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A study of the Nordsieck-type predictor-corrector methods
Predictor-corrector schemes are discussed for the numerical integration of initial value problems by computer. Descloux formulas, which are considered modified Nordsieck formulas are studied because of their desirable stability and truncation properties along with the standard Nordsieck formulas. The stability of Nordsieck and modified Nordsieck algorithms are computed, and the results are graphed. Test problems are included as examples for comparing the efficiency of the algorithms.
Application of numerical methods to extend capabilities for optimal rocket guidance: report on reentry guidance of shuttle orbiter
Analytical models are presented for optimal trajectories and reentry guidance of the space shuttle orbiter. Major emphasis is placed on the development of a "footprint', which refers to a set of reachable destination positions attainable by the shuttle at a specified terminal altitude. An unconstrained reentry footprint was calculated for a shuttle vehicle which enters the earth's atmosphere at 93 km initial altitude after a deboost from a near earth orbit. The method of computation is briefly described, and graphs are presented which illustrate the footprint and the variation of state and control variables along it. The effects of constraints and of variations in initial state upon the footprint are discussed.
Modeling of multi-rotor torsional vibrations in rotating machinery using substructuring
The application of FEM modeling techniques to the analysis of torsional vibrations in complex rotating systems is described and demonstrated, summarizing results reported by Soares (1985). A substructuring approach is used for determination of torsional natural frequencies and resonant-mode shapes, steady-state frequency-sweep analysis, identification of dynamically unstable speed ranges, and characterization of transient linear and nonlinear systems. Results for several sample problems are presented in diagrams, graphs, and tables. STORV, a computer code based on this approach, is in use as a preliminary design tool for drive-train torsional analysis in the High Altitude Wind Tunnel at NASA Lewis.
A model for the distribution of dark matter, galaxies, and the intergalactic medium in a cold dark matter-dominated universe
The spatial distribution of the cold-dark-matter (CDM) and baryonic components of CDM-dominated cosmological models are characterized, summarizing the results of recent theoretical investigations. The evolution and distribution of matter in an Einstein-de Sitter universe on length scales small enough so that the Newtonian approximation is valid is followed chronologically, assuming (1) that the galaxies, CDM, and the intergalactic medium (IGM) are coupled by gravity, (2) that galaxies form by taking mass and momentum from the IGM, and (3) that the IGM responds to the energy input from the galaxies. The results of the numerical computations are presented in extensive graphs and discussed in detail.
Atmospheric absorption of sound - Update
Best current expressions for the vibrational relaxation times of oxygen and nitrogen in the atmosphere are used to compute total absorption. The resulting graphs of total absorption as a function of frequency for different humidities should be used in lieu of the graph published earlier by Evans et al (1972).
Aspects of unstructured grids and finite-volume solvers for the Euler and Navier-Stokes equations
Basic algorithms for unstructured mesh generation and fluid flow calculation are discussed. In particular the following are addressed: preliminaries of graphs and meshes; duality and data structures; basic graph operations important in CFD (Computational Fluid Dynamics); triangulation methods, including Varonoi diagrams and Delaunay triangulation; maximum principle analysis; finite volume schemes for scalar conservation law equations; finite volume schemes for the Euler and Navier-Stokes equations; and convergence acceleration for steady state calculations.
Streaming Matching and Edge Cover in Practice
Graph algorithms with polynomial space and time requirements often become infeasible for massive graphs with billions of edges or more. State-of-the-art approaches therefore employ approximate serial, parallel, and distributed algorithms to tackle these challenges. However, such approaches require storing the entire graph in memory and thus need access to costly computing resources such as clusters and supercomputers. In this paper, we present practical streaming approaches for solving massive graph problems using limited memory for two prototypical graph problems: maximum weighted matching and minimum weighted edge cover. For matching, we conduct a thorough computational study on two of the semi-streaming algorithms including a recent breakthrough result that achieves a $1/(2+\varepsilon)$-approximation of the weight while using $O( n \log W /\epsilon)$ memory (here $n$ is the number of vertices and $W$ is the maximum edge weight), designed by Paz and Schwartzman [SODA, 2017]. Empirically, we show that the semi-streaming algorithms produce matchings whose weight is close to the best $1/2$-approximate offline algorithm while requiring less time and an order-of-magnitude less memory. For minimum weighted edge cover, we develop three novel semi-streaming algorithms. Two of these algorithms require a single pass through the input graph, require $O(n \log n)$ memory, and provide a 2-approximation guarantee on the objective. We also leverage a relationship between approximate maximum weighted matching and approximate minimum weighted edge cover to develop a two-pass $3/2+\epsilon$-approximate algorithm with the memory requirement of Paz and Schwartzman's semi-streaming matching algorithm. These streaming approaches are compared against the state-of-the-art 3/2-approximate offline algorithm. The semi-streaming matching and the novel edge cover algorithms proposed in this paper can process graphs with several billions of edges in under 30 minutes using 6 GB of memory, which is at least an order of magnitude improvement from the offline (non-streaming) algorithms. For the largest graph, the best alternative offline parallel approximation algorithm (GPA+ROMA) could not finish in three hours even while employing hundreds of processors and 1 TB of memory. We also demonstrate an application of the semi-streaming algorithm by computing a matching using linearly bounded memory on item intersection graphs derived from three machine learning datasets, whereas the existing offline algorithms could not complete on one of these datasets since their memory requirements exceeded 1TB.
Distributed Multi-GPU Community Detection on Exascale Computing Platforms
Community detection is a fundamental operation in graph mining, and by uncovering hidden structures and patterns within complex systems it helps solve fundamental problems pertaining to social networks, such as information diffusion, epidemics, and recommender systems. Scaling graph algorithms for massive networks becomes challenging on modern distributed-memory multi-GPU (Graphics Processing Unit) systems due to limitations such as irregular memory access patterns, load imbalances, higher communication-computation ratios, and cross-platform support. We present a novel algorithm HiPDPL-GPU (distributed parallel Louvain) to address these challenges. We conduct experiments involving different partitioning techniques to achieve optimized performance of HiPDPL-GPU on the two largest supercomputers: Frontier and Summit. Remarkably, HiPDPL-GPU processes a graph with 4.2 billion edges in less than 3 minutes using 1024 GPUs. Qualitatively performance of HiPDPL-GPU is similar or better compared to other state-of-the-art CPU- and GPU-based implementations. While prior GPU implementations have predominantly employed CUDA, our first-of-its-kind implementation for community detection is cross-platform, accommodating both AMD and NVIDIA GPUs.
Distributed Multi-GPU Community Detection on Exascale Computing Platforms
Community detection is a fundamental operation in graph mining, and by uncovering hidden structures and patterns within complex systems it helps solve fundamental problems pertaining to social networks, such as information diffusion, epidemics, and recommender systems. Scaling graph algorithms for massive networks becomes challenging on modern distributed-memory multi-GPU (Graphics Processing Unit) systems due to limitations such as irregular memory access patterns, load imbalances, higher communication-computation ratios, and cross-platform support. We present a novel algorithm HiPDPL-GPU (Distributed Parallel Louvain) to address these challenges. We conduct experiments involving different partitioning techniques to achieve an optimized performance of HiPDPL-GPU on the two largest supercomputers: Frontier and Summit. Remarkably, HiPDPL-GPU processes a graph with 4.2 billion edges in less than 3 minutes using 1024 GPUs. Qualitatively, the performance of HiPDPL-GPU is similar or better compared to other state-of-the-art CPU- and GPU-based implementations. While prior GPU implementations have predominantly employed CUDA, our first-of-its-kind implementation for community detection is cross-platform, accommodating both AMD and NVIDIA GPUs.
Process and representation in graphical displays
Our initial model of graphic comprehension has focused on statistical graphs. Like other models of human-computer interaction, models of graphical comprehension can be used by human-computer interface designers and developers to create interfaces that present information in an efficient and usable manner. Our investigation of graph comprehension addresses two primary questions: how do people represent the information contained in a data graph?; and how do they process information from the graph? The topics of focus for graphic representation concern the features into which people decompose a graph and the representations of the graph in memory. The issue of processing can be further analyzed as two questions: what overall processing strategies do people use?; and what are the specific processing skills required?
Extending Power of Nature from Binary Problems to Real-Valued Graph Learning in Real World
Nature performs complex computations constantly at clearly lower cost and higher performance than digital computers. It is crucial to understand how to harness the unique computational power of nature in Machine Learning (ML). In the past decade, besides the development of Neural Networks (NNs), the community has also relentlessly explored nature-powered ML paradigms. Although most of them are still predominantly theoretical, a new practical paradigm enabled by the recent advent of CMOS-compatible room-temperature nature-based computers has emerged. By harnessing the nature's power of entropy increase, this paradigm can solve binary learning problems delivering immense speedup and energy savings compared with NNs, while maintaining comparable accuracy. Regrettably, its values to the real world are highly constrained by its binary nature. A clear pathway to its extension to real-valued problems remains elusive. This paper aims to unleash this pathway by proposing a novel end-to-end Nature-Powered Graph Learning (NP-GL) framework. Specifically, through a three-dimensional co-design, NP-GL can leverage the nature's power of entropy increase to efficiently solve real-valued graph learning problems. Experimental results across 4 real-world applications with 6 datasets demonstrate that NP-GL delivers, on average, 6970X speedup and 10^5x energy consumption reduction with comparable or even higher accuracy than Graph Neural Networks (GNNs).
Advanced Crew Personal Support Computer (CPSC) task
The topics are presented in view graph form and include: background; objectives of task; benefits to the Space Station Freedom (SSF) Program; technical approach; baseline integration; and growth and evolution options. The objective is to: (1) introduce new computer technology into the SSF Program; (2) augment core computer capabilities to meet additional mission requirements; (3) minimize risk in upgrading technology; and (4) provide a low cost way to enhance crew and ground operations support.
Maximum likelihood estimation for distributed parameter models of flexible spacecraft
A distributed-parameter model of the NASA Solar Array Flight Experiment spacecraft structure is constructed on the basis of measurement data and analyzed to generate a priori estimates of modal frequencies and mode shapes. A Newton-Raphson maximum-likelihood algorithm is applied to determine the unknown parameters, using a truncated model for the estimation and the full model for the computation of the higher modes. Numerical results are presented in a series of graphs and briefly discussed, and the significant improvement in computation speed obtained by parallel implementation of the method on a supercomputer is noted.
Geoid undulation computations at laser tracking stations
The accuracy of numerical computations of gravimetric undulations using recently proposed modifications of the classical Stokes formula is investigated. The basic formulations of the methods are outlined, and results from trial computations are presented in tables and graphs and compared with actual gravity data and/or GEOS-3/Seasat sea-surface heights. Although all of the methods gave similar results, the method of Sjoberg (1986) is recommended because of its superior theoretical precision. The importance of including terrain-corrected free-air anomalies in the computations is indicated.
Modern chemical graph theory
Abstract Graph theory has a long history in chemistry. Yet as the breadth and variety of chemical data is rapidly changing, so too do graph encoding methods and analyses that yield qualitative and quantitative insights. Using illustrative cases within a basic mathematical framework, we showcase modern chemical graph theory's utility in Chemists' analysis and model development toolkit. The encoding of both experimental and simulation data is discussed at various levels of granularity of information. This is followed by a discussion of the two major classes of graph theoretical analyses: identifying connectivity patterns and partitioning methods. Measures, metrics, descriptors, and topological indices are then introduced with an emphasis upon enhancing interpretability and incorporation into physical models. Challenging data cases are described that include strategies for studying time dependence. Throughout, we incorporate recent advancements in computer science and applied mathematics that are propelling chemical graph theory into new domains of chemical study. This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Structure and Mechanism > Computational Materials Science Structure and Mechanism > Molecular Structures
Increasing the hardness of posiform planting using random QUBOs for programmable quantum annealer benchmarking
Posiform planting is a method for constructing QUBO instances with a unique planted solution that can be tailored to arbitrary connectivity graphs. In this study we investigate making posiform planted QUBOs computationally harder by fusing many smaller random Ising models, whose global minimum is computed classically, with posiform planted QUBOs. The unique ground state of the resulting QUBO is the concatenation of (exactly one of) the ground states of each smaller problem. Our method generates QUBO instances that have a unique solution, are native to the hardware graph, and have tunable computational hardness. We use our QUBOs to benchmark three D-Wave quantum annealing processors (with 563–5627 qubits), and compare them against simulated annealing and Gurobi. Surprisingly, we find that the D-Wave ground state sampling success rate is not dependent on the glued random QUBO size, and that some QUBO classes are solved at high success rates at short annealing times on the Zephyr processors.
Citation network datasets for benchmarking spiking graph neural networks on experimental neuromorphic hardware
Spiking neural networks (SNNs) running on neuromorphic computers offer an energy-efficient alternative for AI tasks. Recently, spiking graph neural networks (S-GNNs) have been shown to produce encouraging results on benchmark citation network datasets such as Cora, CiteSeer, and PubMed for node classification tasks. These S-GNNs were run on SNN simulators only because they contain up to tens of thousands of neurons and up to millions of synapses, translating poorly to neuromorphic hardware. Therefore, in this paper, we create a suite of benchmark datasets from the CiteSeer dataset that can be accommodated on current neuromorphic hardware platforms. Our contribution consists of a collection of three datasets. First, we have an induced subgraph of CiteSeer, which we call MiniSeer, containing 2110 papers, 3604 binary features, and 6 topics. Second, MicroSeer is a very small dataset consisting of 84 papers, 1227 features, and 6 topics. Lastly, BiteSeer is a collection of 15 binary classification datasets. We present creation of these datasets along with accuracies, running times, and spike counts when simulated. We believe that our results in this paper will be used by the neuromorphic community to benchmark, test, and develop neuromorphic hardware and simulators.