Advances in Generalized Disjunctive and Mixed-Integer Nonlinear Programming Algorithms and Software for Superstructure Optimization.
Abstract not provided.
Bernal, David↗
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Results for “generalized algorithm”
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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Improved LMS algorithm for adaptive beamforming
Two adaptive algorithms which make use of all the available samples to estimate the required gradient are proposed and studied. The first algorithm is referred to as the recursive LMS (least mean squares) and is applicable to a general array. The second algorithm is referred to as the improved LMS algorithm and exploits the Toeplitz structure of the ACM (array correlation matrix); it can be used only for an equispaced linear array.
Godara, Lal C.↗
Two frameworks for integrating knowledge in induction
The use of knowledge in inductive learning is critical for improving the quality of the concept definitions generated, reducing the number of examples required in order to learn effective concept definitions, and reducing the computation needed to find good concept definitions. Relevant knowledge may come in many forms (such as examples, descriptions, advice, and constraints) and from many sources (such as books, teachers, databases, and scientific instruments). How to extract the relevant knowledge from this plethora of possibilities, and then to integrate it together so as to appropriately affect the induction process is perhaps the key issue at this point in inductive learning. Here the focus is on the integration part of this problem; that is, how induction algorithms can, and do, utilize a range of extracted knowledge. Preliminary work on a transformational framework for defining knowledge-intensive inductive algorithms out of relatively knowledge-free algorithms is described, as is a more tentative problems-space framework that attempts to cover all induction algorithms within a single general approach. These frameworks help to organize what is known about current knowledge-intensive induction algorithms, and to point towards new algorithms.
Rosenbloom, Paul S.↗
Analysis of the retinex theory of color vision
Land's (1983) retinex algorithm is a model of human color constancy. The retinex algorithm is analyzed and its general properties are discussed. It is shown that the algorithm is too sensitive to changes in the color of nearby objects to serve as an adequate model of human color constancy.
Brainard, D. H.↗
MCSCF wave functions for excited states of polar molecules - Application to BeO
A previously reported multi-configuration self-consistent field (MCSCF) algorithm based on the generalized Brillouin theorem is extended in order to treat the excited states of polar molecules. In particular, the algorithm takes into account the proper treatment of nonorthogonality in the space of single excitations and invokes, when necessary, a constrained optimization procedure to prevent the variational collapse of excited states. In addition, a configuration selection scheme (suitable for use in conjunction with extended configuration interaction methods) is proposed for the MCSCF procedure. The algorithm is used to study the low-lying singlet states of BeO, a system which has not previously been studied using an MCSCF procedure. MCSCF wave functions are obtained for three 1 Sigma + and two 1 Pi states. The 1 Sigma + results are juxtaposed with comparable results for MgO in order to assess the generality of the description presented here.
Bauschlicher, C. W., Jr.↗
Transform methods for precision continuum and control models of flexible space structures
An open loop optimal control algorithm is developed for general flexible structures, based on Laplace transform methods. A distributed parameter model of the structure is first presented, followed by a derivation of the optimal control algorithm. The control inputs are expressed in terms of their Fourier series expansions, so that a numerical solution can be easily obtained. The algorithm deals directly with the transcendental transfer functions from control inputs to outputs of interest, and structural deformation penalties, as well as penalties on control effort, are included in the formulation. The algorithm is applied to several structures of increasing complexity to show its generality.
Lupi, Victor D.↗
Neuromorphic Graph Algorithms
Graph algorithms enable myriad large-scale applications including cybersecurity, social network analysis, resource allocation, and routing. The scalability of current graph algorithm implementations on conventional computing architectures are hampered by the demise of Moore’s law. We present a theoretical framework for designing and assessing the performance of graph algorithms executing in networks of spiking artificial neurons. Although spiking neural networks (SNNs) are capable of general-purpose computation, few algorithmic results with rigorous asymptotic performance analysis are known. SNNs are exceptionally well-motivated practically, as neuromorphic computing systems with 100 million spiking neurons are available, and systems with a billion neurons are anticipated in the next few years. Beyond massive parallelism and scalability, neuromorphic computing systems offer energy consumption orders of magnitude lower than conventional high-performance computing systems. We employ our framework to design and analyze new spiking algorithms for shortest path and dynamic programming problems. Our neuromorphic algorithms are message-passing algorithms relying critically on data movement for computation. For fair and rigorous comparison with conventional algorithms and architectures, which is challenging but paramount, we develop new models of data-movement in conventional computing architectures. This allows us to prove polynomial-factor advantages, even when we assume a SNN consisting of a simple grid-like network of neurons. To the best of our knowledge, this is one of the first examples of a rigorous asymptotic computational advantage for neuromorphic computing.
97 MATHEMATICS AND COMPUTING↗
Normalization and Implementation of Three Gravitational Acceleration Models
Unlike the uniform density spherical shell approximations of Newton, the consequence of spaceflight in the real universe is that gravitational fields are sensitive to the asphericity of their generating central bodies. The gravitational potential of an aspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities that must be removed to generalize the method and solve for any possible orbit, including polar orbits. Samuel Pines, Bill Lear, and Robert Gottlieb developed three unique algorithms to eliminate these singularities. This paper documents the methodical normalization of two of the three known formulations for singularity-free gravitational acceleration (namely, the Lear and Gottlieb algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre polynomials and Associated Legendre Functions (ALFs) for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.
Eckman, Randy A.↗
Stochastic relativistic viscous hydrodynamics from the Metropolis algorithm
We propose an algorithm for simulating stochastic relativistic fluid dynamics based on Metropolis updates. Each step of the algorithm begins with an update based on ideal hydrodynamics. This is followed by proposing random (spatial) momentum transfers between fluid cells, keeping the total energy fixed. These proposals are then accepted or rejected using the change in entropy as a statistical weight. The algorithm reproduces relativistic viscous hydrodynamics in the “density frame,” which is a formulation of viscous hydrodynamics we review and clarify here. This formulation is first order in time and requires no auxiliary dynamical fields such as Π 𝜇𝜈 . The only parameters are the shear and bulk viscosities and the equation of state. Here, by adopting the 3+1 split of general relativity, we extend the Metropolis algorithm to general space-time coordinates, such as Bjorken coordinates, which are commonly used to simulate heavy-ion collisions.
Hydrodynamic noise↗
A Self-Stabilizing Hybrid Fault-Tolerant Synchronization Protocol
This paper presents a strategy for solving the Byzantine general problem for self-stabilizing a fully connected network from an arbitrary state and in the presence of any number of faults with various severities including any number of arbitrary (Byzantine) faulty nodes. The strategy consists of two parts: first, converting Byzantine faults into symmetric faults, and second, using a proven symmetric-fault tolerant algorithm to solve the general case of the problem. A protocol (algorithm) is also present that tolerates symmetric faults, provided that there are more good nodes than faulty ones. The solution applies to realizable systems, while allowing for differences in the network elements, provided that the number of arbitrary faults is not more than a third of the network size. The only constraint on the behavior of a node is that the interactions with other nodes are restricted to defined links and interfaces. The solution does not rely on assumptions about the initial state of the system and no central clock nor centrally generated signal, pulse, or message is used. Nodes are anonymous, i.e., they do not have unique identities. A mechanical verification of a proposed protocol is also present. A bounded model of the protocol is verified using the Symbolic Model Verifier (SMV). The model checking effort is focused on verifying correctness of the bounded model of the protocol as well as confirming claims of determinism and linear convergence with respect to the self-stabilization period.
Malekpour, Mahyar R.↗
Recent improvements in efficiency, accuracy, and convergence for implicit approximate factorization algorithms
In 1977 and 1978, general purpose centrally space differenced implicit finite difference codes in two and three dimensions have been introduced. These codes, now called ARC2D and ARC3D, can run either in inviscid or viscous mode for steady or unsteady flow. Since the introduction of the ARC2D and ARC3D codes, overall computational efficiency could be improved by making use of a number of algorithmic changes. These changes are related to the use of a spatially varying time step, the use of a sequence of mesh refinements to establish approximate solutions, implementation of various ways to reduce inversion work, improved numerical dissipation terms, and more implicit treatment of terms. The present investigation has the objective to describe the considered improvements and to quantify advantages and disadvantages. It is found that using established and simple procedures, a computer code can be maintained which is competitive with specialized codes.
Pulliam, T. H.↗
On the interpretation of least squares collocation
A demonstration is given of the strict mathematical equivalence between the least squares collocation and the classical minimum variance estimates. It is shown that the least squares collocation algorithms are a special case of the modified minimum variance estimates. The computational efficiency of several forms of the general minimum variance estimation algorithm is discussed. It is pointed out that for certain geodetic applications the least square collocation algorithm may provide a more efficient formulation of the results from the point of view of the computations required.
Tapley, B. D.↗
Automatic control algorithm effects on energy production
A computer model was developed using actual wind time series and turbine performance data to simulate the power produced by the Sandia 17-m VAWT operating in automatic control. The model was used to investigate the influence of starting algorithms on annual energy production. The results indicate that, depending on turbine and local wind characteristics, a bad choice of a control algorithm can significantly reduce overall energy production. The model can be used to select control algorithms and threshold parameters that maximize long term energy production. The results from local site and turbine characteristics were generalized to obtain general guidelines for control algorithm design.
Mcnerney, G. M.↗
Finite elements for Matérn-type random fields: Uncertainty in computational mechanics and design optimization
This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on prevalent applications in computational mechanics and design optimization. We leverage Matérn-type Gaussian random fields (GRFs) generated using the SPDE method to model aleatoric uncertainties, including environmental influences, variating material properties, and geometric ambiguities. Our focus lies on delivering practical GRF realizations that accurately capture imperfections and variations and understanding how they impact the predictions of computational models as well as the shape and topology of optimized designs. Here we describe a numerical algorithm based on solving a generalized SPDE to sample GRFs on arbitrary meshed domains. The algorithm leverages established techniques and integrates seamlessly with the open-source finite element library MFEM and associated scientific computing workflows, like those found in industrial and national laboratory settings. Our solver scales efficiently for large-scale problems and supports various domain types, including surfaces and embedded manifolds. We showcase its versatility through biomechanics and topology optimization applications, emphasizing the potential to influence these domains. The flexibility and efficiency of SPDE-based GRF generation empowers us to run large-scale optimization problems on 2D and 3D domains, including finding optimized designs on embedded surfaces, and to generate design features and topologies beyond the reach of conventional techniques. Moreover, these capabilities allow us to model and quantify geometric uncertainties on reconstructed submanifolds, such as the interpolated surfaces of cerebral aneurysms provided by postprocessing CT scans. In addition to offering benefits in these specific domains, the proposed techniques transcend specific applications and generalize to arbitrary forward and backward problems in uncertainty quantification involving finite elements.
97 MATHEMATICS AND COMPUTING↗
On the utility of the multi-level algorithm for the solution of nearly completely decomposable Markov chains
Recently the Multi-Level algorithm was introduced as a general purpose solver for the solution of steady state Markov chains. In this paper, we consider the performance of the Multi-Level algorithm for solving Nearly Completely Decomposable (NCD) Markov chains, for which special-purpose iteractive aggregation/disaggregation algorithms such as the Koury-McAllister-Stewart (KMS) method have been developed that can exploit the decomposability of the the Markov chain. We present experimental results indicating that the general-purpose Multi-Level algorithm is competitive, and can be significantly faster than the special-purpose KMS algorithm when Gauss-Seidel and Gaussian Elimination are used for solving the individual blocks.
Leutenegger, Scott T.↗
Parallel algorithms for boundary value problems
A general approach to solve boundary value problems numerically in a parallel environment is discussed. The basic algorithm consists of two steps: the local step where all the P available processors work in parallel, and the global step where one processor solves a tridiagonal linear system of the order P. The main advantages of this approach are two fold. First, this suggested approach is very flexible, especially in the local step and thus the algorithm can be used with any number of processors and with any of the SIMD or MIMD machines. Secondly, the communication complexity is very small and thus can be used as easily with shared memory machines. Several examples for using this strategy are discussed.
Lin, Avi↗
Parallel algorithms for boundary value problems
A general approach to solve boundary value problems numerically in a parallel environment is discussed. The basic algorithm consists of two steps: the local step where all the P available processors work in parallel, and the global step where one processor solves a tridiagonal linear system of the order P. The main advantages of this approach are twofold. First, this suggested approach is very flexible, especially in the local step and thus the algorithm can be used with any number of processors and with any of the SIMD or MIMD machines. Secondly, the communication complexity is very small and thus can be used as easily with shared memory machines. Several examples for using this strategy are discussed.
Lin, Avi↗
Some practical universal noiseless coding techniques
Some practical adaptive techniques for the efficient noiseless coding of a broad class of such data sources are developed and analyzed. Algorithms are designed for coding discrete memoryless sources which have a known symbol probability ordering but unknown probability values. A general applicability of these algorithms to solving practical problems is obtained because most real data sources can be simply transformed into this form by appropriate preprocessing. These algorithms have exhibited performance only slightly above all entropy values when applied to real data with stationary characteristics over the measurement span. Performance considerably under a measured average data entropy may be observed when data characteristics are changing over the measurement span.
Rice, R. F.↗