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At least 91 records · Page 5

Parallel algorithms for finding connected components using linear algebra

Finding connected components is one of the most widely used operations on a graph. Optimal serial algorithms for the problem have been known for half a century, and many competing parallel algorithms have been proposed over the last several decades under various different models of parallel computation. This paper presents a class of parallel connected-component algorithms designed using linear-algebraic primitives. These algorithms are based on a PRAM algorithm by Shiloach and Vishkin and can be designed using standard GraphBLAS operations. Here, we demonstrate two algorithms of this class, one named LACC for Linear Algebraic Connected Components, and the other named FastSV which can be regarded as LACC’s simplification. With the support of the highly-scalable Combinatorial BLAS library, LACC and FastSV outperform the previous state-of-the-art algorithm by a factor of up to 12x for small to medium scale graphs. For large graphs with more than 50B edges, LACC and FastSV scale to 4K nodes (262K cores) of a Cray XC40 supercomputer and outperform previous algorithms by a significant margin. This remarkable performance is accomplished by (1) exploiting sparsity that was not present in the original PRAM algorithm formulation, (2) using high-performance primitives of Combinatorial BLAS, and (3) identifying hot spots and optimizing them away by exploiting algorithmic insights.

97 MATHEMATICS AND COMPUTING↗

EQSIM—A multidisciplinary framework for fault-to-structure earthquake simulations on exascale computers part I: Computational models and workflow

Computational simulations have become central to the seismic analysis and design of major infrastructure over the past several decades. Most major structures are now “proof tested” virtually through representative simulations of earthquake-induced response. More recently, with the advancement of high-performance computing (HPC) platforms and the associated massively parallel computational ecosystems, simulation is beginning to play a role in increased understanding and prediction of ground motions for earthquake hazard assessments. However, the computational requirements for regional-scale geophysics-based ground motion simulations are extreme, which has restricted the frequency resolution of direct simulations and limited the ability to perform the large number of simulations required to numerically explore the problem parametric space. In this article, recent developments toward an integrated, multidisciplinary earth science-engineering computational framework for the regional-scale simulation of both ground motions and resulting structural response are described with a particular emphasis on advancing simulations to frequencies relevant to engineered systems. This multidisciplinary computational development is being carried out as part of the US Department of Energy (DOE) Exascale Computing Project with the goal of achieving a computational framework poised to exploit emerging DOE exaflop computer platforms scheduled for the 2022–2023 timeframe.

58 GEOSCIENCES↗

Mitigating Cascading Outages in Severe Weather Using Simulation-Based Optimization

Severe weather events can trigger cascading power outages and lead to significant losses. In this work, we investigate cascading outage mitigation under severe weather conditions. Given day-ahead weather forecasts and component failure models, we aim to identify a set of power lines that can be hardened to minimize the expected impact of potential cascading outages. Since the expected load shedding cannot be expressed as an explicit function of line hardening decisions and system states, we developed a cascading outage simulator to estimate the expected value of load shedding under various initial weather-related disruption scenarios generated using a weather forecast. To avoid massive enumeration of all possible combinations of line hardening decisions and reduce the simulation efforts, we employed an efficient simulation-based optimization approach that quickly identifies the (near) optimal line hardening decisions in the presence of both large simulation noises due to the highly variable initial disturbances and system states, and significant randomness in the subsequent cascades. Furthermore, the algorithm is also able to utilize parallel computing to dramatically reduce computation time to support decision making in preparation for severe weather conditions. We performed a case study on the Northeast Power Coordinating Council (NPCC) 140-bus system model to demonstrate that our approach can significantly improve power grid resilience to adverse weather events.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DL_POLY Quantum 2.0: A modular general-purpose software for advanced path integral simulations

DL_POLY Quantum 2.0, a vastly expanded software based on DL_POLY Classic 1.10, is a highly parallelized computational suite written in FORTRAN77 with a modular structure for incorporating nuclear quantum effects into large-scale/long-time molecular dynamics simulations. This is achieved by presenting users with a wide selection of state-of-the-art dynamics methods that utilize the isomorphism between a classical ring polymer and Feynman’s path integral formalism of quantum mechanics. Here, the flexible and user-friendly input/output handling system allows the control of methodology, integration schemes, and thermostatting. DL_POLY Quantum is equipped with a module specifically assigned for calculating correlation functions and printing out the values for sought-after quantities, such as dipole moments and center-of-mass velocities, with packaged tools for calculating infrared absorption spectra and diffusion coefficients.

36 MATERIALS SCIENCE↗

A New Semistructured Algebraic Multigrid Method

Multigrid methods are well suited to large massively parallel computer architectures because they are mathematically optimal and display good parallelization properties. Since current architecture trends are favoring regular compute patterns to achieve high performance, the ability to express structure has become much more important. The hypre software library provides high-performance multigrid preconditioners and solvers through conceptual interfaces, including a semistructured interface that describes matrices primarily in terms of stencils and logically structured grids. This paper presents a new semistructured algebraic multigrid (SSAMG) method built on this interface. The numerical convergence and performance of a CPU implementation of this method are evaluated for a set of semistructured problems. In conclusion, SSAMG achieves significantly better setup times than hypre’s unstructured AMG solvers and comparable convergence. In addition, the new method is capable of solving more complex problems than hypre’s structured solvers.

97 MATHEMATICS AND COMPUTING↗

Parthenon—a performance portable block-structured adaptive mesh refinement framework

On the path to exascale the landscape of computer device architectures and corresponding programming models has become much more diverse. While various low-level performance portable programming models are available, support at the application level lacks behind. To address this issue, we present the performance portable block-structured adaptive mesh refinement (AMR) framework Parthenon, derived from the well-tested and widely used Athena++ astrophysical magnetohydrodynamics code, but generalized to serve as the foundation for a variety of downstream multi-physics codes. Parthenon adopts the Kokkos programming model, and provides various levels of abstractions from multidimensional variables, to packages defining and separating components, to launching of parallel compute kernels. Parthenon allocates all data in device memory to reduce data movement, supports the logical packing of variables and mesh blocks to reduce kernel launch overhead, and employs one-sided, asynchronous MPI calls to reduce communication overhead in multi-node simulations. Using a hydrodynamics miniapp, we demonstrate weak and strong scaling on various architectures including AMD and NVIDIA GPUs, Intel and AMD x86 CPUs, IBM Power9 CPUs, as well as Fujitsu A64FX CPUs. At the largest scale on Frontier (the first TOP500 exascale machine), the miniapp reaches a total of 1.7 × 10 13 zone-cycles/s on 9216 nodes (73,728 logical GPUs) at [Formula: see text] weak scaling parallel efficiency (starting from a single node). In combination with being an open, collaborative project, this makes Parthenon an ideal framework to target exascale simulations in which the downstream developers can focus on their specific application rather than on the complexity of handling massively-parallel, device-accelerated AMR.

97 MATHEMATICS AND COMPUTING↗

Parallel Algorithms for Efficient Computation of High-Order Line Graphs of Hypergraphs

This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are set-valued. To date, in most situations, entities in a hypergraph are considered connected as long as there is at least one common ``neighbor''. However, minimal commonality sometimes discards the ``strength'' of connections and interactions among groups. To this end, considering the ``width'' of a connection, referred to as the \emph{$s$-overlap} of neighbors, provides more meaningful insights into how closely the communities or entities interact with each other. In addition, $s$-overlap computation is the fundamental kernel to construct the line graph of a hypergraph, a low-order approximation of the hypergraph which can carry significant information about the original hypergraph. Subsequent stages of a data analytics pipeline then can apply highly-tuned graph algorithms on the line graph to reveal important features. Given a hypergraph, computing the $s$-overlaps by exhaustively considering all pairwise entities can be computationally prohibitive. To tackle this challenge, we develop efficient algorithms to compute $s$-overlaps and the corresponding line graph of a hypergraph. We propose several heuristics to avoid execution of redundant work and improve performance of the $s$-overlap computation. Our parallel algorithm, combined with these heuristics, is orders of magnitude (more than $10\times$) faster than the naive algorithm in all cases and the SpGEMM algorithm with filtration in most cases (especially with large $s$ value).

hypergraph algorithms, graph algorithms, parallel ↗

Towards Generic Parallel Programming in Computer Science Education with Kokkos

Parallel patterns, views, and spaces are promising abstractions to capture the programmer's intent as well as the contextual information that can be used by an underlying runtime to efficiently map software to parallel hardware. These abstractions can be valuable in cases where an algorithm must accommodate requirements of code and performance portability across hardware architectures and vendor programming models. Kokkos is a parallel programming model for host- and accelerator architectures that relies on these abstractions and targets these requirements. It consists of a pure C++ interface, a specification, and a programming library. The programming library exposes patterns and types and maps them to an underlying abstract machine model. The abstract machine model offers a generic view of parallel hardware. While Kokkos is gaining popularity in large-scale HPC applications at some DOE laboratories, we believe that the implemented concepts are of interest to a broader audience including academia as they may contribute to a generic, vendor, and architecture-independent education of parallel programming. In this work, we give an insight into the design considerations of this programming model and list important abstractions. Further, we document best practices obtained from giving virtual classes on Kokkos and give pointers to resources that the reader may consider valuable for a lecture on generic parallel programming for students with preexisting knowledge on this matter.

Ciesko, Jan↗

TAO Users Manual (Rev. 3.15)

The Toolkit for Advanced Optimization (TAO) focuses on the development of algorithms and software for the solution of large-scale optimization problems on high-performance architectures. Areas of interest include unconstrained and bound-constrained optimization, nonlinear least squares problems, optimization problems with partial differential equation constraints, and variational inequalities and complementarity constraints. The development of TAO was motivated by the scattered support for parallel computations and the lack of reuse of external toolkits in current optimization software. Our aim is to produce high-quality optimization software for computing environments ranging from workstations and laptops to massively parallel high-performance architectures. Our design decisions are strongly motivated by the challenges inherent in the use of large-scale distributed memory architectures and the reality of working with large, often poorly structured legacy codes for specific applications.

97 MATHEMATICS AND COMPUTING↗

The Portals 4.3 Network Programming Interface

This report presents a specification for the Portals 4 network programming interface. Portals 4 is intended to allow scalable, high-performance network communication between nodes of a parallel computing system. Portals 4 is well suited to massively parallel processing and embedded systems. Portals 4 represents an adaption of the data movement layer developed for massively parallel processing platforms, such as the 4500-node Intel TeraFLOPS machine. Sandia's Cplant cluster project motivated the development of Version 3.0, which was later extended to Version 3.3 as part of the Cray Red Storm machine and XT line. Version 4 is targeted to the next generation of machines employing advanced network interface architectures that support enhanced offload capabilities.

97 MATHEMATICS AND COMPUTING↗

ZERNIPAX: A fast and accurate Zernike polynomial calculator in Python

Zernike polynomials serve as an orthogonal basis on the unit disc, and have proven to be effective in optics simulations, astrophysics, and more recently in plasma simulations. Unlike Bessel functions, Zernike polynomials are inherently finite and smooth at the disc center (r=0), ensuring continuous differentiability along the axis. This property makes them particularly suitable for simulations, requiring no additional handling at the origin. We developed ZERNIPAX, an open-source Python package capable of utilizing CPU/GPUs, leveraging Google's JAX package and available on GitHub as well as the Python software repository PyPI. Furthermore, our implementation of the recursion relation between Jacobi polynomials significantly improves computation time compared to alternative methods by use of parallel computing while still performing more accurately for high-mode numbers.

Astrophysics↗

Accelerated Probabilistic Marching Cubes by Deep Learning for Time-Varying Scalar Ensembles

Visualizing the uncertainty of ensemble simulations is challenging due to the large size and multivariate and temporal features of en-semble data sets. One popular approach to studying the uncertainty of ensembles is analyzing the positional uncertainty of the level sets. Probabilistic marching cubes is a technique that performs Monte Carlo sampling of multivariate Gaussian noise distributions for positional uncertainty visualization of level sets. However, the technique suffers from high computational time, making interactive visualization and analysis impossible to achieve. This paper introduces a deep-learning-based approach to learning the level-set uncertainty for two-dimensional ensemble data with a multivariate Gaussian noise assumption. We train the model using the first few time steps from time-varying ensemble data in our workflow. We demonstrate that our trained model accurately infers uncertainty in level sets for new time steps and is up to 170X faster than that of the original probabilistic model with serial computation and 10X faster than that of the original parallel computation.

Han, Mengjiao↗

AMG Preconditioners based on parallel hybrid coarsening and multi-objective graph matching

We describe preliminary results from a multi-objective graph matching algorithm, in the coarsening step of an aggregation-based Algebraic MultiGrid (AMG) preconditioner, for solving large and sparse linear systems of equations on high-end parallel computers. We have two objectives. First, we wish to improve the convergence behavior of the AMG method when applied to highly anisotropic problems. Second, we wish to extend the parallel package \texttt{PSCToolkit} to exploit multi-threaded parallelism at the node level on multi-core processors. Our matching proposal balances the need to simultaneously compute high weights and large cardinalities by a new formulation of the weighted matching problem combining both these objectives using a parameter $\lambda$. We compute the matching by a parallel $2/3-\varepsilon$-approximation algorithm for maximum weight matchings. Results with the new matching algorithm show that for a suitable choice of the parameter $\lambda$ we compute effective preconditioners in the presence of anisotropy, i.e., smaller solve times, setup times, iterations counts, and operator complexity.

D'Ambra, Pasqua↗

Frequency-domain computing using nonlinear acoustic-wave device on lithium niobate

Abstract Multiply-accumulation are crucial computing operations in signal processing, numerical simulations, and machine learning. In recent years, optical analog approaches have demonstrated higher computing performance and better power efficiency than their digital counterparts. However, analog computing chips usually need large areas and complex structures for parallel computing, as a single device element only executes one computing operation at a single time. Here, we demonstrate frequency-domain computing using the nonlinear acoustic-wave devices on lithium niobate, featuring a normalized external second-harmonic generation conversion efficiency of ~ 5.7 × 10-4 W-1. The second-order sum-frequency nonlinear process of lithium niobate enables multiplication of inputs encoded in the frequency domain. Compared to the analog schemes, our device features a notably simpler design, and nanofabrication requires only one lift-off. Using a single acoustic-wave device within an area of 0.03 mm2, we can simultaneously conduct over 130,000 multiply-accumulation operations. Our acoustic-wave device shows applications in real and complex vector convolutions and image processing. This demonstration sets the stage for experimental realizations into frequency-domain integrated nonlinear acoustic computing systems, potentially shaping future developments in acoustic neural networks and quantum computing.

chai, mingzhao (ORCID:0009000466226341)↗

Active Learning for Metamaterial Optimization on HPC and QC Integrated Systems

Active learning algorithms, integrating machine learning, quantum computing and optics simulation in an iterative loop, offer a promising approach to optimizing metamaterials. However, these algorithms can face difficulties in optimizing highly complex structures due to computational limitations. High-performance computing (HPC) and quantum computing (QC) integrated systems can address these issues by enabling parallel computing. In this study, we develop an active learning algorithm working on HPC-QC integrated systems. We evaluate the performance of optimization processes within active learning (i.e., training a machine learning model, problem-solving with quantum computing, and evaluating optical properties through wave-optics simulation) for highly complex metamaterial cases. Our results showcase that utilizing multiple cores on the integrated system can significantly reduce computational time, thereby enhancing the efficiency of optimization processes. Therefore, we expect that leveraging HPC-QC integrated systems helps effectively tackle large-scale optimization challenges in general.

Kim, Seongmin↗

High-performance computing in water resources hydrodynamics

In this work, we present a vision of future water resources hydrodynamics codes that can fully utilize the strengths of modern high-performance computing. The advances to computing power, formerly driven by the improvement of central processing unit processors, now focus on parallel computing and, in particular, the use of graphics processing units (GPUs). However, this shift to a parallel framework requires refactoring the code to make efficient use of the data as well as changing even the nature of the algorithm that solves the system of equations. These concepts along with other features such as the precision for the computations, dry regions management, and input/output data are analyzed in this paper. A 2D multi-GPU flood code applied to a large-scale test case is used to corroborate our statements and ascertain the new challenges for the next-generation parallel water resources codes.

54 ENVIRONMENTAL SCIENCES↗

Charon User Manual (V.2.1) (Rev.01)

This manual gives usage information for the Charon semiconductor device simulator. Charon was developed to meet the modeling needs of Sandia National Laboratories and to improve on the capabilities of the commercial TCAD simulators; in particular, the additional capabilities are running very large simulations on parallel computers and modeling displacement damage and other radiation effects in significant detail. The parallel capabilities are based around the MPI interface which allows the code to be ported to a large number of parallel systems, including linux clusters and proprietary "big iron" systems found at the national laboratories and in large industrial settings.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Charon User Manual: v. 2.2 (revision1)

This manual gives usage information for the Charon semiconductor device simulator. Charon was developed to meet the modeling needs of Sandia National Laboratories and to improve on the capabilities of the commercial TCAD simulators; in particular, the additional capabilities are running very large simulations on parallel computers and modeling displacement damage and other radiation effects in significant detail. The parallel capabilities are based around the MPI interface which allows the code to be ported to a large number of parallel systems, including linux clusters and proprietary “big iron” systems found at the national laboratories and in large industrial settings.

42 ENGINEERING↗