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At least 1,315 records · Page 73

Performance Analysis of an Optimization Algorithm for Metamaterial Design on the Integrated High-Performance Computing and Quantum Systems

Optimizing metamaterials with complex geometries is a big challenge. Although an active learning algorithm, combining machine learning (ML), quantum computing, and optical simulation, has emerged as an efficient optimization tool, it still faces difficulties in optimizing complex structures that have potentially high performance. In this work, we comprehensively analyze the performance of an optimization algorithm for metamaterial design on the integrated HPC and quantum systems. We demonstrate significant time advantages through message-passing interface (MPI) parallelization on the high-performance computing (HPC) system showing approximately 54% faster ML tasks and 67 times faster optical simulation against serial workloads. Furthermore, we analyze the performance of a quantum algorithm designed for optimization, which runs with various quantum simulators on a local computer or HPC-quantum system. Results showcase ~24 times speedup when executing the optimization algorithm on the HPC-quantum hybrid system. This study paves a way to optimize complex metamaterials using the integrated HPC-quantum system.

Kim, Seongmin↗

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↗

CAST: Contraction Algorithm for Symmetric Tensors

Tensor contractions represent the most compute-intensive core kernels in ab initio computational quantum chemistry and nuclear physics. Symmetries in these tensor contractions makes them difficult to load balance and scale to large distributed systems. In this paper, we develop an efficient and scalable algorithm to contract symmetric tensors. We introduce a novel approach that avoids data redistribution in contracting symmetric tensors while also avoiding redundant storage and maintaining load balance. We present experimental results on two parallel supercomputers for several symmetric contractions that appear in the CCSD quantum chemistry method. We also present a novel approach to tensor redistribution that can take advantage of parallel hyperplanes when the initial distribution has replicated dimensions, and use collective broadcast when the final distribution has replicated dimensions, making the algorithm very efficient.

distributed memory↗

Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations

In this article, we focus on the communication costs of three symmetric matrix computations: (i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) (ii) adding the result of the multiplication of a matrix with the transpose of another matrix and the transpose of that result, known as a symmetric rank-2k update (SYR2K) (iii) performing matrix multiplication with a symmetric input matrix (SYMM). All three computations appear in the Level 3 Basic Linear Algebra Subroutines (BLAS) and have wide use in applications involving symmetric matrices. We establish communication lower bounds for these kernels using sequential and distributed-memory parallel computational models, and we show that our bounds are tight by presenting communication-optimal algorithms for each setting. Our lower bound proofs rely on applying a geometric inequality for symmetric computations and analytically solving constrained nonlinear optimization problems. As a result, the symmetric matrix and its corresponding computations are accessed and performed according to a triangular block partitioning scheme in the optimal algorithms.

Al Daas, Hussam [Rutherford Appleton Laboratory, D↗

Portable interactive visualization of large-scale simulations in geotechnical engineering using Unity3D

Development in large-scale geotechnical engineering simulation places tremendous demand for efficient visualization of such simulation data. This study presents a lightweight software tool, i.e. Geotechnical Interactive Visualization (GIV), as a solution to this challenge, which achieves efficient interactive visualization of large-scale simulations data in geotechnical engineering. Visualization data flow and algorithms specifically optimized for common geotechnical engineering applications are implemented in GIV. GIV can visualize geotechnical structure models with time-varying attributes attached to mesh with fixed topology, and also models with time-varying mesh topologies but no attributes attached, the two most common visualization tasks in geotechnical engineering. Furthermore, challenges for large-scale simulation data visualization, including parallel simulation data redundancy, massive data size, dynamic user interaction, and portability are overcome via specifically designed algorithms for simulation data preprocessing and optimized visualization modules using the powerful 3D rendering and interactive game engine Unity3D. Comparison of GIV with several widely used visualization tools for the visualization of large-scale idealized datasets and realistic geotechnical simulations highlights the visualization efficiency, smooth interactivity, and lightweight features of GIV.

42 ENGINEERING↗

Approaching the exa-scale: a real-world evaluation of rendering extremely large data sets

Extremely large scale analysis is becoming increasingly important as supercomputers and their simulations move from petascale to exascale. The lack of dedicated hardware acceleration for rendering on today's supercomputing platforms motivates our detailed evaluation of the possibility of interactive rendering on the supercomputer. In order to facilitate our understanding of rendering on the supercomputing platform, we focus on scalability of rendering algorithms and architecture envisioned for exascale datasets. To understand tradeoffs for dealing with extremely large datasets, we compare three different rendering algorithms for large polygonal data: software based ray tracing, software based rasterization and hardware accelerated rasterization. We present a case study of strong and weak scaling of rendering extremely large data on both GPU and CPU based parallel supercomputers using Para View, a parallel visualization tool. Wc use three different data sets: two synthetic and one from a scientific application. At an extreme scale, algorithmic rendering choices make a difference and should be considered while approaching exascale computing, visualization, and analysis. We find software based ray-tracing offers a viable approach for scalable rendering of the projected future massive data sizes.

97 MATHEMATICS AND COMPUTING↗

Parallel k-Means Clustering for Quantitative Ecoregion Delineation Using Large Data Sets

Identification of geographic ecoregions has long been of interest to environmental scientists and ecologists for identifying regions of similar ecological and environmental conditions. Such classifications are important for predicting suitable species ranges, for stratification of ecological samples, and to help prioritize habitat preservation and remediation efforts. Hargrove and Hoffman (1999, 2009) have developed geographical spatio-temporal clustering algorithms and codes and have successfully applied them to a variety of environmental science domains, including ecological regionalization; environmental monitoring network design; analysis of satellite-, airborne-, and ground-based remote sensing, and climate model-model and model-measurement intercomparison. With the advances in state-of-the-art satellite remote sensing and climate models, observations and model outputs are available at increasingly high spatial and temporal resolutions. Long time series of these high resolution datasets are extremely large in size and growing. Analysis and knowledge extraction from these large datasets are not just algorithmic and ecological problems, but also pose a complex computational problem. This paper focuses on the development of a massively parallel multivariate geographical spatio-temporal clustering code for analysis of very large datasets using tens of thousands processors on one of the fastest supercomputers in the world.

54 ENVIRONMENTAL SCIENCES↗

Software Synthesis for High Productivity Exascale Computing

Over the three years of our project, we accomplished three key milestones: We demonstrated how ideas from generative programming and software synthesis can help support the development of bulk-synchronous distributed memory kernels. These ideas are realized in a new language called MSL, a C-like language that combines synthesis features with high level notations for array manipulation and bulk-synchronous parallelism to simplify the semantic analysis required for synthesis. We also demonstrated that these high level notations map easily to low level C code and show that the performance of this generated code matches that of handwritten Fortran. Second, we introduced the idea of solver-aided domain-specific languages (SDSLs), which are an emerging class of computer-aided programming systems. SDSLs ease the construction of programs by automating tasks such as verification, debugging, synthesis, and non-deterministic execution. SDSLs are implemented by translating the DSL program into logical constraints. Next, we developed a symbolic virtual machine called Rosette, which simplifies the construction of such SDSLs and their compilers. We have used Rosette to build SynthCL, a subset of OpenCL that supports synthesis. Third, we developed novel numeric algorithms that move as little data as possible, either between levels of a memory hierarchy or between parallel processors over a network. We achieved progress in three aspects of this problem. First we determined lower bounds on communication. Second, we compared these lower bounds to widely used versions of these algorithms, and noted that these widely used algorithms usually communicate asymptotically more than is necessary. Third, we identified or invented new algorithms for most linear algebra problems that do attain these lower bounds, and demonstrated large speed-ups in theory and practice.

97 MATHEMATICS AND COMPUTING↗

Multigrid treatment of implicit continuum diffusion

Implicit treatment of diffusive terms of various differential orders common in continuum mechanics modeling, such as computational fluid dynamics, is investigated with spectral and multigrid algorithms in non-periodic 2D domains. In doubly periodic time dependent problems these terms are handled efficiently by spectral methods, but in non-periodic systems solved with distributed memory parallel computing and 2D domain decomposition, this efficiency is lost for a large number of processors. Here, we built and present here a multigrid algorithm for these types of problems that outperforms a spectral solution employing the highly optimized FFTW library. This solver is suitable for high performance computing and may be able to efficiently treat implicit diffusion of arbitrary order by introducing auxiliary equations of lower order. We test these solvers for fourth and sixth order diffusion with harmonic test functions as well as turbulent 2D magnetohydrodynamic simulations. It is also shown that an anisotropic operator without mixed-derivative terms improves model accuracy and speed, and we examine the impact that the various diffusion operators have on the energy, the enstrophy, and the qualitative aspect of a simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Massively parallel modeling and inversion of electrical resistivity tomography data using PFLOTRAN

Abstract. Electrical resistivity tomography (ERT) is a broadly accepted geophysical method for subsurface investigations. Interpretation of field ERT data usually requires the application of computationally intensive forward modeling and inversion algorithms. For large-scale ERT data, the efficiency of these algorithms depends on the robustness, accuracy, and scalability on high-performance computing resources. In this regard, we present a robust and highly scalable implementation of forward modeling and inversion algorithms for ERT data. The implementation is publicly available and developed within the framework of PFLOTRAN, an open-source, state-of-the-art massively parallel subsurface flow and transport simulation code. The forward modeling is based on a finite-volume discretization of the governing differential equations, and the inversion uses a Gauss–Newton optimization scheme. To evaluate the accuracy of the forward modeling, two examples are first presented by considering layered (1D) and 3D earth conductivity models. The computed numerical results show good agreement with the analytical solutions for the layered earth model and results from a well-established code for the 3D model. Inversion of ERT data, simulated for a 3D model, is then performed to demonstrate the inversion capability by recovering the conductivity of the model. To demonstrate the parallel performance of PFLOTRAN's ERT process model and inversion capabilities, large-scale scalability tests are performed by using up to 131 072 processes on a leadership class supercomputer. These tests are performed for the two most computationally intensive steps of the ERT inversion: forward modeling and Jacobian computation. For the forward modeling, we consider models with up to 122 ×106 degrees of freedom (DOFs) in the resulting system of linear equations and demonstrate that the code exhibits almost linear scalability on up to 10 000 DOFs per process. On the other hand, the code shows superlinear scalability for the Jacobian computation, mainly because all computations are fairly evenly distributed over each process with no parallel communication.

58 GEOSCIENCES↗

FTK: A Simplicial Spacetime Meshing Framework for Robust and Scalable Feature Tracking

In this work, we present the Feature Tracking Kit (FTK), a framework that simplifies, scales, and delivers various feature-tracking algorithms for scientific data. The key of FTK is our simplicial spacetime meshing scheme that generalizes both regular and unstructured spatial meshes to spacetime while tessellating spacetime mesh elements into simplices. The benefits of using simplicial spacetime meshes include (1) reducing ambiguity cases for feature extraction and tracking, (2) simplifying the handling of degeneracies using symbolic perturbations, and (3) enabling scalable and parallel processing. The use of simplicial spacetime meshing simplifies and improves the implementation of several feature-tracking algorithms for critical points, quantum vortices, and isosurfaces. As a software framework, FTK provides end users with VTK/ParaView filters, Python bindings, a command line interface, and programming interfaces for feature-tracking applications. We demonstrate use cases as well as scalability studies through both synthetic data and scientific applications including tokamak, fluid dynamics, and superconductivity simulations. We also conduct end-to-end performance studies on the Summit supercomputer. FTK is open sourced under the MIT license: https://github.com/hguo/ftk.

97 MATHEMATICS AND COMPUTING↗

TeaLeaf: A Mini-Application to Enable Design-Space Explorations for Iterative Sparse Linear Solvers

Iterative sparse linear solvers are an important class of algorithm in high performance computing, and form a crucial component of many scientific codes. As intra and inter node parallelism continues to increase rapidly, the design of new, scalable solvers which can target next generation architectures becomes increasingly important. In this work we present TeaLeaf, a recent mini-app constructed to explore design space choices for highly scalable solvers. We then use TeaLeaf to compare the standard CG algorithm with a Chebyshev Polynomially Preconditioned Conjugate Gradient (CPPCG) iterative sparse linear solver. CPPCG is a communication-avoiding algorithm, requiring less global communication than previous approaches. TeaLeaf includes support for many-core processors, such as GPUs and Xeon Phi, and we include strong-scaling results across a range of world-leading Petascale supercomputers, including Titan and Piz Daint.

97 MATHEMATICS AND COMPUTING↗

BSTC: A Novel Binarized-Soft-Tensor-Core Design for Accelerating Bit-Based Approximated Neural Nets

Binarized neural network (or BNN) promises tremendous performance improvement over traditional DNNs through simplified bit-level computation and significantly reduced memory access/storage cost. In addition, it has other advantages of low-cost, low-energy and high-robustness, showing great utilization potential in resources-constrained, volatile and latency-critical applications, which are critical for future HPC execution. However, the promised significant performance gain of BNN inference has never been fully demonstrated on general-purpose processors, particularly on GPUs, due to: (i) the challenge to extract and leverage sufficient fine-grained bit-level-parallelism to saturate GPU cores when batch is small; (ii) the fundamental design conflict between bit-based BNN algorithm and underlying word-based architecture; (iii) architecture \& performance unfriendly BNN network design. To address (i) and (ii), we propose binarized-soft-tensor-core as a software-hardware codesign approach to construct bit-manipulation capability for modern GPUs to effectively harvest the emerging bit-level-parallelism. To tackle (iii), we propose intra- and inter-layer fusion techniques so that the entire BNN inference can be packed into a single GPU kernel, to avoid high-cost frequent launching. Experiments demonstrate that our design can achieve over 1000x speedup for raw inference latency and 10x for inference throughput over the state-of-the-art full-precision simulated BNN inference for AlexNet on ImageNet.

Li, Ang↗

Conservative explicit local time-stepping schemes for the shallow water equations

Here we develop explicit local time-stepping (LTS) schemes with second and third order accuracy for the shallow water equations. The system is discretized in space by a C-grid staggering method, namely the TRiSK scheme adopted in MPAS-Ocean, a global ocean model with the capability of resolving multiple resolutions within a single simulation. The time integration is designed based on the strong stability preserving Runge–Kutta (SSP-RK) methods, but different time step sizes can be used in different regions of the domain through the coupling of coarse-fine time discretizations on the interface, and are only restricted by respective local CFL conditions. The proposed LTS schemes are of predictor–corrector type in which the predictors are constructed based on Taylor series expansions and SSP-RK stepping algorithms. The schemes preserve some important physical quantities in the discrete sense, such as exact conservation of the mass and potential vorticity and conservation of the total energy within time truncation errors. Moreover, they inherit the natural parallelism of the original explicit global time-stepping schemes. Extensive numerical tests are presented to illustrate the performance of the proposed algorithms.

58 GEOSCIENCES↗

A Visual Analytics Framework for Reviewing Streaming Performance Data

Understanding and tuning the performance of extreme-scale parallel computing systems demands a streaming approach due to the computational cost of applying offline algorithms to vast amounts of performance log data. Analyzing large streaming data is challenging because the rate of receiving data and limited time to comprehend data make it difficult for the analysts to sufficiently examine the data without missing important changes or patterns. To support streaming data analysis, we introduce a visual analytic framework comprising of three modules: data management, analysis, and interactive visualization. The data management module collects various computing and communication performance metrics from the monitored system using streaming data processing techniques and feeds the data to the other two modules. The analysis module automatically identifies important changes and patterns at the required latency. In particular, we introduce a set of online and progressive analysis methods for not only controlling the computational costs but also helping analysts better follow the critical aspects of the analysis results. Finally, the interactive visualization module provides the analysts with a coherent view of the changes and patterns in the continuously captured performance data. Through a multi-faceted case study on performance analysis of parallel discrete-event simulation, we demonstrate the effectiveness of our framework for identifying bottlenecks and locating outliers.

Human-centered computing↗

MetaStrider: Architectures for Scalable Memory-centric Reduction of Sparse Data Streams

Reduction is an operation performed on the values of two or more key-value pairs that share the same key. Reduction of sparse data streams finds application in a wide variety of domains such as data and graph analytics, cybersecurity, machine learning, and HPC applications. However, these applications exhibit low locality of reference, rendering traditional architectures and data representations inefficient. This article presents MetaStrider, a significant algorithmic and architectural enhancement to the state-of-the-art, SuperStrider. Furthermore, these enhancements enable a variety of parallel, memory-centric architectures that we propose, resulting in demonstrated performance that scales near-linearly with available memory-level parallelism.

97 MATHEMATICS AND COMPUTING↗

New Results on Communication- and Memory-Aware Load Balancing Model and Algorithms

While load balancing in distributed-memory computing has been well-studied, we present an innovative approach to this problem: a unified, reduced-order model that combines three key components to describe “work” in a distributed system: computation, communication, and memory. Our model enables an optimizer to explore complex tradeoffs in task placement, such as augmented parallelism, at the expense of data replication increasing memory usage. We propose a fully distributed, heuristic-based load balancing optimization algorithm, and demonstrate that it quickly finds close-to-optimal solutions. We formalize the complex optimization problem as a mixed-integer linear program, and compare it to our strategy. Finally, we show that when applied to an electromagnetics code, our approach obtains up to 2.3x speedups for the imbalanced execution.

97 MATHEMATICS AND COMPUTING↗