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At least 451 records · Page 25

Optimal Padding for the Two-Dimensional Fast Fourier Transform

One-dimensional Fast Fourier Transform (FFT) operations work fastest on grids whose size is divisible by a power of two. Because of this, padding grids (that are not already sized to a power of two) so that their size is the next highest power of two can speed up operations. While this works well for one-dimensional grids, it does not work well for two-dimensional grids. For a two-dimensional grid, there are certain pad sizes that work better than others. Therefore, the need exists to generalize a strategy for determining optimal pad sizes. There are three steps in the FFT algorithm. The first is to perform a one-dimensional transform on each row in the grid. The second step is to transpose the resulting matrix. The third step is to perform a one-dimensional transform on each row in the resulting grid. Steps one and three both benefit from padding the row to the next highest power of two, but the second step needs a novel approach. An algorithm was developed that struck a balance between optimizing the grid pad size with prime factors that are small (which are optimal for one-dimensional operations), and with prime factors that are large (which are optimal for two-dimensional operations). This algorithm optimizes based on average run times, and is not fine-tuned for any specific application. It increases the amount of times that processor-requested data is found in the set-associative processor cache. Cache retrievals are 4-10 times faster than conventional memory retrievals. The tested implementation of the algorithm resulted in faster execution times on all platforms tested, but with varying sized grids. This is because various computer architectures process commands differently. The test grid was 512 512. Using a 540 540 grid on a Pentium V processor, the code ran 30 percent faster. On a PowerPC, a 256x256 grid worked best. A Core2Duo computer preferred either a 1040x1040 (15 percent faster) or a 1008x1008 (30 percent faster) grid. There are many industries that can benefit from this algorithm, including optics, image-processing, signal-processing, and engineering applications.

Dean, Bruce H.↗

Enabling Highly Efficient Capsule Networks Processing Through A PIM-Based Architecture Design

In recent years, the CNNs have achieved great successes in the image processing tasks, e.g., image recognition and object detection. Unfortunately, traditional CNN's classication is found to be easily misled by increasingly complex image features due to the usage of pooling operations, hence unable to preserve accurate position and pose information of the objects. To address this challenge, a novel neural network structure called Capsule Network has been proposed, which introduces equivariance through capsules to signicantly enhance the learning ability for image segmentation and object detection. Due to its requirement of performing a high volume of matrix operations, CapsNets have been generally accelerated on modern GPU platforms that provide highly optimized software library for common deep learning tasks. However, based on our performance characterization on modern GPUs, CapsNets exhibit low effciency due to the special program and execution features of their routing procedure, including massive unshareable intermediate variables and intensive syn- chronizations, which are very dicult to optimize at software level. To address these challenges, we propose a hybrid computing architecture design named PIM-CapsNet. It preserves GPU's on-chip computing capability for accelerating CNN types of layers in CapsNet, while pipelining with an off-chip in-memory acceleration solution that effectively tackles routing procedure's ineffciency by leveraging the processing-in-memory capability of today's 3D stacked memory. Using routing procedure's inherent parallellization feature, our design enables hierarchical improvements on CapsNet inference effciency through minimizing data movement and maximizing parallel processing in memory. Evaluation results demonstrate that our proposed design can achieve substantial improvement on both performance and energy savings for CapsNet inference, with almost zero accuracy loss. The results also suggest good performance scalability in optimizing the routing procedure with increasing network size.

Zhang, Xingyao↗

Distributed merge trees

Improved simulations and sensors are producing datasets whose increasing complexity exhausts our ability to visualize and comprehend them directly. To cope with this problem, we can detect and extract significant features in the data and use them as the basis for subsequent analysis. Topological methods are valuable in this context because they provide robust and general feature definitions. As the growth of serial computational power has stalled, data analysis is becoming increasingly dependent on massively parallel machines. To satisfy the computational demand created by complex datasets, algorithms need to effectively utilize these computer architectures. The main strength of topological methods, their emphasis on global information, turns into an obstacle during parallelization. We present two approaches to alleviate this problem. We develop a distributed representation of the merge tree that avoids computing the global tree on a single processor and lets us parallelize subsequent queries. To account for the increasing number of cores per processor, we develop a new data structure that lets us take advantage of multiple shared-memory cores to parallelize the work on a single node. Finally, we present experiments that illustrate the strengths of our approach as well as help identify future challenges. Copyright © 2013 ACM 978-1-4503-1922-5/13/ 02...$15.00.

Morozov, D↗

Basic Energy Sciences Exascale Requirements Review. An Office of Science review sponsored jointly by Advanced Scientific Computing Research and Basic Energy Sciences, November 3-5, 2015, Rockville, Maryland

Computers have revolutionized every aspect of our lives. Yet in science, the most tantalizing applications of computing lie just beyond our reach. The current quest to build an exascale computer with one thousand times the capability of today’s fastest machines (and more than a million times that of a laptop) will take researchers over the next horizon. The field of materials, chemical reactions, and compounds is inherently complex. Imagine millions of new materials with new functionalities waiting to be discovered — while researchers also seek to extend those materials that are known to a dizzying number of new forms. We could translate massive amounts of data from high precision experiments into new understanding through data mining and analysis. We could have at our disposal the ability to predict the properties of these materials, to follow their transformations during reactions on an atom-by-atom basis, and to discover completely new chemical pathways or physical states of matter. Extending these predictions from the nanoscale to the mesoscale, from the ultrafast world of reactions to long-time simulations to predict the lifetime performance of materials, and to the discovery of new materials and processes will have a profound impact on energy technology. In addition, discovery of new materials is vital to move computing beyond Moore’s law. To realize this vision, more than hardware is needed. New algorithms to take advantage of the increase in computing power, new programming paradigms, and new ways of mining massive data sets are needed as well. This report summarizes the opportunities and the requisite computing ecosystem needed to realize the potential before us. In addition to pursuing new and more complete physical models and theoretical frameworks, this review found that the following broadly grouped areas relevant to the U.S. Department of Energy (DOE) Office of Advanced Scientific Computing Research (ASCR) would directly affect the Basic Energy Sciences (BES) mission need. Simulation, visualization, and data analysis are crucial for advances in energy science and technology. Revolutionary mathematical, software, and algorithm developments are required in all areas of BES science to take advantage of exascale computing architectures and to meet data analysis, management, and workflow needs. In partnership with ASCR, BES has an emerging and pressing need to develop new and disruptive capabilities in data science. More capable and larger high-performance computing (HPC) and data ecosystems are required to support priority research in BES. Continued success in BES research requires developing the next-generation workforce through education and training and by providing sustained career opportunities.

97 MATHEMATICS AND COMPUTING↗

A parallel evolutionary multiple-try metropolis Markov chain Monte Carlo algorithm for sampling spatial partitions

We develop an Evolutionary Markov Chain Monte Carlo (EMCMC) algorithm for sampling spatial partitions that lie within a large, complex, and constrained spatial state space. Our algorithm combines the advantages of evolutionary algorithms (EAs) as optimization heuristics for state space traversal and the theoretical convergence properties of Markov Chain Monte Carlo algorithms for sampling from unknown distributions. Local optimality information that is identified via a directed search by our optimization heuristic is used to adaptively update a Markov chain in a promising direction within the framework of a Multiple-Try Metropolis Markov Chain model that incorporates a generalized Metropolis-Hastings ratio. We further expand the reach of our EMCMC algorithm by harnessing the computational power afforded by massively parallel computing architecture through the integration of a parallel EA framework that guides Markov chains running in parallel.

97 MATHEMATICS AND COMPUTING↗

Si/SiGe QuBus for single electron information-processing devices with memory and micron-scale connectivity function

The connectivity within single carrier information-processing devices requires transport and storage of single charge quanta. Single electrons have been adiabatically transported while confined to a moving quantum dot in short, all-electrical Si/SiGe shuttle device, called quantum bus (QuBus). Here we show a QuBus spanning a length of 10 μm and operated by only six simply-tunable voltage pulses. We introduce a characterization method, called shuttle-tomography, to benchmark the potential imperfections and local shuttle-fidelity of the QuBus. The fidelity of the single-electron shuttle across the full device and back (a total distance of 19 μm) is (99.7 ± 0.3) %. Using the QuBus, we position and detect up to 34 electrons and initialize a register of 34 quantum dots with arbitrarily chosen patterns of zero and single-electrons. The simple operation signals, compatibility with industry fabrication and low spin-environment-interaction in 28 Si/SiGe, promises long-range spin-conserving transport of spin qubits for quantum connectivity in quantum computing architectures.

97 MATHEMATICS AND COMPUTING↗

Modern Computational Techniques for the HMMER Sequence Analysis

This paper focuses on the latest research and critical reviews on modern computing architectures, software and hardware accelerated algorithms for bioinformatics data analysis with an emphasis on one of the most important sequence analysis applications—hidden Markov models (HMM). We show the detailed performance comparison of sequence analysis tools on various computing platforms recently developed in the bioinformatics society. The characteristics of the sequence analysis, such as data and compute-intensive natures, make it very attractive to optimize and parallelize by using both traditional software approach and innovated hardware acceleration technologies.

59 BASIC BIOLOGICAL SCIENCES↗

An introduction to the Gilgamesh PIM architecture

The focus of the work conducted is on a class of structures made possible by the merger of logic and memory. Processing In Memory (PIM) extends the design space much farther by closely associating the logic with the memory interface to realize innovative structures never previously possible and thus exposing entirely new opportunities for computer architecture.

Gilgamesh PIM CMOS↗

Exascale computing and big data

Scientific discovery and engineering innovation requires unifying traditionally separated high-performance computing and big data analytics. The tools and cultures of high-performance computing and big data analytics have diverged, to the detriment of both; unification is essential to address a spectrum of major research domains. The challenges of scale tax our ability to transmit data, compute complicated functions on that data, or store a substantial part of it; new approaches are required to meet these challenges. Finally, the international nature of science demands further development of advanced computer architectures and global standards for processing data, even as international competition complicates the openness of the scientific process.

97 MATHEMATICS AND COMPUTING↗

Parallel Programming in MCNP6

Monte Carlo N-Particle (MCNP)1 is a general-purpose Monte Carlo particle transport code developed by Los Alamos National Laboratory (LANL). To efficiently handle long simulations, MCNP version 6 (MCNP6) supports parallel execution using two primary programming models: • Shared-memory task-based threading using OpenMP (Open Multi-Processing), and • Distributed-memory calculations using MPI (Message Passing Interface). The OpenMP and MPI programming models enable MCNP6 to scale from desktop systems to high-performance computing (HPC) clusters, allowing users to run MCNP in one of three parallel modes: • OpenMP-only, • MPI-only, and • Hybrid (MPI + OpenMP). The choice of parallelization mode depends on the underlying computer architecture and the characteristics of the simulation problem.

97 MATHEMATICS AND COMPUTING↗

Sparse Matrix-Matrix Multiplication on Multilevel Memory Architectures: Algorithms and Experiments

Architectures with multiple classes of memory media are becoming a common part of mainstream supercomputer deployments. So called multi-level memories offer differing characteristics for each memory component including variation in bandwidth, latency and capacity. This paper investigates the performance of sparse matrix multiplication kernels on two leading highperformance computing architectures — Intel's Knights Landing processor and NVIDIA's Pascal GPU. We describe a data placement method and a chunking-based algorithm for our kernels that exploits the existence of the multiple memory spaces in each hardware platform. We evaluate the performance of these methods w.r.t. standard algorithms using the auto-caching mechanisms Our results show that standard algorithms that exploit cache reuse performed as well as multi-memory-aware algorithms for architectures such as Ki\iLs where the memory subsystems have similar latencies. However, for architectures such as GPUS where memory subsystems differ significantly in both bandwidth and latency, multi-memory-aware methods are crucial for good performance. In addition, our new approaches permit the user to run problems that require larger capacities than the fastest memory of each compute node without depending on the software-managed cache mechanisms.

97 MATHEMATICS AND COMPUTING↗

Faster than Real-Time Dynamic Simulation for Large-Size Power System with Detailed Dynamic Models using High-Performance Computing Platform

This paper presents a faster-than-real-time dynamic simulation software package that is designed for large-size power system dynamic simulation. It was developed on the GridPACKTM high-performance computing (HPC) framework. The key features of the developed software package include (1) faster-than-real-time dynamic simulation for a WECC system (17,000 buses) with different types of detailed generator, controller, and relay dynamic models, (2) a decoupled parallel dynamic simulation algorithm with optimized computation architecture to better leverage HPC resources and technologies, (3) options for HPC-based linear and iterative solvers, (4) hidden HPC details, such as data communication and distribution, to enable development centered on mathematical models and algorithms rather than on computational details for power system researchers, and (5) easy integration of new dynamic models and related algorithms into the software package.

Huang, Renke↗

A Parallel-in-Time Multigrid Approach to Constrained Optimization

Valuable computer simulations such as weather prediction, traffic flow, and resource allocation are time dependent problems. One such example is the viscous Burgers’ equation which can model various systems such as fluids and traffic flow. Further, many of these models require optimization routines to meet the needs of many businesses. Unfortunately, traditional sequential-in-time algorithms have become bottlenecks in solution model generation. This is because computer architectures have begun to rely more and more on concurrency (parallel processing) as opposed to processor power to provide greater performance. To avoid this bottleneck, many researchers use parallelization methods to take advantage of the increasing number of processors in computers. This approach allows for variables in a problem to be solved for simultaneously. As such, parallelization is a crucial requirement to achieve high-performance computing.

97 MATHEMATICS AND COMPUTING↗

Vectorization of a particle simulation method for hypersonic rarefied flow

An efficient particle simulation technique for hypersonic rarefied flows is presented at an algorithmic and implementation level. The implementation is for a vector computer architecture, specifically the Cray-2. The method models an ideal diatomic Maxwell molecule with three translational and two rotational degrees of freedom. Algorithms are designed specifically for compatibility with fine grain parallelism by reducing the number of data dependencies in the computation. By insisting on this compatibility, the method is capable of performing simulation on a much larger scale than previously possible. A two-dimensional simulation of supersonic flow over a wedge is carried out for the near-continuum limit where the gas is in equilibrium and the ideal solution can be used as a check on the accuracy of the gas model employed in the method. Also, a three-dimensional, Mach 8, rarefied flow about a finite-span flat plate at a 45 degree angle of attack was simulated. It utilized over 10 to the 7th particles carried through 400 discrete time steps in less than one hour of Cray-2 CPU time. This problem was chosen to exhibit the capability of the method in handling a large number of particles and a true three-dimensional geometry.

Mcdonald, Jeffrey D.↗

GPU Acceleration of the Locally Selfconsistent Multiple Scattering Code for First Principles Calculation of the Ground State and Statistical Physics of Materials

The Locally Self-consistent Multiple Scattering (LSMS) code solves the first principles Density Functional theory Kohn-Sham equation for a wide range of materials with a special focus on metals, alloys and metallic nano-structures. It has traditionally exhibited near perfect scalability on massively parallel high performance computer architectures. We present our efforts to exploit GPUs to accelerate the LSMS code to enable first principles calculations of O(100,000) atoms and statistical physics sampling of finite temperature properties. Using the Cray XK7 system Titan at the Oak Ridge Leadership Computing Facility we achieve a sustained performance of 14.5PFlop/s and a speedup of 8.6 compared to the CPU only code.

Eisenbach, Markus↗

Educating HPC Users in the use of advanced computing technology

We examine a multi-modal approach to educating and training users of an advanced computing technology testbed at the Institute for Advanced Computational Science at Stony Brook University. Ookami provides researchers worldwide with access to 176 Fujitsu A64FX compute nodes, this being the same processor technology powering the Japanese Fugaku supercomputer, the fastest computer in the world since June 2020. However, achieving high-performance on this Arm-based, leadership computing technology requires that users be familiar with details of computer architecture, performance analysis and modeling, and high-performance programming models that are commonly omitted in introductory programming courses. Indeed, regardless of their seniority, many of the testbed users are surprisingly unfamiliar with basic concepts such as vectorization, pipelining, latency/bandwidth, roofline models, computing energy/power, threads, and non-uniform memory access. These same concepts also pervade mainstream x86 technologies, so this is of widespread concern. Due to the national/global nature of our user community that is also very diverse in both discipline and experience, the inability to offer formal classes, and our experience that most people do not tend to read online documentation or training materials in sufficient depth, we have consciously employed multiple approaches that heavily emphasize (online) personal interactions and transfer of skills. Online documentation has been organized around best-practices and FAQs; twice-weekly hackathons and office hours via Zoom enable deep dives by both the team and the user community with multiple broad benefits; a Slack channel provides both real time and archived answers and discussions; and workshops, training and webinars target community needs as they arise. Furthermore, the perspective that these tools are being used in an educational setting rather than just for project communication makes them more effective and contributes to community success.

A64FX↗

Recovery Act: Advanced Interaction, Computation, and Visualization Tools for Sustainable Building Design

Current building energy simulation technology requires excessive labor, time and expertise to create building energy models, excessive computational time for accurate simulations and difficulties with the interpretation of the results. These deficiencies can be ameliorated using modern graphical user interfaces and algorithms which take advantage of modern computer architectures and display capabilities. To prove this hypothesis, we developed an experimental test bed for building energy simulation. This novel test bed environment offers an easy-to-use interactive graphical interface, provides access to innovative simulation modules that run at accelerated computational speeds, and presents new graphics visualization methods to interpret simulation results. Our system offers the promise of dramatic ease of use in comparison with currently available building energy simulation tools. Its modular structure makes it suitable for early stage building design, as a research platform for the investigation of new simulation methods, and as a tool for teaching concepts of sustainable design. Improvements in the accuracy and execution speed of many of the simulation modules are based on the modification of advanced computer graphics rendering algorithms. Significant performance improvements are demonstrated in several computationally expensive energy simulation modules. The incorporation of these modern graphical techniques should advance the state of the art in the domain of whole building energy analysis and building performance simulation, particularly at the conceptual design stage when decisions have the greatest impact. More importantly, these better simulation tools will enable the transition from prescriptive to performative energy codes, resulting in better, more efficient designs for our future built environment.

99 GENERAL AND MISCELLANEOUS↗