Computing polynomial resultants - Bezout's determinant vs. Collins' reduced P.R.S. algorithm.
Algorithms for polynominal resultants computation, considering extraneous factors, truncation errors, memory and computing speed
Adler, R. J.↗
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Results for “compute in memory”
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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Transonic aerodynamics - History and statement of the problem
An historical account is given of the state of transonic aerodynamics research and theorization before 1940, and at selected points between that year and 1975, in order to provide a basis for the understanding and evaluation of the most recent developments in the field. Intensive development began during the Second World War, when fighter aircraft diving at speeds in excess of Mach 0.8 underwent buffeting and longitudinal trim shift effects. By 1960, transonic small disturbance theory had been established as a mathematical model for the prediction of the aerodynamic properties of airfoils, wings, and bodies throughout the Mach number range from zero to 1.5. In the years leading up to 1975, which saw the formulation of the transonic equivalence rule, improvements in the computational speed and memory capacity of computers became the most significant factor in the development of theory.
Spreiter, J. R.↗
Application of the Hughes-LIU algorithm to the 2-dimensional heat equation
An implicit explicit algorithm for the solution of transient problems in structural dynamics is described. The method involved dividing the finite elements into implicit and explicit groups while automatically satisfying the conditions. This algorithm is applied to the solution of the linear, transient, two dimensional heat equation subject to an initial condition derived from the soluton of a steady state problem over an L-shaped region made up of a good conductor and an insulating material. Using the IIT/PRIME computer with virtual memory, a FORTRAN computer program code was developed to make accuracy, stability, and cost comparisons among the fully explicit Euler, the Hughes-Liu, and the fully implicit Crank-Nicholson algorithms. The Hughes-Liu claim that the explicit group governs the stability of the entire region while maintaining the unconditional stability of the implicit group is illustrated.
Malkus, D. S.↗
LANDSAT-D flight segment operations manual. Appendix B: OBC software operations
The LANDSAT 4 satellite contains two NASA standard spacecraft computers and 65,536 words of memory. Onboard computer software is divided into flight executive and applications processors. Both applications processors and the flight executive use one or more of 67 system tables to obtain variables, constants, and software flags. Output from the software for monitoring operation is via 49 OBC telemetry reports subcommutated in the spacecraft telemetry. Information is provided about the flight software as it is used to control the various spacecraft operations and interpret operational OBC telemetry. Processor function descriptions, processor operation, software constraints, processor system tables, processor telemetry, and processor flow charts are presented.
Talipsky, R.↗
Design applications for supercomputers
The complexity of codes for solutions of real aerodynamic problems has progressed from simple two-dimensional models to three-dimensional inviscid and viscous models. As the algorithms used in the codes increased in accuracy, speed and robustness, the codes were steadily incorporated into standard design processes. The highly sophisticated codes, which provide solutions to the truly complex flows, require computers with large memory and high computational speed. The advent of high-speed supercomputers, such that the solutions of these complex flows become more practical, permits the introduction of the codes into the design system at an earlier stage. The results of several codes which either were already introduced into the design process or are rapidly in the process of becoming so, are presented. The codes fall into the area of turbomachinery aerodynamics and hypersonic propulsion. In the former category, results are presented for three-dimensional inviscid and viscous flows through nozzle and unducted fan bladerows. In the latter category, results are presented for two-dimensional inviscid and viscous flows for hypersonic vehicle forebodies and engine inlets.
Studerus, C. J.↗
Research in Computational Aeroscience Applications Implemented on Advanced Parallel Computing Systems
Improving the numerical linear algebra routines for use in new Navier-Stokes codes, specifically Tim Barth's unstructured grid code, with spin-offs to TRANAIR is reported. A fast distance calculation routine for Navier-Stokes codes using the new one-equation turbulence models is written. The primary focus of this work was devoted to improving matrix-iterative methods. New algorithms have been developed which activate the full potential of classical Cray-class computers as well as distributed-memory parallel computers.
Wigton, Larry↗
Structure-preserving neural networks for the regularized entropy-based closure of a linear, kinetic, radiative transport equation
The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural network-based approximation to the entropy-based closure method to accurately compute the solution of the multi-dimensional moment system with a low memory footprint and competitive computational time. We extend methods developed for the standard entropy-based closure to the regularized entropy-based closures. The main idea is to interpret structure-preserving neural network approximations of the regularized entropy-based closure as a two-stage approximation to the original entropy-based closure. We conduct a numerical analysis of this approximation and investigate optimal parameter choices. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive computation times and simulation accuracy. The code and all trained networks are provided on GitHub.
entropy closure↗
Towards memristor supremacy with novel machine learning algorithms
The von Neumann architecture for current computers is slowly showing signs of limitations, due to the finite bus rate between the RAM (memory) and the CPU (computing unit). In-Memory computing is an alternative to this architecture, which however is still in the early stages of development. Memristors are an analog and classical alternative, as these components can act both as a memory, or as a simple computing unit. When wired together, these can in fact be used for a variety of applications. During the course of our research, we have developed an in-depth experimental understanding of both the limitations and the real possibilities of these devices, and developed automated algorithms for their characterization; at the theoretical level, we have incorporated the experimental features to implement novel analog computing units for specific tasks. We have shown that memristors can tackle QUBO and cubic optimization problems, and exhibit tunneling phenomena.
97 MATHEMATICS AND COMPUTING↗
Computer technologies and institutional memory
NASA programs for manned space flight are in their 27th year. Scientists and engineers who worked continuously on the development of aerospace technology during that period are approaching retirement. The resulting loss to the organization will be considerable. Although this problem is general to the NASA community, the problem was explored in terms of the institutional memory and technical expertise of a single individual in the Man-Systems division. The main domain of the expert was spacecraft lighting, which became the subject area for analysis in these studies. The report starts with an analysis of the cumulative expertise and institutional memory of technical employees of organizations such as NASA. A set of solutions to this problem are examined and found inadequate. Two solutions were investigated at length: hypertext and expert systems. Illustrative examples were provided of hypertext and expert system representation of spacecraft lighting. These computer technologies can be used to ameliorate the problem of the loss of invaluable personnel.
Bell, Christopher↗
Automatic Code Generation for High-Performance Graph Algorithms
Graph problems are common across fields of scientific computing and social sciences. However, despite their importance, implementing graph algorithms effectively on modern computing systems is a challenging task that requires significant programming effort and generally results in customized implementations. Current computing and memory hierarchies are not architected for irregular computations resulting in challenges for graph algorithms to achieve high performance on those architectures. In this paper, we present GraphX, a novel compiler framework and DSL designed to simplify the development of efficient graph algorithms and achieve high performance on modern computing systems. GraphX consists of a DSL for efficient implementation of graph algorithms, various optimizations, such as support for sparse linear algebra and workspace transformations, optimized graph primitives, including semiring and masking, and a high-performance code generation engine. Using GraphX, users can implement graph algorithms using a semantically-rich language with graph-oriented operators. GraphX uses these semantics to automatically generate efficient code for target architectures, increasing performance and portability across architectures. The composable nature of GraphX makes it possible to extend the set of optimizations and architectures without modifying the source code. We demonstrate GraphX outperforms state-of-the-art graph libraries, such as LAGraph, up to $3.7 speedup in semiring operations, $2.19 speedup in an important sparse computational kernel, and $9.05 speedup in graph processing algorithms.
compiler, graph algorithms, semiring, masking, wor↗
Frame-Synchronization-Assisting Module
Auxiliary data processor does computations related to synchronization of frames of telemetry data, relieving main processor of task. Called frame-synchronization-assisting module (FSAM), sorts through large amounts of data to determine whether valid and how configured. Module connected to main processor of computer through direct-memory-access (interface) module. Examines data in computer memory to find frame-synchronizing codes.
Desilveira, C.↗
Electrostatic Particle-In-Cell Code For Hypercube Computer
Code simulates two-dimensional motions of plasma particles in self-consistent electrostatic field and externally applied magnetic field developed for execution on Mark IIIfp hypercube computer. Based on generalization of one-dimensional particle-in-cell algorithm applicable to many different parallel computing architectures. Intermediate product of continuing effort to speed particle-in-cell computations by taking advantage of distributed-memory parallel computers like those of hypercube class.
Ferraro, Robert D.↗
First- and Second-Order Sensitivity Analysis of a P-Version Finite Element Equation Via Automatic Differentiation
Sensitivity analysis is a technique for determining derivatives of system responses with respect to design parameters. Among many methods available for sensitivity analysis, automatic differentiation has been proven through many applications in fluid dynamics and structural mechanics to be an accurate and easy method for obtaining derivatives. Nevertheless, the method can be computational expensive and can require a high memory space. This project will apply an automatic differentiation tool, ADIFOR, to a p-version finite element code to obtain first- and second- order then-nal derivatives, respectively. The focus of the study is on the implementation process and the performance of the ADIFOR-enhanced codes for sensitivity analysis in terms of memory requirement, computational efficiency, and accuracy.
Hou, Gene↗
Finding MIDDLE Ground: Scalable and Secure Distributed Learning
Edge computing methods allow devices to efficiently train a high-performing, robust, and personalized model for predictive tasks. However, these methods succumb to privacy and scalability concerns such as adversarial data recovery and expensive model communication. Furthermore, edge computing methods unrealistically assume that all devices train an identical model. In practice, edge devices have varying computational and memory constraints which may not allow certain devices to have the space or speed to train a specific model. To overcome these issues, we propose MIDDLE: a model independent distributed learning algorithm which allows heterogeneous edge devices to assist each other’s training while communicating only non-sensitive information. MIDDLE unlocks the ability for edge devices, regardless of computational or memory constraints, to assist each other even with completely different model architectures. Furthermore, MIDDLE does not require model or gradient communication which greatly reduces communication size and time. We prove that MIDDLE attains the optimal convergence rate O(1/sqrt(TM)) of stochastic gradient descent for convex and non-convex smooth optimization (for total iterations T and batch size M). Finally, our experimental results demonstrate that MIDDLE (even in non-IID data settings) attains robust and high-performing models without model or gradient communication.
Bornstein, Marc I.↗
SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guarantees
Deep unfolding networks have recently gained popularity for solving imaging inverse problems. However, the computational and memory complexity of data-consistency layers within traditional deep unfolding networks scales with the number of measurements, limiting their applicability to large-scale imaging inverse problems. We propose SGD-Net as a new methodology for improving the efficiency of deep unfolding through stochastic approximations of the data-consistency layers. Our theoretical analysis shows that SGD-Net can be trained to approximate batch deep unfolding networks to an arbitrary precision. Our simulations on intensity diffraction tomography and sparse-view computed tomography show that SGD-Net can match the performance of the traditional batch network at a fraction of training and testing complexity.Deep unfolding networks have recently gained popularity for solving imaging inverse problems. However, the computational and memory complexity of data-consistency layers within traditional deep unfolding networks scales with the number of measurements, limiting their applicability to large-scale imaging inverse problems. We propose SGD-Net as a new methodology for improving the efficiency of deep unfolding through stochastic approximations of the data-consistency layers. Our theoretical analysis shows that SGD-Net can be trained to approximate batch deep unfolding networks to an arbitrary precision. Our simulations on intensity diffraction tomography and sparse-view computed tomography show that SGD-Net can match the performance of the traditional batch network at a fraction of training and testing complexity.
97 MATHEMATICS AND COMPUTING↗
Recent Experiences Calculating g-functions for Use in Simulation of Ground Heat Exchangers
Temperature response functions, known as g-functions, are a computationally efficient method for simulating ground heat exchangers (GHEs), used with ground-source heat pump (GSHP) systems, either as part of a whole-building energy simulation or as part of a dedicated ground heat exchanger design tool. In fact, at present, they are the only feasible way to simulate a ground-source heat pump system in a whole-building energy simulation. This paper summarizes recent developments in the field and recent experience using a new open-source g-function calculation tool known as pygfunction (Cimmino 2018a, 2018b). This experience includes accuracy, computation time, memory requirements and sensitivity to boundary conditions. With larger ground heat exchangers, e.g. in excess of 100 boreholes, the computational time and memory requirements can create challenges.
Spitler, Jeffery↗
Efficiently evaluating loop integrals in the EFTofLSS using QFT integrals with massive propagators
We develop a new way to analytically calculate loop integrals in the Effective Field Theory of Large Scale-Structure. Previous available methods show severe limitations beyond the one-loop power spectrum due to analytical challenges and computational and memory costs. Our new method is based on fitting the linear power spectrum with cosmology-independent functions that resemble integer powers of quantum field theory massive propagators with complex masses. A remarkably small number of them is sufficient to reach enough accuracy. Similarly to former approaches, the cosmology dependence is encoded in the coordinate vector of the expansion of the linear power spectrum in our basis. We first produce cosmology-independent tensors where each entry is the loop integral evaluated on a given combination of basis vectors. For each cosmology, the evaluation of a loop integral amounts to contracting this tensor with the coordinate vector of the linear power spectrum. The 3-dimensional loop integrals for our basis functions can be evaluated using techniques familiar to particle physics, such as recursion relations and Feynman parametrization. We apply our formalism to evaluate the one-loop bispectrum of galaxies in redshift space. The final analytical expressions are quite simple and can be evaluated with little computational and memory cost. We show that the same expressions resolve the integration of all one-loop N-point function in the EFTofLSS. This method, which is originally presented here, has already been applied in the first one-loop bispectrum analysis of the BOSS data to constraint ΛCDM parameters and primordial non-Gaussianities [1, 2].
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
A memory-driven mapping algorithm for heterogeneous systems
mpibind is a memory-driven algorithm to map parallel hybrid applications to the underlying hardware resources transparently, efficiently, and portably. There are two fundamental aspects of this algorithm. First, unlike existing mappings, its primary design point is the memory system. Compute elements are selected based on the identified memory components and not vice versa. Second, it embodies a global awareness of hybrid programming abstractions as well as heterogeneous devices.
Leon Borja, EdgarA↗