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At least 721 records · Page 40

Computing Bounds on Resource Levels for Flexible Plans

A new algorithm efficiently computes the tightest exact bound on the levels of resources induced by a flexible activity plan (see figure). Tightness of bounds is extremely important for computations involved in planning because tight bounds can save potentially exponential amounts of search (through early backtracking and detection of solutions), relative to looser bounds. The bound computed by the new algorithm, denoted the resource-level envelope, constitutes the measure of maximum and minimum consumption of resources at any time for all fixed-time schedules in the flexible plan. At each time, the envelope guarantees that there are two fixed-time instantiations one that produces the minimum level and one that produces the maximum level. Therefore, the resource-level envelope is the tightest possible resource-level bound for a flexible plan because any tighter bound would exclude the contribution of at least one fixed-time schedule. If the resource- level envelope can be computed efficiently, one could substitute looser bounds that are currently used in the inner cores of constraint-posting scheduling algorithms, with the potential for great improvements in performance. What is needed to reduce the cost of computation is an algorithm, the measure of complexity of which is no greater than a low-degree polynomial in N (where N is the number of activities). The new algorithm satisfies this need. In this algorithm, the computation of resource-level envelopes is based on a novel combination of (1) the theory of shortest paths in the temporal-constraint network for the flexible plan and (2) the theory of maximum flows for a flow network derived from the temporal and resource constraints. The measure of asymptotic complexity of the algorithm is O(N O(maxflow(N)), where O(x) denotes an amount of computing time or a number of arithmetic operations proportional to a number of the order of x and O(maxflow(N)) is the measure of complexity (and thus of cost) of a maximumflow algorithm applied to an auxiliary flow network of 2N nodes. The algorithm is believed to be efficient in practice; experimental analysis shows the practical cost of maxflow to be as low as O(N1.5). The algorithm could be enhanced following at least two approaches. In the first approach, incremental subalgorithms for the computation of the envelope could be developed. By use of temporal scanning of the events in the temporal network, it may be possible to significantly reduce the size of the networks on which it is necessary to run the maximum-flow subalgorithm, thereby significantly reducing the time required for envelope calculation. In the second approach, the practical effectiveness of resource envelopes in the inner loops of search algorithms could be tested for multi-capacity resource scheduling. This testing would include inner-loop backtracking and termination tests and variable and value-ordering heuristics that exploit the properties of resource envelopes more directly.

Muscvettola, Nicola↗

Robust tuning of robot control systems

The computed torque control problem is examined for a robot arm with flexible, geared, joint drive systems which are typical in many industrial robots. The standard computed torque algorithm is not directly applicable to this class of manipulators because of the dynamics introduced by the joint drive system. The proposed approach to computed torque control combines a computed torque algorithm with torque controller at each joint. Three such control schemes are proposed. The first scheme uses the joint torque control system currently implemented on the robot arm and a novel form of the computed torque algorithm. The other two use the standard computed torque algorithm and a novel model following torque control system based on model following techniques. Standard tasks and performance indices are used to evaluate the performance of the controllers. Both numerical simulations and experiments are used in evaluation. The study shows that all three proposed systems lead to improved tracking performance over a conventional PD controller.

Minis, I.↗

Cloud identification using genetic algorithms and massively parallel computation

As a Guest Computational Investigator under the NASA administered component of the High Performance Computing and Communication Program, we implemented a massively parallel genetic algorithm on the MasPar SIMD computer. Experiments were conducted using Earth Science data in the domains of meteorology and oceanography. Results obtained in these domains are competitive with, and in most cases better than, similar problems solved using other methods. In the meteorological domain, we chose to identify clouds using AVHRR spectral data. Four cloud speciations were used although most researchers settle for three. Results were remarkedly consistent across all tests (91% accuracy). Refinements of this method may lead to more timely and complete information for Global Circulation Models (GCMS) that are prevalent in weather forecasting and global environment studies. In the oceanographic domain, we chose to identify ocean currents from a spectrometer having similar characteristics to AVHRR. Here the results were mixed (60% to 80% accuracy). Given that one is willing to run the experiment several times (say 10), then it is acceptable to claim the higher accuracy rating. This problem has never been successfully automated. Therefore, these results are encouraging even though less impressive than the cloud experiment. Successful conclusion of an automated ocean current detection system would impact coastal fishing, naval tactics, and the study of micro-climates. Finally we contributed to the basic knowledge of GA (genetic algorithm) behavior in parallel environments. We developed better knowledge of the use of subpopulations in the context of shared breeding pools and the migration of individuals. Rigorous experiments were conducted based on quantifiable performance criteria. While much of the work confirmed current wisdom, for the first time we were able to submit conclusive evidence. The software developed under this grant was placed in the public domain. An extensive user's manual was written and distributed nationwide to scientists whose work might benefit from its availability. Several papers, including two journal articles, were produced.

Buckles, Bill P.↗

The Locus Algorithm III: A Grid Computing system to generate catalogues of optimised pointings for Differential Photometry

This paper discusses the hardware and software components of the Grid Computing system used to implement the Locus Algorithm to identify optimum pointings for differential photometry of 61,662,376 stars and 23,799 quasars. The scale of the data, together with initial operational assessments demanded a High Performance Computing (HPC) system to complete the data analysis. Grid computing was chosen as the HPC solution as the optimum choice available within this project. The physical and logical structure of the National Grid computing Infrastructure informed the approach that was taken. That approach was one of layered separation of the different project components to enable maximum flexibility and extensibility.

Creaner, Oisń↗

Computer architecture for efficient algorithmic executions in real-time systems: New technology for avionics systems and advanced space vehicles

Improvements and advances in the development of computer architecture now provide innovative technology for the recasting of traditional sequential solutions into high-performance, low-cost, parallel system to increase system performance. Research conducted in development of specialized computer architecture for the algorithmic execution of an avionics system, guidance and control problem in real time is described. A comprehensive treatment of both the hardware and software structures of a customized computer which performs real-time computation of guidance commands with updated estimates of target motion and time-to-go is presented. An optimal, real-time allocation algorithm was developed which maps the algorithmic tasks onto the processing elements. This allocation is based on the critical path analysis. The final stage is the design and development of the hardware structures suitable for the efficient execution of the allocated task graph. The processing element is designed for rapid execution of the allocated tasks. Fault tolerance is a key feature of the overall architecture. Parallel numerical integration techniques, tasks definitions, and allocation algorithms are discussed. The parallel implementation is analytically verified and the experimental results are presented. The design of the data-driven computer architecture, customized for the execution of the particular algorithm, is discussed.

Carroll, Chester C.↗

Implementation of a Wavefront-Sensing Algorithm

A computer program has been written as a unique implementation of an image-based wavefront-sensing algorithm reported in "Iterative-Transform Phase Retrieval Using Adaptive Diversity" (GSC-14879-1), NASA Tech Briefs, Vol. 31, No. 4 (April 2007), page 32. This software was originally intended for application to the James Webb Space Telescope, but is also applicable to other segmented-mirror telescopes. The software is capable of determining optical-wavefront information using, as input, a variable number of irradiance measurements collected in defocus planes about the best focal position. The software also uses input of the geometrical definition of the telescope exit pupil (otherwise denoted the pupil mask) to identify the locations of the segments of the primary telescope mirror. From the irradiance data and mask information, the software calculates an estimate of the optical wavefront (a measure of performance) of the telescope generally and across each primary mirror segment specifically. The software is capable of generating irradiance data, wavefront estimates, and basis functions for the full telescope and for each primary-mirror segment. Optionally, each of these pieces of information can be measured or computed outside of the software and incorporated during execution of the software.

Smith, Jeffrey S.↗

Computing rank‐revealing factorizations of matrices stored out‐of‐core

This paper describes efficient algorithms for computing rank-revealing factorizations of matrices that are too large to fit in main memory (RAM), and must instead be stored on slow external memory devices such as disks (out-of-core or out-of-memory). Traditional algorithms for computing rank-revealing factorizations (such as the column pivoted QR factorization and the singular value decomposition) are very communication intensive as they require many vector-vector and matrix-vector operations, which become prohibitively expensive when data is not in RAM. Randomization allows to reformulate new methods so that large contiguous blocks of the matrix are processed in bulk. The paper describes two distinct methods. The first is a blocked version of column pivoted Householder QR, organized as a “left-looking” method to minimize the number of the expensive write operations. The second method results employs a UTV factorization. It is organized as an algorithm-by-blocks to overlap computations and I/O operations. As it incorporates power iterations, it is much better at revealing the numerical rank. Numerical experiments on several computers demonstrate that the new algorithms are almost as fast when processing data stored on slow memory devices as traditional algorithms are for data stored in RAM.

97 MATHEMATICS AND COMPUTING↗

Uncontrolled Learning: Codesign of Neuromorphic Hardware Topology for Neuromorphic Algorithms

Neuromorphic computing has the potential to revolutionize future technologies and our understanding of intelligence, yet it remains challenging to realize in practice. The learning-from-mistakes algorithm, inspired by the brain's simple learning rules of inhibition and pruning, is one of the few brain-like training methods. This algorithm is implemented in neuromorphic memristive hardware through a codesign process that evaluates essential hardware trade-offs. While the algorithm effectively trains small networks as binary classifiers and perceptrons, performance declines significantly with increasing network size unless the hardware is tailored to the algorithm. This work investigates the trade-offs between depth, controllability, and capacity—the number of learnable patterns—in neuromorphic hardware. This highlights the importance of topology and governing equations, providing theoretical tools to evaluate a device's computational capacity based on its measurements and circuit structure. The findings show that breaking neural network symmetry enhances both controllability and capacity. Additionally, by pruning the circuit, neuromorphic algorithms in all-memristive circuits can utilize stochastic resources to create local contrasts in network weights. Through combined experimental and simulation efforts, the parameters are identified that enable networks to exhibit emergent intelligence from simple rules, advancing the potential of neuromorphic computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Study of the mapping of Navier-Stokes algorithms onto multiple-instruction/multiple-data-stream computers

Implicit approximate-factored algorithms have certain properties that are suitable for parallel processing. A particular computational fluid dynamics (CFD) code, using this algorithm, is mapped onto a multiple-instruction/multiple-data-stream (MIMD) computer architecture. An explanation of this mapping procedure is presented, as well as some of the difficulties encountered when trying to run the code concurrently. Timing results are given for runs on the Ames Research Center's MIMD test facility which consists of two VAX 11/780's with a common MA780 multi-ported memory. Speedups exceeding 1.9 for characteristic CFD runs were indicated by the timing results.

Eberhardt, D. S.↗

From NWChem to NWChemEx: Evolving with the Computational Chemistry Landscape

Since the advent of the first computers, chemists have been at the forefront of using computers to understand and solve complex chemical problems. As the hardware and software have evolved, so have the theoretical and computational chemistry methods and algorithms. Parallel computers clearly changed the common computing paradigm in the late 1970s and 80s, and the field has again seen a paradigm shift with the advent of graphical processing units. This review explores the challenges and some of the solutions in transforming software from the terascale to the petascale and now to the upcoming exascale computers. While discussing the field in general, NWChem and its redesign, NWChemEx, will be highlighted as one of the early codesign projects to take advantage of massively parallel computers and emerging software standards to enable large scientific challenges to be tackled.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms

The computational capabilities of near-term quantum computers are limited by the noisy execution of gate operations and a limited number of physical qubits. Hybrid variational algorithms are well-suited to near-term quantum devices because they allow for a wide range of tradeoffs between the amount of quantum and classical resources used to solve a problem. This paper investigates tradeoffs available at both the algorithmic and hardware levels by studying a specific case – applying the Quantum Approximate Optimization Algorithm (QAOA) to instances of the Maximum Independent Set (MIS) problem. We consider three variants of the QAOA which offer different tradeoffs at the algorithmic level in terms of their required number of classical parameters, quantum gates, and iterations of classical optimization needed. Since MIS is a constrained combinatorial optimization problem, the QAOA must respect the problem constraints. This can be accomplished by using many multi-controlled gate operations which must be decomposed into gates executable by the target hardware. We study the tradeoffs available at this hardware level, combining the gate fidelities and decomposition efficiencies of different native gate sets into a single metric called the gate decomposition cost .

Tomesh, Teague↗

Avoiding excess computation in asynchronous evolutionary algorithms

Abstract Asynchronous evolutionary algorithms are becoming increasingly popular as a means of making full use of many processors while solving computationally expensive search and optimization problems. These algorithms excel at keeping large clusters fully utilized, but may sometimes inefficiently sample an excess of fast‐evaluating solutions at the expense of higher‐quality, slow‐evaluating ones. We have previously introduced a steady‐state parent selection strategy, SWEET (“Selection whilE EvaluaTing”), that sometimes selects individuals that are still being evaluated and allows them to reproduce early. We perform a takeover‐time analysis that confirms that this strategy gives slow‐evaluating individuals that have higher fitnesses an increased ability to multiply in the population. We also find that SWEET appears effective at improving optimization performance on problems in which solution quality is positively correlated with evaluation time. We evaluate our approach on six simulated real‐valued optimization problems and three real‐world applications: an autonomous vehicle controller problem that involves tuning a spiking neural network and two adversarial EA problems. We further evaluate SWEET versus a basic asynchronous process in a simulated setting. We present evidence that SWEET outperforms basic asynchronous processes in a use‐case in which performance is positively correlated with evaluation time, and performs comparably (and often better) than basic asynchronous processes in several use‐cases where performance is negatively correlated with evaluation time. That said, in the cases where performance and evaluation time are negatively correlated the variance of outcomes for SWEET is notably high.

97 MATHEMATICS AND COMPUTING↗

Computation of Symmetric Discrete Cosine Transform Using Bakhvalov's Algorithm

A number of algorithms for recursive computation of the discrete cosine transform (DCT) have been developed recently. This paper presents a new method for computing the discrete cosine transform and its inverse using Bakhvalov's algorithm, a method developed for evaluation of a polynomial at a point. In this paper, we will focus on both the application of the algorithm to the computation of the DCT-I and its complexity. In addition, Bakhvalov s algorithm is compared with Clenshaw s algorithm for the computation of the DCT.

Aburdene, Maurice F.↗

Improving Computational Efficiency of Prognostics Algorithms in Resource-Constrained Settings

The field of prognostics and health management provides quantitative methods for monitoring and predicting the health of physical systems. Prognostics algorithms are useful in that they can be employed to assess the current state of a system, propagate the system state throughout time, and predict potential anomalies or failures that may occur. However, effective prognosis can be challenging to achieve in resource-constrained settings due to computational limitations and high computational latency, leading to obsolete predictions. Thus, computationally efficient and accurate algorithms are necessary for some prognostics applications. In this work, we implement three new algorithmic approaches to prediction (sampling methods, variable prediction time step, variable prediction sample size) with the goal of improving computational efficiency while minimizing decrease in model accuracy. To quantitatively analyze our results, we examine a use-case of degradation of a Lithium-ion battery. Notably, through this work it was found that none of the sampling approaches had a significant impact on computational efficiency or model accuracy in predicting EOD of the battery. However, our results show that prediction accuracy is highly dependent on the time step used, and that an appropriate time step can optimize both model accuracy and simulation efficiency. Finally, implementing a variable sample size also affected prediction, and our results show that tuning both the magnitude and timing of the sample size adjustment in an application-specific manner may prove useful in some applications. Taken together, our findings highlight the challenge of performing prognostics in resource-constrained settings, and illustrate the potential of developing new prediction algorithms to improve computational efficiency of prognosis.

Prognostics↗

Principal Landau determinants

We reformulate the Landau analysis of Feynman integrals with the aim of advancing the state of the art in modern particle-physics computations. We contribute new algorithms for computing Landau singularities, using tools from polyhedral geometry and symbolic/numerical elimination. Inspired by the work of Gelfand, Kapranov, and Zelevinsky (GKZ) on generalized Euler integrals, we define the principal Landau determinant of a Feynman diagram. We illustrate with a number of examples that this algebraic formalism allows to compute many components of the Landau singular locus. We adapt the GKZ framework by carefully specializing Euler integrals to Feynman integrals. For instance, ultraviolet and infrared singularities are detected as irreducible components of an incidence variety, which project dominantly to the kinematic space. We compute principal Landau determinants for the infinite families of one-loop and banana diagrams with different mass configurations, and for a range of cutting-edge Standard Model processes. Furthermore, our algorithms build on the Julia package this http URL and are implemented in the new open-source package this http URL available at this https URL.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Quantum tensor network algorithms for evaluation of spectral functions on quantum computers

We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we call a quantum tensor network (QTN), we demonstrate algorithms to prepare ground and excited states on a quantum computer and apply them to molecular nanomagnets (MNMs) as a paradigmatic example. In this setting, we develop two approaches for extracting the spectral correlation functions measured in neutron-scattering experiments: (a) a generalization of the SWAP test for computing wave function overlaps and, (b) a generalization of the notion of matrix product operators to the QTN setting which generates a linear combination of unitaries. The latter method is discussed in detail for translationally invariant spin-half systems, where it is shown to reduce the qubit resource requirements compared with the SWAP method and may be generalized to other systems. We demonstrate the versatility of our approaches by simulating spin-1/2 and spin-3/2 MNMs, with the latter being an experimentally relevant model of a Cr$^{3+}_{8}$ ring. Here, our approach has qubit requirements that are independent of the number of constituents of the many-body system and scale only logarithmically with the bond dimension of the MPS representation, making them appealing for implementation on near-term quantum hardware with mid-circuit measurement and reset.

Neutron scattering↗

Efficient computation of N -point correlation functions in D dimensions

We present efficient algorithms for computing the N-point correlation functions (NPCFs) of random fields in arbitrary D-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences and provide a natural tool to describe stochastic processes. Typically, algorithms for computing the NPCF components have $\mathscr O$(n N ) complexity (for a dataset containing n particles); their application is thus computationally infeasible unless N is small. By projecting the statistic onto a suitably defined angular basis, we show that the estimators can be written in a separable form, with complexity $\mathscr O$(n 2 ) or $\mathscr O$(n g log n g ) if evaluated using a Fast Fourier Transform on a grid of size n g . Our decomposition is built upon the D-dimensional hyperspherical harmonics; these form a complete basis on the (D – 1) sphere and are intrinsically related to angular momentum operators. Concatenation of (N – 1) such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. As N and D grow, the number of basis components quickly becomes large, providing a practical limitation to this (and all other) approaches: However, the dimensionality is greatly reduced in the presence of symmetries; for example, isotropic correlation functions require only states of zero combined angular momentum. We provide a Julia package implementing our estimators and show how they can be applied to a variety of scenarios within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.

97 MATHEMATICS AND COMPUTING↗