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At least 1,081 records · Page 60
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DOE OSTI2021

Randomized algorithms for generalized singular value decomposition with application to sensitivity analysis

The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential sensitivity analysis (HDSA), in this work we propose new randomized algorithms for computing the GSVD which use randomized subspace iteration and weighted QR factorization. Detailed error analysis is given which provides insight into the accuracy of the algorithms and the choice of the algorithmic parameters. We demonstrate the performance of our algorithms on test matrices and a large-scale model problem where HDSA is used to study subsurface flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

OpenMP Parallelization and Optimization of Graph-Based Machine Learning Algorithms

In this paper, we investigate the OpenMP parallelization and optimization of two novel data classification algorithms. The new algorithms are based on graph and PDE solution techniques and provide significant accuracy and performance advantages over traditional data classification algorithms in serial mode. The methods leverage the Nystrom extension to calculate eigenvalue/eigenvectors of the graph Laplacian and this is a self-contained module that can be used in conjunction with other graph-Laplacian based methods such as spectral clustering. We use performance tools to collect the hotspots and memory access of the serial codes and use OpenMP as the parallelization language to parallelize the most time-consuming parts. Where possible, we also use library routines. We then optimize the OpenMP implementations and detail the performance on traditional supercomputer nodes (in our case a Cray XC30), and test the optimization steps on emerging testbed systems based on Intel’s Knights Corner and Landing processors. We show both performance improvement and strong scaling behavior. Finally, a large number of optimization techniques and analyses are necessary before the algorithm reaches almost ideal scaling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The Optimal Wavelengths for Light Absorption Spectroscopy Measurements Based on Genetic Algorithm–Particle Swarm Optimization

To select the optimal wavelengths in the light extinction spectroscopy measurement, genetic algorithm–particle swarm optimization (GAPSO) based on genetic algorithm (GA) and particle swarm optimization (PSO) is adopted. The change of the optimal wavelength positions in different feature size parameters and distribution parameters is evaluated. Moreover, the Monte Carlo method based on random probability is used to identify the number of optimal wavelengths, and good inversion effects of the particle size distribution are obtained. The method proved to have the advantage of resisting noise. In order to verify the feasibility of the algorithm, spectra with bands ranging from 200 to 1000 nm are computed. Based on this, the measured data of standard particles are used to verify the algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Population parametrization of costly black box models using iterations between SAEM algorithm and kriging

In this article we focus on parametrization of black box models from repeated measurements among several individuals (population parametrization). We introduce a variant of the SAEM algorithm, called KSAEM algorithm, which couples the standard SAEM algorithm with the dynamic construction of an approximate metamodel. The costly evaluation of the genuine black box is replaced by a kriging step, using a basis of precomputed values, basis which is enlarged during SAEM algorithm to improve the accuracy of the metamodel in regions of interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Exact and heuristic algorithms for minimizing Tardy/Lost penalties on a single-machine scheduling problem

This paper addresses minimizing Tardy/Lost penalties with common due dates on a single machine. According to this penalty criterion, if tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. The problem is formulated as an integer programming model, and a heuristic algorithm is constructed. Then, using the proposed dominance rules and lower bounds, we develop two dynamic programming algorithms as well as a branch and bound. Experimental results show that the heuristic algorithm has an average optimality gap less than 2 % in all problem sizes. Instances up to 250 jobs with low variety of process times are optimally solved and for high process time varieties, the algorithms solved all instances up to 75 jobs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A variant nonmonotone smoothing algorithm with improved numerical results for large-scale LWCPs

This paper considers the linear weighted complementarity problem (denoted by LWCP) introduced by Potra (SIAM J Optim 22:1634–1654, 2012). Based on two weighted smoothing functions, we propose a new nonmonotone smoothing algorithm for solving the LWCP and establish its global and local quadratic convergence without the strict complementarity assumption. Compared to existing nonmonotone smoothing algorithms, the proposed algorithm solves the linear system only approximately which can save the computation work when one solves large-scale LWCPs. Moreover, the nonmonotone line search technique adopted in this paper includes the usual monotone line search and some existing nonmonotone line searches as special cases. Numerical results show that our algorithm is considerably efficient for solving large-scale LWCPs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Exploring temporal community evolution: algorithmic approaches and parallel optimization for dynamic community detection

Abstract Dynamic (temporal) graphs are a convenient mathematical abstraction for many practical complex systems including social contacts, business transactions, and computer communications. Community discovery is an extensively used graph analysis kernel with rich literature for static graphs. However, community discovery in a dynamic setting is challenging for two specific reasons. Firstly, the notion of temporal community lacks a widely accepted formalization, and only limited work exists on understanding how communities emerge over time. Secondly, the added temporal dimension along with the sheer size of modern graph data necessitates new scalable algorithms. In this paper, we investigate how communities evolve over time based on several graph metrics under a temporal formalization. We compare six different algorithmic approaches for dynamic community detection for their quality and runtime. We identify that a vertex-centric (local) optimization method works as efficiently as the classical modularity-based methods. To its advantage, such local computation allows for the efficient design of parallel algorithms without incurring a significant parallel overhead. Based on this insight, we design a shared-memory parallel algorithm DyComPar , which demonstrates between 4 and 18 fold speed-up on a multi-core machine with 20 threads, for several real-world and synthetic graphs from different domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

An improved target velocity sampling algorithm for free gas elastic scattering

We present an improved algorithm for sampling the target velocity when simulating elastic scattering in a Monte Carlo neutron transport code that correctly accounts for the energy dependence of the scattering cross section. The algorithm samples the relative velocity directly, thereby avoiding a potentially inefficient rejection step based on the ratio of cross sections. Here, we have shown that this algorithm requires only one rejection step, whereas other methods of similar accuracy require two rejection steps. The method was verified against stochastic and deterministic reference results for upscattering percentages in 238 U. Simulations of a light water reactor pin cell problem demonstrate that using this algorithm results in a 3% or less penalty in performance when compared with an approximate method that is used in most production Monte Carlo codes

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

Building fault detection and diagnostics: Achieved savings, and methods to evaluate algorithm performance

Fault detection and diagnosis (FDD) represents one of the most active areas of research and commercial product development in the buildings industry. This paper addresses two questions concerning FDD implementation and advancement 1) What are today's users of FDD saving and spending on the technology? 2) What methods and datasets can be used to evaluate and benchmark FDD algorithm performance? Relevant to the first question, 26 organizations that use FDD across a total 550 buildings and 97 M sf achieved median savings of 8%. Twenty-seven FDD users reported that the median base cost for FDD software, annual recurring software cost, and annual labor cost were $8, $2.7 and $8 per monitoring point, with a median implementation size of approximately 1300 points. To address the second question, this paper describes a systematic methodology for evaluating the performance of FDD algorithms, curates an initial test dataset of air handling unit (AHU) system faults, and completes a trial to demonstrate the evaluation process on three sample FDD algorithms. The work provided a first step toward a standard evaluation of different FDD technologies. Finally, it showed the test methodology is indeed scalable and repeatable, provided an understanding of the types of insights that can be gained from algorithm performance testing, and highlighted the priorities for further expanding the test dataset.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2013

Application of stochastic weighted algorithms to a multidimensional silica particle model

Highlights: •Stochastic weighted algorithms (SWAs) are developed for a detailed silica model. •An implementation of SWAs with the transition kernel is presented. •The SWAs’ solutions converge to the direct simulation algorithm’s (DSA) solution. •The efficiency of SWAs is evaluated for this multidimensional particle model. •It is shown that SWAs can be used for coagulation problems in industrial systems. -- Abstract: This paper presents a detailed study of the numerical behaviour of stochastic weighted algorithms (SWAs) using the transition regime coagulation kernel and a multidimensional silica particle model. The implementation in the SWAs of the transition regime coagulation kernel and associated majorant rates is described. The silica particle model of Shekar et al. [S. Shekar, A.J. Smith, W.J. Menz, M. Sander, M. Kraft, A multidimensional population balance model to describe the aerosol synthesis of silica nanoparticles, Journal of Aerosol Science 44 (2012) 83–98] was used in conjunction with this coagulation kernel to study the convergence properties of SWAs with a multidimensional particle model. High precision solutions were calculated with two SWAs and also with the established direct simulation algorithm. These solutions, which were generated using large number of computational particles, showed close agreement. It was thus demonstrated that SWAs can be successfully used with complex coagulation kernels and high dimensional particle models to simulate real-world systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Numerical stability analysis of the pseudo-spectral analytical time-domain PIC algorithm

The pseudo-spectral analytical time-domain (PSATD) particle-in-cell (PIC) algorithm solves the vacuum Maxwell's equations exactly, has no Courant time-step limit (as conventionally defined), and offers substantial flexibility in plasma and particle beam simulations. It is, however, not free of the usual numerical instabilities, including the numerical Cherenkov instability, when applied to relativistic beam simulations. This paper derives and solves the numerical dispersion relation for the PSATD algorithm and compares the results with corresponding behavior of the more conventional pseudo-spectral time-domain (PSTD) and finite difference time-domain (FDTD) algorithms. In general, PSATD offers superior stability properties over a reasonable range of time steps. More importantly, one version of the PSATD algorithm, when combined with digital filtering, is almost completely free of the numerical Cherenkov instability for time steps (scaled to the speed of light) comparable to or smaller than the axial cell size.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A stochastic thermostat algorithm for coarse-grained thermomechanical modeling of large-scale soft matters: Theory and application to microfilaments

As all-atom molecular dynamics method is limited by its enormous computational cost, various coarse-grained strategies have been developed to extend the length scale of soft matters in the modeling of mechanical behaviors. However, the classical thermostat algorithm in highly coarse-grained molecular dynamics method would underestimate the thermodynamic behaviors of soft matters (e.g. microfilaments in cells), which can weaken the ability of materials to overcome local energy traps in granular modeling. Based on all-atom molecular dynamics modeling of microfilament fragments (G-actin clusters), a new stochastic thermostat algorithm is developed to retain the representation of thermodynamic properties of microfilaments at extra coarse-grained level. The accuracy of this stochastic thermostat algorithm is validated by all-atom MD simulation. This new stochastic thermostat algorithm provides an efficient way to investigate the thermomechanical properties of large-scale soft matters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A fast marching algorithm for the factored eikonal equation

The eikonal equation is instrumental in many applications in several fields ranging from computer vision to geoscience. This equation can be efficiently solved using the iterative Fast Sweeping (FS) methods and the direct Fast Marching (FM) methods. However, when used for a point source, the original eikonal equation is known to yield inaccurate numerical solutions, because of a singularity at the source. In this case, the factored eikonal equation is often preferred, and is known to yield a more accurate numerical solution. One application that requires the solution of the eikonal equation for point sources is travel time tomography. This inverse problem may be formulated using the eikonal equation as a forward problem. While this problem has been solved using FS in the past, the more recent choice for applying it involves FM methods because of the efficiency in which sensitivities can be obtained using them. However, while several FS methods are available for solving the factored equation, the FM method is available only for the original eikonal equation. In this paper we develop a Fast Marching algorithm for the factored eikonal equation, using both first and second order finite-difference schemes. Our algorithm follows the same lines as the original FM algorithm and requires the same computational effort. In addition, we show how to obtain sensitivities using this FM method and apply travel time tomography, formulated as an inverse factored eikonal equation. Numerical results in two and three dimensions show that our algorithm solves the factored eikonal equation efficiently, and demonstrate the achieved accuracy for computing the travel time. We also demonstrate a recovery of a 2D and 3D heterogeneous medium by travel time tomography using the eikonal equation for forward modeling and inversion by Gauss–Newton.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

An explicitly solvable energy-conserving algorithm for pitch-angle scattering in magnetized plasmas

In this work, we develop an Explicitly Solvable Energy-Conserving (ESEC) algorithm for the Stochastic Differential Equation (SDE) describing the pitch-angle scattering process in magnetized plasmas. The Cayley transform is used to calculate both the deterministic gyromotion and stochastic scattering, affording the algorithm to be explicitly solvable and exactly energy conserving. An unusual property of the SDE for pitch-angle scattering is that its coefficients diverge at the zero velocity and do not satisfy the global Lipschitz condition. Consequently, when standard numerical methods, such as the Euler-Maruyama (EM), are applied, numerical convergence is difficult to establish. For the proposed ESEC algorithm, its energy-preserving property enables us to overcome this obstacle. We rigorously prove that the ESEC algorithm is order 1/2 strongly convergent. This result is confirmed by detailed numerical studies. For the case of pitch-angle scattering in a magnetized plasma with a constant magnetic field, the numerical solution is benchmarked against the analytical solution, and excellent agreements are found.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

HPC formulations of optimization algorithms for tensor completion

Tensor completion is a powerful tool used to estimate or recover missing values in multi-way data. It has seen great success in domains such as product recommendation and healthcare. Tensor completion is most often accomplished via low-rank sparse tensor factorization, a computationally expensive non-convex optimization problem which has only recently been studied in the context of parallel computing. In this work, we study three optimization algorithms that have been successfully applied to tensor completion: alternating least squares (ALS), stochastic gradient descent (SGD), and coordinate descent (CCD++). We explore opportunities for parallelism on shared- and distributed-memory systems and address challenges such as memory- and operation-efficiency, load balance, cache locality, and communication. Among our advancements are a communication-efficient CCD++ algorithm, an ALS algorithm rich in level-3 BLAS routines, and an SGD algorithm which combines stratification with asynchronous communication. Furthermore, we show that introducing randomization during ALS and CCD++ can accelerate convergence. We evaluate our parallel formulations on a variety of real datasets on a modern supercomputer and demonstrate speedups through 16384 cores. Further, these improvements reduce time-to-solution from hours to seconds on real-world datasets. We show that after our optimizations, ALS is advantageous on parallel systems of small-to-moderate scale, while both ALS and CCD++ provide the lowest time-to-solution on large-scale distributed systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A junction-tree based learning algorithm to optimize network wide traffic control: A coordinated multi-agent framework

Our study develops a novel reinforcement learning algorithm for the challenging coordinated signal control problem. Traffic signals are modeled as intelligent agents interacting with the stochastic traffic environment. The model is built on the framework of coordinated reinforcement learning. The Junction Tree Algorithm (JTA) based reinforcement learning is proposed to obtain an exact inference of the best joint actions for all the coordinated intersections. Moreover, the algorithm is implemented and tested with a network containing 18 signalized intersections in VISSIM. Finally, our results show that the JTA based algorithm outperforms independent learning (Q-learning), real-time adaptive learning, and fixed timing plans in terms of average delay, number of stops, and vehicular emissions at the network level.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Novel Multiagent Resource Sharing Algorithm for Control of Advanced Energy Systems

This paper implements a novel resource sharing control strategy on a fuel cell–gas turbine hybrid power system at the National Energy Technology Laboratory’s Hybrid Performance Facility (Hyper). In a fuel cell–gas turbine hybrid power system, the simultaneous interaction of the gas turbine and the fuel cell creates a tightly coupled environment characterized by conflicting dynamics. In this paper, a model-free control approach is applied to solve the tightly coupled control problem posed by this challenging environment. Specifically, this control problem is presented as a resource sharing problem that can be solved using a resource sharing algorithm that is defined based on the distribution construction concept. This algorithm creates computational agents and solves the problem through the distribution and redistribution of shared resources defined as blocks. Furthermore, two agents were created; the first agent (agent 1) controls the gas turbine speed by adjusting the electric load, and the second agent (agent 2) controls the cathode mass flow through the fuel cell using the cold-air bypass valve. A parametric study was performed over the course of 15 experimental tests for both agents 1 and 2 through an evaluation of the responses based on setpoint changes. The algorithm was shown to have behavior comparable to a previously implemented multi-input multioutput state-space controller, which was designed through a model-based control approach. The resource sharing algorithm was able to find stable performance during run-time operations without any prior system knowledge identification on the power plant and without creating models used in traditional control strategies.

25 ENERGY STORAGE↗
DOE OSTI2013

Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence

In this article, we demonstrate that Tully's fewest-switches surface hopping (FSSH) algorithm approximately obeys the mixed quantum-classical Liouville equation (QCLE), provided that several conditions are satisfied – some major conditions, and some minor. The major conditions are: (1) nuclei must be moving quickly with large momenta; (2) there cannot be explicit recoherences or interference effects between nuclear wave packets; (3) force-based decoherence must be added to the FSSH algorithm, and the trajectories can no longer rigorously be independent (though approximations for independent trajectories are possible). We furthermore expect that FSSH (with decoherence) will be most robust when nonadiabatic transitions in an adiabatic basis are dictated primarily by derivative couplings that are presumably localized to crossing regions, rather than by small but pervasive off-diagonal force matrix elements. In the end, our results emphasize the strengths of and possibilities for the FSSH algorithm when decoherence is included, while also demonstrating the limitations of the FSSH algorithm and its inherent inability to follow the QCLE exactly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗