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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Direction-optimizing Label Propagation Framework for Structure Detection in Graphs: Design, Implementation, and Experimental Analysis

Label Propagation is not only a well-known machine learning algorithm for classification but also an effective method for discovering communities and connected components in networks. We propose a new Direction-optimizing Label Propagation Algorithm (DOLPA) framework that enhances the performance of the standard Label Propagation Algorithm (LPA), increases its scalability, and extends its versatility and application scope. As a central feature, the DOLPA framework relies on the use of frontiers and alternates between label push and label pull operations to attain high performance. It is formulated in such a way that the same basic algorithm can be used for finding communities or connected components in graphs by only changing the objective function used. Additionally, DOLPA has parameters for tuning the processing order of vertices in a graph to reduce the number of edges visited and improve the quality of solution obtained. We present the design and implementation of the enhanced algorithm as well as our shared-memory parallelization of it using OpenMP. We also present an extensive experimental evaluation of our implementations using the LFR benchmark and real-world networks drawn from various domains. Compared with an implementation of LPA for community detection available in a widely used network analysis software, we achieve at most five times the F-Score while maintaining similar runtime for graphs with overlapping communities. We also compare DOLPA against an implementation of the Louvain method for community detection using the same LFR-graphs and show that DOLPA achieves about three times the F-Score at just 10% of the runtime. For connected component decomposition, our algorithm achieves orders of magnitude speedups over the basic LP-based algorithm on large-diameter graphs, up to 13.2× speedup over the Shiloach-Vishkin algorithm, and up to 1.6× speedup over Afforest on an Intel Xeon processor using 40 threads.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Resilient off-grid microgrids: Capacity planning and N-1 security

Over the past century the electric power industry has evolved to support the delivery of power over long distances with highly interconnected transmission systems. Despite this evolution, some remote communities are not connected to these systems. These communities rely on small, disconnected distribution systems, i.e., microgrids to deliver power. However, as microgrids often are not held to the same reliability standards as transmission grids, remote communities can be at risk for extended blackouts. To address this issue, we develop an optimization model and an algorithm for capacity planning and operations of microgrids that include N-1 security and other practical modeling features like AC power flow physics, component efficiencies and thermal limits. Lastly, we demonstrate the computational effectiveness of our approach on two test systems; a modified version of the IEEE 13 node test feeder and a model of a distribution system in a remote community in Alaska.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Data-Centric Approach to Capture Non-Polynomial Nonlinear Dynamics

We propose an analytical construction of observable functions in the extended dynamic mode decomposition (EDMD) algorithm. EDMD is a numerical method for approximating the spectral properties of the Koopman operator. The choice of observable functions is fundamental for applying EDMD to nonlinear problems arising in systems and control. Existing methods either start from a set of dictionary functions and look for the subset that best fits the underlying nonlinear dynamics or rely on machine learning algorithms to “learn” observable functions. Conversely, in this paper, we start from the dynamical system model and lift it through the Lie derivatives, rendering it into a polynomial form. This proposed transformation into a polynomial form is exact and provides an adequate set of observable functions. The strength of the proposed approach is its applicability to a broader class of nonlinear dynamical systems, particularly those with nonpolynomial functions and compositions thereof. Moreover, it retains the physical interpretability of the underlying dynamical system and can be readily integrated into existing numerical libraries. We demonstrate the proposed approach with an application to electric power systems. The modeled system consists of a single generator connected to an infinite bus, where nonlinear terms include sine and cosine functions. The results demonstrate the effectiveness of the proposed procedure in off-attractor nonlinear dynamics for estimation and prediction; the observable functions obtained from the proposed construction outperform methods that use dictionary functions comprising monomials or radial basis functions.

extended dynamic mode decomposition↗
DOE OSTI2025

A Parametric, Data-Driven, Non-Intrusive Reduced-Order Model Framework for Crystal Plasticity Simulations of Voids

The influence of the internal structure at micrometer length scales on the deformation of polycrystalline materials can be effectively captured using crystal plasticity finite element methods (CPFEM). However, the complexity and nonlinearity of the deformation equations CPFEM solves demand significant computational power and resources to achieve accurate predictions, limiting its broader application. To address this challenge, we have identified a reduced-order representation of the complex data in order to establish a computationally efficient reduced-order models (ROM) and drastically reduce the computational expense of CPFEM. Specifically, in this work, we developed a parametric, data-driven, and non-intrusive ROM framework for CPFEM using proper orthogonal decomposition (POD) and sparse variational Gaussian process (SVGP) regression for single-crystal microstructures under tensile loading conditions. The developed protocol enables one to compress field into a latent/low-dimensional space described by principal component analysis (PCA) via the singular value decomposition (SVD) algorithm. As a result, the high-dimensional data are reduced to a significantly smaller amount of dimensions with POD bases and POD coefficients. Furthermore, we deployed an ensemble of SVGPs—extended from the classical Gaussian process (GP) regression for scalability and handling big data—in a massively parallel manner to train and predict latent POD coefficients using known POD bases from a set of previously obtained simulations results. Lastly, using the predicted POD coefficients, we reconstructed the full-field results and showed reasonable agreement compared with the true values obtained from running CPFEM. The developed framework is validated with a set of CPFEM simulations of a single embedded void in single-crystal aluminum alloy. While the framework is broadly applicable, this work specifically focuses on single-crystal microstructures, a single load case (e.g., tensile), and a specific void geometry (spherical).

Anisotropy↗
DOE OSTI2016

Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication

Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. Even though 3D (or 2.5D) algorithms have been proposed and theoretically analyzed in the flat MPI model on Erdös-Rényi matrices, those algorithms had not been implemented in practice and their complexities had not been analyzed for the general case. In this work, we present the first implementation of the 3D SpGEMM formulation that exploits multiple (intranode and internode) levels of parallelism, achieving significant speedups over the state-of-the-art publicly available codes at all levels of concurrencies. We extensively evaluate our implementation and identify bottlenecks that should be subject to further research.

2.5D algorithms↗
DOE OSTI2026

ORBIT CORRECTION STUDIES ON THE ELECTRON TRANSPORT LINE FROM RCS TO ESR

A dedicated electron transfer line from Rapid Cycling Synchrotron (RCS) to Electron Storage Ring (ESR), referred to as the RTE line has been designed for the Electron-Ion Collider (EIC). The beamline follows a straight-line geometry, with a length of 133 m, and is consists with two matching sections and a FODO section for beam diagnostics. Imperfections with magnet alignments introduce orbit distortions, making orbit correction scheme a critical component in the design. To facilitate orbit correction, each quadrupole magnet is equipped with a pair of beam position monitors (BPMs) and kickers. The Singular Value Decomposition (SVD) algorithm is used for orbit correction and tolerance studies. This paper presents the ongoing progress in the optics design and error correction scheme of the RTE line.

Neththikumara, I. [Thomas Jefferson National Accel↗
DOE OSTI2022

Algebraic Bethe Circuits

The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA into unitary form, for its direct implementation on a quantum computer. This is achieved by distilling the non-unitary R matrices that make up the ABA into unitaries using the QR decomposition. Our algorithm is deterministic and works for both real and complex roots of the Bethe equations. We illustrate our method on the spin-$\frac{1}{2}$ XX and XXZ models. We show that using this approach one can efficiently prepare eigenstates of the XX model on a quantum computer with quantum resources that match previous state-of-the-art approaches. We run small-scale error mitigated implementations on the IBM quantum computers, including the preparation of the ground state for the XX and XXZ models on 4 sites. Finally, we derive a new form of the Yang-Baxter equation using unitary matrices, and also verify it on a quantum computer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A quasi-static particle-in-cell algorithm based on an azimuthal Fourier decomposition for highly efficient simulations of plasma-based acceleration: QPAD

The three-dimensional (3D) quasi-static particle-in-cell (PIC) algorithm is a very efficient method for modeling short-pulse laser or relativistic charged particle beam–plasma interactions. In this algorithm, the plasma response, i.e., plasma wave wake, to a non-evolving laser or particle beam is calculated using a set of Maxwell’s equations based on the quasi-static approximate equations that exclude radiation. The plasma fields are then used to advance the laser or beam forward using a large time step. The algorithm is many orders of magnitude faster than a 3D fully explicit relativistic electromagnetic PIC algorithm. It has been shown to be capable to accurately model the evolution of lasers and particle beams in a variety of scenarios. Additionally, at the same time, an algorithm in which the fields, currents and Maxwell equations are decomposed into azimuthal harmonics has been shown to reduce the algorithmic complexity of a 3D explicit PIC algorithm to that of a 2D algorithm when the expansion is truncated while maintaining accuracy for problems with near azimuthal symmetry. This hybrid algorithm uses a PIC description in r–z and a gridless description in . We describe a novel method that combines the quasi-static and hybrid PIC methods. This algorithm expands the fields, charge and current density into azimuthal harmonics. A set of the quasi-static field equations is derived for each harmonic. The complex amplitudes of the fields are then solved using the finite difference method. The beam and plasma particles are advanced in Cartesian coordinates using the total fields. Details on how this algorithm was implemented using a similar workflow to an existing quasi-static code, QuickPIC, are presented. The new code is called QPAD for QuickPIC with Azimuthal Decomposition. Benchmarks and comparisons between a fully 3D explicit PIC code (OSIRIS), a full 3D quasi-static code (QuickPIC), and the new quasi-static PIC code with azimuthal decomposition (QPAD) are also presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Theoretically and practically efficient parallel nucleus decomposition

This paper studies the nucleus decomposition problem, which has been shown to be useful in finding dense substructures in graphs. We present a novel parallel algorithm that is efficient both in theory and in practice. Our algorithm achieves a work complexity matching the best sequential algorithm while also having low depth (parallel running time), which significantly improves upon the only existing parallel nucleus decomposition algorithm (Sariyüce et al. , PVLDB 2018). The key to the theoretical efficiency of our algorithm is a new lemma that bounds the amount of work done when peeling cliques from the graph, combined with the use of a theoretically-efficient parallel algorithms for clique listing and bucketing. We introduce several new practical optimizations, including a new multi-level hash table structure to store information on cliques space-efficiently and a technique for traversing this structure cache-efficiently. On a 30-core machine with two-way hyper-threading on real-world graphs, we achieve up to a 55x speedup over the state-of-the-art parallel nucleus decomposition algorithm by Sariyüce et al. , and up to a 40x self-relative parallel speedup. We are able to efficiently compute larger nucleus decompositions than prior work on several million-scale graphs for the first time.

Computer Science↗
DOE OSTI2015

Integration of progressive hedging and dual decomposition in stochastic integer programs

We present a method for integrating the Progressive Hedging (PH) algorithm and the Dual Decomposition (DD) algorithm of Carøe and Schultz for stochastic mixed-integer programs. Based on the correspondence between lower bounds obtained with PH and DD, a method to transform weights from PH to Lagrange multipliers in DD is found. Fast progress in early iterations of PH speeds up convergence of DD to an exact solution. As a result, we report computational results on server location and unit commitment instances.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Parallel deterministic transport sweeps of structured and unstructured meshes with overloaded mesh decompositions

Here, the efficiency of discrete ordinates transport sweeps depends on the scheduling algorithm, the domain decomposition, the problem to be solved, and the computational platform. Sweep scheduling algorithms may be categorized by their approach to several issues. In this paper we examine the strategy of domain overloading for mesh partitioning as one of the components of such algorithms. In particular, we extend the domain overloading strategy, previously defined and analyzed for structured meshes, to the general case of unstructured meshes. We also present computational results for both the structured and unstructured domain overloading cases. We find that an appropriate amount of domain overloading can greatly improve the efficiency of parallel sweeps for both structured and unstructured partitionings of the test problems examined on up to 10 5 processor cores.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Embedding spatial decomposition in parareal in time power system simulation

We propose an approach for combining two decompositions in power system simulation, temporal and spatial, with a goal to achieve faster simulation time than utilizing either one of them alone. The proposed approach builds upon the structure of the Parareal algorithm for temporal decomposition and explores an efficient way of embedding the spatial decomposition into its coarse and fine solutions. This introduces two types of simultaneous parallelism in power system simulations - parallelism between system areas and between coarse integration intervals for time integration. The results from the application of the proposed approach are shown on a two-area system comprised of the IEEE 16-machine, 68-bus, and the IEEE 50-machine, 145-bus system.

Duan, Nan↗
DOE OSTI2016

Isotopic determination of uranium in soil by laser induced breakdown spectroscopy

Laser-induced breakdown spectroscopy (LIBS) operated under ambient pressure has been evaluated for isotopic analysis of uranium in real-world samples such as soil, with U concentrations in the single digit percentage levels. The study addresses the requirements for spectral decomposition of 235 U and 238 U atomic emission peaks that are only partially resolved. Although non-linear least-square fitting algorithms are typically able to locate the optimal combination of fitting parameters that best describes the experimental spectrum even when all fitting parameters are treated as free independent variables, the analytical results of such an unconstrained free-parameter approach are ambiguous. In this work, five spectral decomposition algorithms were examined, with different known physical properties (e.g., isotopic splitting, hyperfine structure) of the spectral lines sequentially incorporated into the candidate algorithms as constraints. It was found that incorporation of such spectral-line constraints into the decomposition algorithm is essential for the best isotopic analysis. The isotopic abundance of 235 U was determined from a simple two-component Lorentzian fit on the U II 424.437 nm spectral profile. For six replicate measurements, each with only fifteen laser shots, on a soil sample with U concentration at 1.1% w/w, the determined 235 U isotopic abundance was (64.6 ± 4.8)%, and agreed well with the certified value of 64.4%. Another studied U line - U I 682.691 nm possesses hyperfine structure that is comparatively broad and at a significant fraction as the isotopic shift. Thus, 235 U isotopic analysis with this U I line was performed with spectral decomposition involving individual hyperfine components. For the soil sample with 1.1% w/w U, the determined 235 U isotopic abundance was (60.9 ± 2.0)%, which exhibited a relative bias about 6% from the certified value. The bias was attributed to the spectral resolution of our measurement system - the measured line width for this U I line was larger than its isotopic splitting. In conclusion, although not the best emission line for isotopic analysis, this U I emission line is sensitive for element analysis with a detection limit of 500 ppm U in the soil matrix; the detection limit for the U II 424.437 nm line was 2000 ppm.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Alternating Direction Decomposition with Strong Bounding and Convexification (ADDSBC) for Solving Security Constrained AC Unit Commitment Problems

This project aims to develop efficient and robust computational methods for solving the security-constrained unit commitment and alternating current optimal power flow problem (SC-UC-ACOPF). The SC-UC-ACOPF problem is at the center of the short-term operation of the U.S. Power Grid. It is solved every week, every day, and every 10 minutes to plan for the optimal action of electricity generation and consumption by minimizing the generation cost and maintaining power system reliability against potential disruptions of equipment failures. In mathematical terms, SC-UC-ACOPF is a challenging large-scale mixed-integer nonlinear optimization model. This means that the decisions involve both discrete variables, e.g. the turning on and off of generators and switching of transmission lines and transformers, and continuous decisions, e.g. the amount of energy generated by each generator and the power flows in the power grid. The physics of the power flow is described by nonlinear equations involving real and reactive power and bus voltages. Another key feature is the large number of contingencies, i.e. the system needs to stay reliable in face of failure of any one equipment, such as transmission lines and generators. The U.S. power grids are extremely complicated and large scale with more than 5,000 generators, 50,000 buses, and 100,000 high-voltage transmission lines, making the SC-UC-ACOPF a very large-scale computation challenge. The research developed in this project aims to solve the SC-UC-ACOPF problems in the three timescales, i.e. weekly, daily, and every 10-min. The proposed computational methods are built on a principled algorithmic approach of decomposition and penalization. More specifically, the algorithm develops spatial and temporal decomposition by exploiting the strong temporal coupling and weak spatial coupling of the UC problem and the complementary feature, i.e. weak temporal coupling and strong spatial coupling of the ACOPF problem. The algorithm also leverages recent progresses in strong convex relaxation of ACOPF. A unique feature of the proposed approach is that it generates a valid, global upper bound on the optimal maximum profit. In this way, a global optimality gap is available to measure the quality of the solution. To further speed up computation, the research team has developed a plethora of effective heuristics to strengthen the iterative penalty-based decomposition framework. For instance, a heuristic is developed to construct inner approximations of the time coupling constraints within the time decoupled problems. Contingencies are pre-screened and low-rank matrix computation is exploited to find the almost unique solution to each contingency. A novel heuristic for line switching is proposed and tested with positive impacts on instances where line switching is beneficial. Taking a systematic approach and carefully handling every detail of the problem pays off. The TIM-GO’s performance throughout the trials and the final event was stellar. TIM-GO garnered the second highest total prize money and is ranked in the top three positions across all categories of comparison.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

An Infinite Domain 3D Poisson Solver Based on the Barnes-Hut Algorithm

We present a domain decomposition method for the solution of the 3D Poisson equation with infinite domain boundary conditions. The method is based on an application of the Barnes-Hut tree particle scheme adapted to gridded data. Long range interactions are computed using the first two terms in the Cartesian multipole expansion of Green’s function convoluted with the charge while short range computations are performed using Hockney’s domain doubling algorithm. A standard domain decomposition strategy requires O(N 2 ) applications of Hockney’s algorithm, where N is the number of subdomains that intersect that charge support, while in the present approach only O(Nlog 2 N) such computations suffice. The discretization scheme employed is a sixth order Mehrstellen approximation of the 3D Laplace opera tor. The method exhibits satisfactory accuracy at a substantially reduced computational cost compared to the full domain decomposition Hockney’s algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

MO-FG-204-03: Using Edge-Preserving Algorithm for Significantly Improved Image-Domain Material Decomposition in Dual Energy CT

Purpose: To significantly improve dual energy CT (DECT) imaging by establishing a new theoretical framework of image-domain material decomposition with incorporation of edge-preserving techniques. Methods: The proposed algorithm, HYPR-NLM, combines the edge-preserving non-local mean filter (NLM) with the HYPR-LR (Local HighlY constrained backPRojection Reconstruction) framework. Image denoising using HYPR-LR framework depends on the noise level of the composite image which is the average of the different energy images. For DECT, the composite image is the average of high- and low-energy images. To further reduce noise, one may want to increase the window size of the filter of the HYPR-LR, leading resolution degradation. By incorporating the NLM filtering and the HYPR-LR framework, HYPR-NLM reduces the boost material decomposition noise using energy information redundancies as well as the non-local mean. We demonstrate the noise reduction and resolution preservation of the algorithm with both iodine concentration numerical phantom and clinical patient data by comparing the HYPR-NLM algorithm to the direct matrix inversion, HYPR-LR and iterative image-domain material decomposition (Iter-DECT). Results: The results show iterative material decomposition method reduces noise to the lowest level and provides improved DECT images. HYPR-NLM significantly reduces noise while preserving the accuracy of quantitative measurement and resolution. For the iodine concentration numerical phantom, the averaged noise levels are about 2.0, 0.7, 0.2 and 0.4 for direct inversion, HYPR-LR, Iter- DECT and HYPR-NLM, respectively. For the patient data, the noise levels of the water images are about 0.36, 0.16, 0.12 and 0.13 for direct inversion, HYPR-LR, Iter-DECT and HYPR-NLM, respectively. Difference images of both HYPR-LR and Iter-DECT show edge effect, while no significant edge effect is shown for HYPR-NLM, suggesting spatial resolution is well preserved for HYPR-NLM. Conclusion: HYPR-NLM provides an effective way to reduce the generic magnified image noise of dual–energy material decomposition while preserving resolution. This work is supported in part by NIH grants 7R01HL111141 and 1R01-EB016777. This work is also supported by the Natural Science Foundation of China (NSFC Grant No. 81201091), Fundamental Research Funds for the Central Universities in China, and Fund Project for Excellent Abroad Scholar Personnel in Science and Technology.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Efficient Ab Initio Auxiliary-Field Quantum Monte Carlo Calculations in Gaussian Bases via Low-Rank Tensor Decomposition

We describe an algorithm to reduce the cost of auxiliary-field quantum Monte Carlo (AFQMC) calculations for the electronic structure problem. The technique uses a nested low-rank factorization of the electron repulsion integral (ERI). While the cost of conventional AFQMC calculations in Gaussian bases scales as O(N 4 ), where N is the size of the basis, we show that ground-state energies can be computed through tensor decomposition with reduced memory requirements and subquartic scaling. Here, the algorithm is applied to hydrogen chains and square grids, water clusters, and hexagonal BN. In all cases, we observe significant memory savings and, for larger systems, reduced, subquartic simulation time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗