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At least 397 records · Page 22

F-Nets and Software Cabling: Deriving a Formal Model and Language for Portable Parallel Programming

Parallel programming is still being based upon antiquated sequence-based definitions of the terms "algorithm" and "computation", resulting in programs which are architecture dependent and difficult to design and analyze. By focusing on obstacles inherent in existing practice, a more portable model is derived here, which is then formalized into a model called Soviets which utilizes a combination of imperative and functional styles. This formalization suggests more general notions of algorithm and computation, as well as insights into the meaning of structured programming in a parallel setting. To illustrate how these principles can be applied, a very-high-level graphical architecture-independent parallel language, called Software Cabling, is described, with many of the features normally expected from today's computer languages (e.g. data abstraction, data parallelism, and object-based programming constructs).

DiNucci, David C.↗

Multiobjective Aerodynamic Shape Optimization Using Pareto Differential Evolution and Generalized Response Surface Metamodels

Differential Evolution (DE) is a simple, fast, and robust evolutionary algorithm that has proven effective in determining the global optimum for several difficult single-objective optimization problems. The DE algorithm has been recently extended to multiobjective optimization problem by using a Pareto-based approach. In this paper, a Pareto DE algorithm is applied to multiobjective aerodynamic shape optimization problems that are characterized by computationally expensive objective function evaluations. To improve computational expensive the algorithm is coupled with generalized response surface meta-models based on artificial neural networks. Results are presented for some test optimization problems from the literature to demonstrate the capabilities of the method.

Madavan, Nateri K.↗

Implementation, Realization and an Effective Solver of Two-Equation Turbulence Models

Currently, when the Reynolds-Averaged Navier-Stokes (RANS) equations are solved using turbulence modeling, most often the one-equation model of Spalart and Allmaras is used. Then, it is only necessary to solve the RANS equations in conjunction with a single transport equation for modeling turbulence. For this model, considerable assessment and analysis has been performed, allowing the possibility of a reliable solution method for an eddy viscosity required to compute the Reynolds stresses in the RANS equations. Such evaluation along with analysis has not been achieved to realize similar performance with two-equation models of the k-w type. The primary objective of this paper is to present and discuss the components of an effective numerical algorithm for solving the RANS equations and the two transport equations of k-w type turbulence models. All the important details of the turbulence model as actually implemented are given, which is sometimes not done in various papers considering such modeling. The viability and effectiveness of this solution algorithm are demonstrated by solving both two-dimensional and three-dimensional aerodynamic flows. In all applications, a linear rate of convergence without oscillations or other evidence of unstable behavior is observed. This behavior is also particularly true when the proposed algorithm is applied to systematically renewed mesh sequences, which is generally not observed with algorithms solving more than one transport equation. Thus, numerical integration errors are systematically reduced, allowing for a significantly more reliable assessment of the effectiveness of the turbulence model. Additionally, in this paper, analysis of the solution algorithm, including linear stability, is also performed for a particular flow problem.

Turbulence↗

Postbuckling analysis using a general purpose code

A new capability for solving postbuckling problems in shell structures is described. The matrix theory to adapt Newton's method to nonlinear finite element shell analysis is outlined first. The matrix theory is directed at writing consistent linear algebratic equations for problems where the tangent stiffness matrix is singular or nearly singular. The matrix theory suggests a change of variables as part of the usual iterative procedure in Newton's method. The change of variables is shown to be feasible for introduction into the algorithm programmed in general purpose codes for finite element analysis of structures. Numerical results from a new option that has been programmed in an existing general purpose code are presented. The analysis of shell structures for collapse and for branching at bifurcation loads is illustrated by the numerical examples.

Thurston, G. A.↗

Quantum-classical hybrid algorithm for the simulation of all-electron correlation

While chemical systems containing hundreds to thousands of electrons remain beyond the reach of quantum devices, hybrid quantum-classical algorithms present a promising pathway toward a quantum advantage. Hybrid algorithms treat the exponentially scaling part of the calculation-the static correlation-on the quantum computer and the non-exponentially scaling part-the dynamic correlation-on the classical computer. While a variety of algorithms have been proposed, the dependence of many methods on the total wave function limits the development of easy-to-use classical post-processing implementations. Here, we present a novel combination of quantum and classical algorithms, which computes the all-electron energy of a strongly correlated molecular system on the classical computer from the 2-electron reduced density matrix (2-RDM) evaluated on the quantum device. Significantly, we circumvent the wave function in the all-electron calculations by using density matrix methods that only require input of the statically correlated 2-RDM. Although the algorithm is completely general, we test it with two classical density matrix methods, the anti-Hermitian contracted Schrödinger equation (ACSE) and multiconfiguration pair-density functional theories, using the recently developed quantum ACSE method for simulating the statically correlated 2-RDM. Furthermore, we obtain experimental accuracy for the relative energies of all three benzyne isomers and thereby demonstrate the ability of the developed algorithm to achieve chemically relevant and accurate results on noisy intermediate-scale quantum devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

MISR-GOES 3D Winds: Implications for Future LEO-GEO and LEO-LEO Winds

Global wind observations are fundamental for studying weather and climate dynamics and for operational forecasting. Most wind measurements come from atmospheric motion vectors (AMVs) by tracking the displacement of cloud or water vapor features. These AMVs generally rely on thermal infrared (IR) techniques for their height assignments, which are subject to large uncertainties in the presence of weak or reversed vertical temperature gradients near the planetary boundary layer (PBL)and tropopause folds. Stereo imaging can overcome the height assignment problem using geometric parallax for feature height determination. In this study we develop a stereo 3D-Wind algorithm to simultaneously retrieve AMV and height from geostationary (GEO) and low Earth orbit (LEO) satellite imagery and apply it to collocated Geostationary Operational Environmental Satellite (GOES)and Multi-angle Imaging SpectroRadiometer (MISR) imagery. The new algorithm improves AMV and height relative to products from GOES or MISR alone, with an estimated accuracy of <0.5 m/s in AMV and <200 m in height with 2.2 km sampling. The algorithm can be generalized to other LEO-GEO or LEO-LEO combinations for greater spatiotemporal coverage. The technique demonstrated with MISR and GOES has important implications for future high-quality AMV observations, for which a low-cost constellation of CubeSats can play a vital role.

MISR↗

SCONCE : a cosmic web finder for spherical and conic geometries

The latticework structure known as the cosmic web provides a valuable insight into the assembly history of large-scale structures. Despite the variety of methods to identify the cosmic web structures, they mostly rely on the assumption that galaxies are embedded in a Euclidean geometric space. Here, we present a novel cosmic web identifier called SCONCE (Spherical and CONic Cosmic wEb finder) that inherently considers the 2D (RA, DEC) spherical or the 3D (RA, DEC, z) conic geometry. The proposed algorithms in sconce generalize the well-known subspace constrained mean shift (SCMS) method and primarily address the predominant filament detection problem. They are intrinsic to the spherical/conic geometry and invariant to data rotations. We further test the efficacy of our method with an artificial cross-shaped filament example and apply it to the SDSS galaxy catalogue, revealing that the 2D spherical version of our algorithms is robust even in regions of high declination. Finally, using N-body simulations from Illustris, we show that the 3D conic version of our algorithms is more robust in detecting filaments than the standard SCMS method under the redshift distortions caused by the peculiar velocities of haloes. Our cosmic web finder is packaged in python as SCONCE-SCMS and has been made publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗

Three-dimensional unstructured grid generation via incremental insertion and local optimization

Algorithms for the generation of 3D unstructured surface and volume grids are discussed. These algorithms are based on incremental insertion and local optimization. The present algorithms are very general and permit local grid optimization based on various measures of grid quality. This is very important; unlike the 2D Delaunay triangulation, the 3D Delaunay triangulation appears not to have a lexicographic characterization of angularity. (The Delaunay triangulation is known to minimize that maximum containment sphere, but unfortunately this is not true lexicographically). Consequently, Delaunay triangulations in three-space can result in poorly shaped tetrahedral elements. Using the present algorithms, 3D meshes can be constructed which optimize a certain angle measure, albeit locally. We also discuss the combinatorial aspects of the algorithm as well as implementational details.

Barth, Timothy J.↗

ALESQP: An Augmented Lagrangian Equality-Constrained SQP Method for Optimization with General Constraints

Here we present a new algorithm for infinite-dimensional optimization with general constraints, called ALESQP. In short, ALESQP is an augmented Lagrangian method that penalizes inequality constraints and solves equality-constrained nonlinear optimization subproblems at every iteration. The subproblems are solved using a matrix-free trust-region sequential quadratic programming (SQP) method that takes advantage of iterative, i.e., inexact linear solvers, and is suitable for large-scale applications. A key feature of ALESQP is a constraint decomposition strategy that allows it to exploit problem-specific variable scalings and inner products. We analyze convergence of ALESQP under different assumptions. We show that strong accumulation points are stationary. Consequently, in finite dimensions ALESQP converges to a stationary point. In infinite dimensions we establish that weak accumulation points are feasible in many practical situations. Under additional assumptions we show that weak accumulation points are stationary. We present several infinite-dimensional examples where ALESQP shows remarkable discretization-independent performance in all of its iterative components, requiring a modest number of iterations to meet constraint tolerances at the level of machine precision. Also, we demonstrate a fully matrix-free solution of an infinite-dimensional problem with nonlinear inequality constraints.

97 MATHEMATICS AND COMPUTING↗

Probabilistic Structural Analysis Program

NASA/NESSUS 6.2c is a general-purpose, probabilistic analysis program that computes probability of failure and probabilistic sensitivity measures of engineered systems. Because NASA/NESSUS uses highly computationally efficient and accurate analysis techniques, probabilistic solutions can be obtained even for extremely large and complex models. Once the probabilistic response is quantified, the results can be used to support risk-informed decisions regarding reliability for safety-critical and one-of-a-kind systems, as well as for maintaining a level of quality while reducing manufacturing costs for larger-quantity products. NASA/NESSUS has been successfully applied to a diverse range of problems in aerospace, gas turbine engines, biomechanics, pipelines, defense, weaponry, and infrastructure. This program combines state-of-the-art probabilistic algorithms with general-purpose structural analysis and lifting methods to compute the probabilistic response and reliability of engineered structures. Uncertainties in load, material properties, geometry, boundary conditions, and initial conditions can be simulated. The structural analysis methods include non-linear finite-element methods, heat-transfer analysis, polymer/ceramic matrix composite analysis, monolithic (conventional metallic) materials life-prediction methodologies, boundary element methods, and user-written subroutines. Several probabilistic algorithms are available such as the advanced mean value method and the adaptive importance sampling method. NASA/NESSUS 6.2c is structured in a modular format with 15 elements.

Pai, Shantaram S.↗

Modeling Chemical Reactions in Classical Molecular Dynamics Simulations

An algorithm capable of incorporating multi-step reaction mechanisms into atomistic molecular dynamics (MD) simulations using traditional fixed valence force fields is proposed and implemented within the framework of LAMMPS (Large-scale Atomic Molecular Massively Parallel Simulator). This extension, referred to as fix bond/react, enables bonding topology modifications during a running MD simulation using pre- and post-reaction bonding templates to carry out a pre-specified reaction. Candidate reactants are first identified by interatomic separation, followed by the application of a generalized topology matching algorithm to confirm they match the pre-reaction template. This is followed by a topology conversion to match the post-reaction template and a dynamic relaxation to minimize high energy configurations. Two case studies, the condensation polymerization of nylon 6,6 and the formation of a highly-crosslinked epoxy, are simulated to demonstrate the robustness, stability, and speed of the algorithm. Improvements which could increase its utility are discussed.

Jacob R Gissinger↗

Goal Directed Model Inversion: Learning Within Domain Constraints

Goal Directed Model Inversion (GDMI) is an algorithm designed to generalize supervised learning to the case where target outputs are not available to the learning system. The output of the learning system becomes the input to some external device or transformation, and only the output of this device or transformation can be compared to a desired target. The fundamental driving mechanism of GDMI is to learn from success. Given that a wrong outcome is achieved, one notes that the action that produced that outcome "would have been right if the outcome had been the desired one." The algorithm makes use of these intermediate "successes" to achieve the final goal. A unique and potentially very important feature of this algorithm is the ability to modify the output of the learning module to force upon it a desired syntactic structure. This differs from ordinary supervised learning in the following way: in supervised learning the exact desired output pattern must be provided. In GDMI instead, it is possible to require simply that the output obey certain rules, i.e., that it "make sense" in some way determined by the knowledge domain. The exact pattern that will achieve the desired outcome is then found by the system. The ability to impose rules while allowing the system to search for its own answers in the context of neural networks is potentially a major breakthrough in two ways: 1) it may allow the construction of networks that can incorporate immediately some important knowledge, i.e. would not need to learn everything from scratch as normally required at present, and 2) learning and searching would be limited to the areas where it is necessary, thus facilitating and speeding up the process. These points are illustrated with examples from robotic path planning and parametric design.

Colombano, Silvano P.↗

Goal Directed Model Inversion: Learning Within Domain Constraints

Goal Directed Model Inversion (GDMI) is an algorithm designed to generalize supervised learning to the case where target outputs are not available to the learning system. The output of the learning system becomes the input to some external device or transformation, and only the output of this device or transformation can be compared to a desired target. The fundamental driving mechanism of GDMI is to learn from success. Given that a wrong outcome is achieved, one notes that the action that produced that outcome "would have been right if the outcome had been the desired one." The algorithm makes use of these intermediate "successes" to achieve the final goal. A unique and potentially very important feature of this algorithm is the ability to modify the output of the learning module to force upon it a desired syntactic structure. This differs from ordinary supervised learning in the following way: in supervised learning the exact desired output pattern must be provided. In GDMI instead, it is possible to require simply that the output obey certain rules, i.e., that it "make sense" in some way determined by the knowledge domain. The exact pattern that will achieve the desired outcome is then found by the system. The ability to impose rules while allowing the system to search for its own answers in the context of neural networks is potentially a major breakthrough in two ways: (1) it may allow the construction of networks that can incorporate immediately some important knowledge, i.e., would not need to learn everything from scratch as normally required at present; and (2) learning and searching would be limited to the areas where it is necessary, thus facilitating and speeding up the process. These points are illustrated with examples from robotic path planning and parametric design.

Colombano, Silvano P.↗

Goal Directed Model Inversion: A Study of Dynamic Behavior

Goal Directed Model Inversion (GDMI) is an algorithm designed to generalize supervised learning to the case where target outputs are not available to the learning system. The output of the learning system becomes the input to some external device or transformation, and only the output of this device or transformation can be compared to a desired target. The fundamental driving mechanism of GDMI is to learn from success. Given that a wrong outcome is achieved, one notes that the action that produced that outcome 0 "would have been right if the outcome had been the desired one." The algorithm then proceeds as follows: (1) store the action that produced the wrong outcome as a "target" (2) redefine the wrong outcome as a desired goal (3) submit the new desired goal to the system (4) compare the new action with the target action and modify the system by using a suitable algorithm for credit assignment (Back propagation in our example) (5) resubmit the original goal. Prior publications by our group in this area focused on demonstrating empirical results based on the inverse kinematic problem for a simulated robotic arm. In this paper we apply the inversion process to much simpler analytic functions in order to elucidate the dynamic behavior of the system and to determine the sensitivity of the learning process to various parameters. This understanding will be necessary for the acceptance of GDMI as a practical tool.

Colombano, Silvano P.↗

Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators

Krylov subspace methods in quantum dynamics identify the minimal subspace in which a process unfolds. To date, their use is restricted to time evolutions governed by time-independent generators. Here, we introduce a generalization valid for driven quantum systems governed by a time-dependent Hamiltonian that maps the evolution to a diffusion problem in a one-dimensional lattice with nearest-neighbor hopping probabilities that are inhomogeneous and time dependent. This representation is used to establish a novel class of fundamental limits to the quantum speed of evolution and operator growth. We also discuss generalizations of the algorithm, adapted to discretized time evolutions and periodic Hamiltonians, with applications to many-body systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hierarchical Distributed Optimal Power Flow of HV and MV Distribution Networks With Continuous and Discrete Devices

With large-scale distributed photovoltaics (PVs) being integrated into distribution networks (DNs), coordinated optimal power flow (OPF) of high voltage (HV) and medium voltage (MV) DNs should be investigated to optimally dispatch the distributed PVs and other network devices. Here, this paper presents a hierarchical distributed OPF method for HV and MV DNs with on-load tap changers, reactive power compensators, feeder switches and distributed PVs. A hierarchical master-slave control architecture is applied to implement coordinated OPF of two-layer DNs. The HV master problem and MV subproblems are transformed into mixed-integer convex problems respectively with second order cone programming and LinDistFlow approximation. Since there is no efficient distributed algorithm to solve such OPF models with integer subproblems, a novel distributed algorithm is proposed in this paper to efficiently solve the hierarchical coordinated OPF model with integer subproblems in a distributed manner. In the proposed algorithm, the coordinated OPF model is solved in a branch-and-bound framework, where in each branch node generalized Benders decomposition (GBD) algorithm is applied to decompose the coordinated OPF model into a master problem and relaxed subproblems and solves them iteratively to get optimal solution. The GBD optimal and feasible cutting planes generated in a branch node are proved to be valid for its descendants. Moreover, three acceleration techniques are introduced into the proposed algorithm to improve computational efficiency. Finally, the effectiveness and accuracy of the proposed method are verified via simulation tests in Jinzhai DNs of China.

42 ENGINEERING↗

A Quantum-Assisted Algorithm for Sampling Applications in Machine Learning

An increase in the efficiency of sampling from Boltzmann distributions would have a significant impact in deep learning and other machine learning applications. Recently, quantum annealers have been proposed as a potential candidate to speed up this task, but several limitations still bar these state-of-the-art technologies from being used effectively. One of the main limitations is that, while the device may indeed sample from a Boltzmann-like distribution, quantum dynamical arguments suggests it will do so with an instance-dependent effective temperature, different from the physical temperature of the device. Unless this unknown temperature can be unveiled, it might not be possible to effectively use a quantum annealer for Boltzmann sampling. In this talk, we present a strategy to overcome this challenge with a simple effective-temperature estimation algorithm. We provide a systematic study assessing the impact of the effective temperatures in the learning of a kind of restricted Boltzmann machine embedded on quantum hardware, which can serve as a building block for deep learning architectures. We also provide a comparison to k-step contrastive divergence (CD-k) with k up to 100. Although assuming a suitable fixed effective temperature also allows to outperform one step contrastive divergence (CD-1), only when using an instance-dependent effective temperature we find a performance close to that of CD-100 for the case studied here. We discuss generalizations of the algorithm to other more expressive generative models, beyond restricted Boltzmann machines.

Perdomo-Ortiz, Alejandro↗

A Predictive Attitude Determination Algorithm

In this paper, a new and efficient algorithm is developed for attitude determination from vector observations. The new algorithm, called the Predictive Attitude Determination (PAD) algorithm, is derived from a general nonlinear predictive filter approach. Traditional deterministic algorithms are shown to be suboptimal for anisotropic measurement errors. The major advantage of the PAD algorithm is that it can be easily applied to the case where anisotropic measurement errors exist. Also, an analytical expression is derived for the steady-state attitude error covariance, which is shown to be equivalent to the optimal covariance derived from maximum likelihood techniques. Simulation studies indicate that the new algorithm is able to accurately determine the attitude of a spacecraft, even for radically anisotropic measurement errors.

Markley, F. Landis↗