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At least 811 records · Page 45

A Study on Particle Trajectory Error in Finite-Element Particle-in-Cell Algorithms

Particle-in-cell (PIC) algorithms are widely used for the simulation of kinetic plasmas. PIC algorithms account for the interaction between charged particles in a plasma and the electromagnetic field in ambient space, including self-field interactions. The objective of this article is to study the error in charged particle trajectories present in finite-element (FE)-based PIC algorithms on unstructured meshes. We study how the trajectory error behaves according to the FE mesh resolution and the matrix solver employed in the FE algorithm. The study is performed by considering a trajectory established by a parabolic electric potential and an axial magnetic force acting on the charged particle. Under a proper choice combination of electric and magnetic field parameters, the 2-D particle trajectories comprise closed orbits. Numerical errors cause small perturbations on the trajectories, with cumulative effects. As a result, the resulting orbital trajectories exhibit distortions including spurious apsidal precession. These distortions provide a clear imprint of the numerical error. Here, we also study the numerical error in a quantitative fashion by computing the distance norm between the trajectories obtained by the exact fields and numerical fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Diesel Generator Model Parameterization for Microgrid Simulation Using Hybrid Box-Constrained Levenberg-Marquardt Algorithm

Existing generator parameterization methods, typically developed for large turbine generator units, are difficult to apply to small kW-level diesel generators in microgrid applications. Here, this article presents a model parameterization method that estimates a complete set of kW-level diesel generator parameters simultaneously using only load-step-change tests with limited measurement points. This method provides a more cost-efficient and robust approach to achieve high-fidelity modeling of diesel generators for microgrid dynamic simulation. A two-stage hybrid box-constrained Levenberg-Marquardt (H-BCLM) algorithm is developed to search the optimal parameter set given the parameter bounds. A heuristic algorithm, namely Generalized Opposition-based Learning Genetic Algorithm (GOL-GA), is applied to identify proper initial estimates at the first stage, followed by a modified Levenberg-Marquardt algorithm designed to fine tune the solution based on the first-stage result. The proposed method is validated against dynamic simulation of a diesel generator model and field measurements from a 16kW diesel generator unit.

42 ENGINEERING↗

A Parallel Cut-Cell Algorithm for the Free-Boundary Grad--Shafranov Problem

A parallel cut-cell algorithm is described to solve the free-boundary problem of the Grad--Shafranov equation. The algorithm reformulates the free-boundary problem in an irregular bounded domain and its important aspects include a searching algorithm for the magnetic axis and separatrix, a surface integral along the irregular boundary to determine the boundary values, an approach to optimize the coil current based on a targeting plasma shape, Picard iterations with Aitken's acceleration for the resulting nonlinear problem, and a Cartesian grid embedded boundary method to handle the complex geometry. Here the algorithm is implemented in parallel using a standard domain-decomposition approach and a good parallel scaling is observed. Numerical results verify the accuracy and efficiency of the free-boundary Grad--Shafranov solver.

97 MATHEMATICS AND COMPUTING↗

Surrogate-Based Autotuning for Randomized Sketching Algorithms in Regression Problems

Algorithms from Randomized Numerical Linear Algebra (RandNLA) are known to be effective in handling high-dimensional computational problems, providing high-quality empirical performance as well as strong probabilistic guarantees. However, their practical application is complicated by the fact that the user needs to set various algorithm-specific tuning parameters which are different from those used in traditional NLA. This paper demonstrates how a surrogate-based autotuning approach can be used to address fundamental problems of parameter selection in RandNLA algorithms. In particular, we provide a detailed investigation of surrogate-based autotuning for sketch-and-precondition (SAP)-based randomized least squares methods, which have been one of the great success stories in modern RandNLA. Empirical results show that our surrogate-based autotuning approach can achieve near-optimal performance with much less tuning cost than a random search (up to about 7.6x fewer trials of different parameter configurations). Moreover, while our experiments focus on least squares, our results demonstrate a general-purpose autotuning pipeline applicable to any kind of RandNLA algorithm.

Cho, Younghyun↗

Algorithms in Diffraction Profile Analysis

This chapter introduces several approaches to crystallographic structure refinement from diffraction profile data including the Rietveld method, global optimization methods, and Bayesian modeling. First, the Rietveld method and related nonlinear least squares approaches to analyzing diffraction profiles are briefly discussed. We then review the most common algorithms within global optimization as alternative methods of structure solution: grid search, simulated annealing, and genetic algorithms. As the Rietveld method is the standard tool for analyzing diffraction profile data, we catalogue its challenges and limitations. A Bayesian approach to diffraction profile analysis is presented as an alternative, along with several sampling algorithms including Gibbs sampling, variants of Metropolis sampling, Hamiltonian Monte Carlo, and approximate Bayesian computing. These sampling algorithms are applied to the fitting of a neutron diffraction profile from a National Institute of Standards and Technology silicon standard reference material, and their results are compared.

Singh, Susheela↗

Neuromorphic Graph Algorithms: Cycle Detection, Odd Cycle Detection, and Max Flow

Neuromorphic computing is poised to become a promising computing paradigm in the post Moore’s law era due to its extremely low power usage and inherent parallelism. Spiking neural networks are the traditional use case for neuromorphic systems, and have proven to be highly effective at machine learning tasks such as control problems. More recently, neuromorphic systems have been applied outside of the arena of machine learning, primarily in the field of graph algorithms. Neuromorphic systems have been shown to perform graph algorithms faster and with lower power consumption than their traditional (GPU/CPU) counterparts, and are hence an attractive option for a co-processing unit in future high performance computing systems, where graph algorithms play a critical role. In this paper, we present a neuromorphic implementation of cycle detection, odd cycle detection, and the Ford-Fulkerson max-flow algorithm. We further evaluate the performance of these implementations using the NEST neuromorphic simulator by using spike counts and simulation time as proxies for energy consumption and run time. In addition to gains inherent in neuromorphic systems, we show that within the neuromorphic implementations early stopping criteria can be implemented to further improve performance.

Kay, Bill↗

Algorithms for Forward and Inverse Problem Solutions in Phase Contrast Tomography

PhaseTorch is a python package that implements algorithms for forward and inverse problem solutions in X-ray phase contrast tomography (XPCT). XPCT is useful to reconstruct the 3D distribution of the refractive index decrement and absorption index of an imaged object. PhaseTorch implements algorithms for simulation, reconstruction, and analysis of XPCT data. PhaseTorch provides algorithms for simulation of XPCT data of an object with known refractive and absorption indices. It contains algorithms for reconstructing the projections of the absorption index and refractive index decrement.

Sridhar, Venkatesh↗

Confidentiality-preserving machine learning algorithms for soft-failure detection in optical communication networks

Automated fault management is at the forefront of next-generation optical communication networks. The increase in complexity of modern networks has triggered the need for programmable and software-driven architectures to support the operation of agile and self-managed systems. In these scenarios, the European Telecommunications Standards Institute zero-touch network and service management approach is imperative. The need for machine learning algorithms to process the large volume of telemetry data brings safety concerns as distributed cloud-computing solutions become the preferred approach for deploying reliable communication network automation. This paper’s contribution is twofold. First, we propose a simple yet effective method to guarantee the confidentiality of the telemetry data based on feature scrambling. The method allows the operation of third-party computational services without direct access to the full content of the collected data. Additionally, the effectiveness of four unsupervised machine learning algorithms for soft-failure detection is evaluated when applied to the scrambled telemetry data. The methods are based on factor analysis, principal component analysis, nonlinear principal component analysis, and singular value decomposition. Most dimensionality reduction algorithms have the common property that they can maintain similar levels of fault classification performance while hiding the data structure from unauthorized access. Evaluations of the proposed algorithms demonstrate this capability.

97 MATHEMATICS AND COMPUTING↗

Proton pulse charge calculation algorithm in Beam Power Limiting System at Spallation Neutron Source

A proton pulse charge calculation algorithm in the Beam Power Limiting System (BPLS) at the Spallation Neutron Source (SNS) was developed and implemented in an FPGA. The algorithm calculates one-minute running average of the pulse charges and issues a fault to the Personal Protection System (PPS) and the Machine Protection System (MPS) when a limit is reached. A bit-accurate model of the algorithm was first developed and tested in Matlab® and then implemented and simulated in VHDL using Vivado® design environment. Finally, the algorithm was verified on a µTCA-based hardware platform.

Bobrek, Miljko [ORNL] (ORCID:0000000332763451)↗

Graupel and Hail Identification Algorithm for the Dual-frequency Precipitation Radar (DPR) on the GPM Core Satellite

Precipitation consists of many types of hydrometeors, such as raindrops, ice crystals, graupel, and hail. Due to their impacts, graupel and hail (GH) have received particular attention in the literature. Global Precipitation Measurement (GPM) dual-frequency radar (DPR) has proved to be a very reliable system for global precipitation retrievals. This paper aims to develop a GH identification algorithm for GPM DPR. This algorithm is constructed using a precipitation type index (PTI) defined for DPR. The PTI is effective in separating hydrometeor types and is calculated using measurements of reflectivity, dual-frequency ratio, and storm top height data. The output of the algorithm is a Boolean product representing the existence of graupel or hail along with the vertical profile for each Ku- and Ka-band matched footprint. Cross validation is performed with the Weather Service Radar (WSR-88D) network over continental United States as well as during the Remote sensing of Electrification, Lightning, and Mesoscale/Microscale Processes with Adaptive Ground Observations (RELAMPAGO) experiment. Evaluation of the GH identification algorithm is performed on a global basis, which illustrates promising comparisons with the global lightning and hail precipitation maps generated using radar and radiometer.

54 ENVIRONMENTAL SCIENCES↗

Preliminary Enhanced LAW Glass Formulation Algorithm

This report summarizes the Preliminary Enhanced LAW Glass Formulation Algorithm, its background information, and the calculations it performs. The Preliminary Enhanced LAW Glass Formulation Algorithm is a tool that has been developed in MATLAB to formulate glass at a given a waste composition, while attempting to maximize waste loading. It is intended for use at the Hanford Waste Treatment and Immobilization Plant, where nuclear waste will be vitrified into glass for safe, long-term storage. The formulated glass is required to meet several processing and product quality constraints. In addition, calculations must account for associated uncertainties in constraint prediction and measurement. The algorithm also allows for the ability to hold glass compositions closer to tested regions in order to increase confidence in the output. The algorithm must also follow nuclear quality assurance procedures and submit to rigorous validation and verification testing.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Algorithms and Statistical Models for Scientific Discovery in the Petabyte Era

The field of astronomy has arrived at a turning point in terms of size and complexity of both datasets and scientific collaboration. Commensurately, algorithms and statistical models have begun to adapt --- e.g., via the onset of artificial intelligence --- which itself presents new challenges and opportunities for growth. This white paper aims to offer guidance and ideas for how we can evolve our technical and collaborative frameworks to promote efficient algorithmic development and take advantage of opportunities for scientific discovery in the petabyte era. We discuss challenges for discovery in large and complex data sets; challenges and requirements for the next stage of development of statistical methodologies and algorithmic tool sets; how we might change our paradigms of collaboration and education; and the ethical implications of scientists' contributions to widely applicable algorithms and computational modeling. We start with six distinct recommendations that are supported by the commentary following them. This white paper is related to a larger corpus of effort that has taken place within and around the Petabytes to Science Workshops (https://petabytestoscience.github.io/).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Prototype for Unclassified Algorithm

Continuing previous efforts to investigate and develop the Unclassified Radioisotope Algorithm, the goal of the FY19-FY20 effort was to develop a prototype detector system which uses the algorithm to confirm warhead attributes related to the presence of either weapons grade plutonium (WGPu) or highly enriched uranium (HEU). The final deliverable is a prototype attribute measurement system built with common, commercially available gamma radiation detector components, capable of confirming the presence of specific, complex radioactive sources of interest, without the collection and storage of gamma energy spectra. This is accomplished by processing each gamma pulse as it is received, applying weight values based on the energy and incrementing or decrementing scalar counters which can be compared with expected values to determine if the measured source is consistent with WGPu or HEU. This report documents the design of the prototype system as well as the development of the algorithm and performance testing results. While the previously conceptualized, simple algorithm resulted in a prohibitive amount of false positives, the goal for a simple attribute measurement system capable of verifying Ba-133 and Ra-226 (weapons grade plutonium and highly enriched uranium surrogate testing sources) at over 95% accuracy with sub 5% false positive rate was demonstrated.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

A Block-Based Triangle Counting Algorithm on Heterogeneous Environments

Triangle counting is a fundamental building block in graph algorithms. In this paper, we propose a block-based triangle counting algorithm to reduce data movement during both sequential and parallel execution. Our block-based formulation makes the algorithm naturally suitable for heterogeneous architectures. The problem of partitioning the adjacency matrix of a graph is well-studied. Our task decomposition goes one step further: it partitions the set of triangles in the graph. By streaming these small tasks to compute resources, we can solve problems that do not fit on a device. We demonstrate the effectiveness of our approach by providing an implementation on a compute node with multiple sockets, cores and GPUs. The current state-of-the-art in triangle enumeration processes the Friendster graph in 2.1 seconds, not including data copy time between CPU and GPU. Using that metric, our approach is 20 percent faster. When copy times are included, our algorithm takes 3.2 seconds. This is 5.6 times faster than the fastest published CPU-only time.

97 MATHEMATICS AND COMPUTING↗

Fast Computational Algorithms for Partial Differential Equations and Uncertainty Quantifications

This project concerned the construction, testing and analysis of computational algorithms for solving parameterized and stochastic partial differential equations. The study and understanding of equations of this type is of fundamental importance in numerous engineering and scientific applications. Examples include simulation of plasma dynamics in models of electric propulsion and nuclear fusion, simulation of multiphase flows, such as the flow of water, gas and oil in reservoirs, and structural analysis of the dependence of structures on materials. Parametrization is used in such settings when properties of the models such as viscosity of fluids or electric resistivity of materials are not precisely understood and instead are treated as random variables. The resulting solutions are themselves random, and having such solutions will enable engineers to use probabilistic methods to assess the likelihood of events, for example, whether a pollutant in a liquid will exceed a limit, and to use such analyses to develop ways to ensure positive outcomes. Construction of accurate (high resolution) computational solutions is expensive, requiring significant computer time and computational resources, and there is need to reduce computational cost to make simulation useful and effective. The aim of the project was to construct algorithms to efficiently compute surrogate solutions to parameterized problems to allow for efficient and accurate simulation. The technical approach used focused on two related strategies, based on rank-reduction methods and reduced-order models. These methods construct surrogate solutions of parameter-dependent models by projection or interpolation into low-dimensional approximation spaces. Cost savings are achieved if the low-dimensional spaces can be identified and constructed efficiently and if the resulting low-dimensional algebraic systems can be solved cheaply. Accomplishments include: Theoretical and empirical demonstration of the effectiveness of fast multigrid solution strategies for computing low-rank representations of parameter-dependent solutions to discrete partial differential equations, including the first proof establishing so-called textbook convergence properties for low-rank methods. Development of efficient solution algorithms for solving nonlinear parameter-dependent partial differential equations used in models of fluid dynamics. Developent of efficient algorithms for low-rank representation of solutions of time-dependent simulations of fluid dynamics using multi-dimensional tensor representations of solutions.

97 MATHEMATICS AND COMPUTING↗

Using Grover's search algorithm to characterize the Rigetti Quantum Computing Platform

Performance of the Rigetti quantum computing platform was tested during the period of time from 12/16/2019 to 05/18/2020. The Grover's search (GS) algorithm was used as a testing tool, in particular, 3- and 4-level versions of the algorithm. As a result, a number of hardware issues were revealed, so the algorithm was split to smaller blocks and individual gates, and all of them were tested separately. The fidelity decay was found to be due to both decoherent processes and coherent errors of the native hardware gates. These errors were estimated from RX gate benchmarks and were in a form of extra rotation of the quantum state. As a consequence of that, performance of the algorithm was shown to be strongly dependent on the native gate decomposition of the program. Suggestions and possible improvements of the future Rigetti runs are made based on the obtained observations.

97 MATHEMATICS AND COMPUTING↗

Optimization-based algorithms for nonlinear mechanics and frictional contact

An optimization-based strategy for solving nonlinear mechanics problems is proposed. In contrast to typical nonlinear equation solver algorithms that aim to find zeros in the residual force function, we minimize an energy (or energy-like) function to encourage solutions which are locally stable equilibria. These smooth and potentially non-convex objective functions are minimized using a preconditioned conjugate-gradient trust-region algorithm. Contact is formulated as an inequality constrained minimization problem, and is solved with an augmented Lagrangian algorithm. Friction is included in the approach via a regularized quasi-potential energy, and other dissipative behavior is included through the use of variational constitutive updates. Finally, to accelerate convergence rates for the Lagrange multipliers, we propose a novel multiplier update algorithm utilizing the Fischer-Burmeister function, and demonstrate super-linear solver convergence for some applications.

42 ENGINEERING↗

Implementation of an Orificing Optimization Algorithm in the DASSH Subchannel Analysis Code

The Ducted Assembly Steady-State Heat transfer code (DASSH) performs full-core subchannel thermal hydraulics calculations in liquid metal fast reactors. One of the applications of subchannel codes is to optimize coolant flow orificing. As a design activity, the primary task is to determine the best way to divide assemblies into groups and distribute coolant flow rates among them. This report documents an algorithm implemented in DASSH to automatically optimize coolant orificing. Over the course of multiple iterations, DASSH determines the orifice grouping and flow distribution that minimizes peak coolant, clad, or fuel temperatures across all timesteps for a user-specified number of assembly groups. The total coolant flow rate in the reactor is constrained to achieve the specified core-average outlet temperature. The flow rate to each orifice group may also be constrained by the allowable pressure drop. The distribution of coolant flow among groups is accelerated using a predictor-corrector algorithm based on interpolated results from single-assembly parametric calculations. The assembly orificing grouping is initially predicted based on assembly power but can be refined if results demonstrate that an assembly would fit better in another group. The algorithm is demonstrated with two case studies. The first is a simple model for a reactor core consisting of just fuel assemblies; the pin power distributions are specified to create a situation where the initial assembly grouping prediction is suboptimal. This example is used to describe the initial grouping, demonstrate convergence over multiple iterations, and highlight the impact of regrouping. Then, the algorithm is applied to minimize peak clad and fuel temperatures in an example sodium-cooled fast reactor, the Versatile Test Reactor. The multicycle optimization confirms prior calculations for the reference core design. The example highlights how optimizing for different peak temperatures affects the results and demonstrates the use of the pressure drop constraint to limit the maximum flow rate.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗