 50 papers were presented. Technical topics addressed included adaptive systems; learning algorithms; network architectures; vision; robotics; neurobiological connections; speech recognition and synthesis; fuzzy set theory and application, control and dynamics processing; space applications; fuzzy logic and neural network computers; approximate reasoning; and multiobject decision making.

Culbert, Christopher J.↗

Proceedings of the Third International Workshop on Neural Networks and Fuzzy Logic, volume 1

Documented here are papers presented at the Neural Networks and Fuzzy Logic Workshop sponsored by the National Aeronautics and Space Administration and cosponsored by the University of Houston, Clear Lake. The workshop was held June 1-3, 1992 at the Lyndon B. Johnson Space Center in Houston, Texas. During the three days approximately 50 papers were presented. Technical topics addressed included adaptive systems; learning algorithms; network architectures; vision; robotics; neurobiological connections; speech recognition and synthesis; fuzzy set theory and application, control, and dynamics processing; space applications; fuzzy logic and neural network computers; approximate reasoning; and multiobject decision making.

Culbert, Christopher J.↗

Methods and approximations for the computation of transmission profiles in the v4 band of methane in the atmosphere of Jupiter.

This note discusses the validity of certain band models and scaling approximations for computing transmissions in the v4 band of methane along inhomogeneous paths in the atmosphere of Jupiter. It is shown that Goody's random band model approximates the results of a rigorous numerical line-by-line calculation of the transmission profile of a Jovian model atmosphere.

Taylor, F. W.↗

Experimental Investigation of Impact in Landing on Water

The extent of agreement of the theoretical impact computations with the actual phenomenon has not as yet been fully clarified. There is on the one hand a certain imperfection in the theory (simplifying assumptions made) and on the other an insufficiency in the experimental data available. The object of our present paper is to show how far test results agree with the available approximate computation methods, to investigate in greater detail the physical nature of impact on water, and to perfect the experimental method of studying the phenomenon.

Kreps, R. L.↗

Estimates of Quantum Tunneling Effects for Hydrogen Diffusion in PuO 2

We detail the estimation of activation energies and quantum nuclear vibrational tunneling effects for hydrogen diffusion in PuO 2 based on Density Functional Theory calculations and a quantum double well approximation. We find that results are relatively insensitive to choice of exchange correlation functional. In addition, the representation of spin in the system and use of an extended Hubbard U correction has only a small effect on hydrogen point defect formation energies when the PuO 2 lattice is held fixed at the experimental density. We then compute approximate activation energies for transitions between hydrogen interstitial sites seeded by a semi-empirical quantum model and determine the quantum tunneling enhancement relative to classical kinetic rates. Our model indicates that diffusion rates in H/PuO 2 systems could be enhanced by more than one order of magnitude at ambient conditions and that these effects persist at high temperature. The method we propose here can be used as a fast screening tool for assessing possible quantum nuclear vibrational effects in any number of condensed phase materials and surfaces, where hydrogen hopping tends to follow well defined minimum energy pathways.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗