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Advances in patch-based adaptive mesh refinement scalability

JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING 2016年 89卷 65-84页

作者： Gunney, Brian T. N. Anderson, Robert W. Lawrence Livermore Natl Lab Ctr Appl Sci Comp L-561 Livermore CA 94550 USA

Patch-based structured adaptive mesh refinement (SAMR) is widely used for high-resolution simulations. Combined with modern supercomputers, it could provide simulations of unprecedented size and resolution. A persistent challenge for this combination has been managing dynamically adaptive meshes on more and more MPI tasks. The distributed mesh management scheme in SAMRAI has made some progress SAMR scalability, but early algorithms still had trouble scaling past the regime of 105 MPI tasks. This work provides two critical SAMR regridding algorithms, which are integrated into that scheme to ensure efficiency of the whole. The clustering algorithm is an extension of the tile-clustering approach, making it more flexible and efficient in both clustering and parallelism. The partitioner is a new algorithm designed to prevent the network congestion experienced by its predecessor. We evaluated performance using weak- and strong-scaling benchmarks designed to be difficult for dynamic adaptivity. Results show good scaling on up to 1.5M cores and 2M MPI tasks. Detailed timing diagnostics suggest scaling would continue well past that. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Adaptive mesh refinement Dynamic adaptivity scalable algorithm Partitioning algorithm Clustering algorithm Data locality

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Scaling Probabilistic Tensor Canonical Polyadic Decomposition to Massive Data

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2018年第21期66卷 5534-5548页

作者： Cheng, Lei Wu, Yik-Chung Poor, H. Vincent Univ Hong Kong Dept Elect & Elect Engn Hong Kong Hong Kong Peoples R China Princeton Univ Dept Elect Engn Princeton NJ 08544 USA

Tensor canonical polyadic decomposition (CPD) has recently emerged as a promising mathematical tool in multidimensional data analytics. Traditionally, the alternating least-squares method is the workhorse for tensor CPD, but it requires knowing the tensor rank. A probabilistic approach overcomes this challenge by incorporating the tensor rank determination as an integral part of the CPD process. However, the current probabilistic tensor CPD method is derived for batch-mode operation, meaning that it needs to process the whole dataset at the same time. Obviously, this is no longer suitable for large datasets. To enable tensor CPD in a massive data paradigm, in this paper, the idea of stochastic optimization is introduced into the probabilistic tensor CPD, rendering a scalable algorithm that only processes mini-batch data at a time. Numerical studies on synthetic data and real-world applications are presented to demonstrate that the proposed scalable tensor CPD algorithm performs almost identically to the corresponding batch-mode algorithm while saving a significant amount of computation time.

关键词： Large-scale tensor decomposition scalable algorithm variational inference automatic rank determination

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A scalable Space-Time Domain Decomposition Approach for Solving Large Scale Nonlinear Regularized Inverse Ill Posed Problems in 4D Variational Data Assimilation

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JOURNAL OF SCIENTIFIC COMPUTING 2022年第2期91卷 1-31页

作者： D'Amore, Luisa Constantinescu, Emil Carracciuolo, Luisa Univ Naples Federico II Naples Italy Argonne Natl Lab Math & Comp Sci Div Lemont IL USA Ist & Polimeri Compositi & Biomat CNR IPCB CNR Naples Italy

We address the development of innovative algorithms designed to solve the strong-constraint Four Dimensional Variational Data Assimilation (4DVar DA) problems in large scale applications. We present a space-time decomposition approach which employs the whole domain decomposition, i.e. both along the spacial and temporal direction in the overlapping case, and the partitioning of both the solution and the operator. Starting from the global functional defined on the entire domain, we get to a sort of regularized local functionals on the set of sub domains providing the order reduction of both the predictive and the Data Assimilation models. The algorithm convergence is developed. Performance in terms of reduction of time complexity and algorithmic scalability is discussed on the Shallow Water Equations on the sphere. The number of state variables in the model, the number of observations in an assimilation cycle, as well as numerical parameters as the discretization step in time and in space domain are defined on the basis of discretization grid used by data available at repository Ocean Synthesis/Reanalysis Directory of Hamburg University.

关键词： Data assimilation Space and time decomposition scalable algorithm Inverse problems Nonlinear least squares problems

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scalable SYMMETRIC TUCKER TENSOR DECOMPOSITION

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2024年第4期45卷 1746-1781页

作者： Jin, Ruhui Kileel, Joe Kolda, Tamara g. Ward, Rachel Univ Texas Austin Dept Math Austin TX 78712 USA MathSci Ai Dublin CA 94568 USA

We study the best low-rank Tucker decomposition of symmetric tensors. The motivating application is decomposing higher-order multivariate moments. Moment tensors have special structure and are important to various data science problems. We advocate for a projected graas computation schemes. Most importantly, we develop scalable adaptations of the basic PGD and HOEVD methods to decompose sample moment tensors. With the help of implicit and streaming techniques, we evade the overhead cost of building and storing the moment tensor. Such reductions make computing the Tucker decomposition realizable for large data instances in high dimensions. Numerical experiments demonstrate the efficiency of the algorithms and the applicability of moment tensor decompositions to real-world datasets. Finally we study the convergence on the Grassmannian manifold and prove that the update sequence derived by the PGD solver achieves first- and second-order criticality.

关键词： symmetric tensor Tucker decomposition scalable algorithm

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An Accurate and Efficient Large-Scale Regression Method Through Best Friend Clustering

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2022年第11期33卷 3129-3140页

作者： Li, Kun Yuan, Liang Zhang, Yunquan Chen, Gongwei Chinese Acad Sci Inst Comp Technol State Key Lab Comp Architecture Beijing 100190 Peoples R China Univ Chinese Acad Sci UCAS Sch Comp Sci & Technol Beijing 100190 Peoples R China Chinese Acad Sci Inst Comp Technol Key Lab Intelligent Informat Proc Beijing 100190 Peoples R China

As the data size in Machine Learning fields grows exponentially, it is inevitable to accelerate the computation by utilizing the ever-growing large number of available cores provided by high-performance computing hardware. However, existing parallel methods for clustering or regression often suffer from problems of low accuracy, slow convergence, and complex hyperparameter-tuning. Furthermore, the parallel efficiency is usually difficult to improve while striking a balance between preserving model properties and partitioning computing workloads on distributed systems. In this article, we propose a novel and simple data structure capturing the most important information among data samples. It has several advantageous properties supporting a hierarchical clustering strategy that contains well-defined metrics for determining optimal hierarchy, balanced partition for maintaining the clustering property, and efficient parallelization for accelerating computation phases. Then we combine the clustering with regression techniques as a parallel library and utilize a hybrid structure of data and model parallelism to make predictions. Experiments illustrate that our library obtains remarkable performance on convergence, accuracy, and scalability.

关键词： Clustering algorithms Training Mathematical models Computational modeling Libraries Kernel Support vector machines Distributed machine learning scalable algorithm large-scale clustering parallel regression

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L₂ vector median filters on arrays with reconfigurable optical buses

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2001年第12期12卷 1281-1292页

作者： Wu, CH Horng, SJ Chinese Naval Acad Dept Informat Management Kaohsiung Taiwan Natl Taiwan Univ Sci & Technol Dept Elect Engn Taipei Taiwan

In spite of their good filtering characteristics for vector-valued image processing, the usability of vector median filters is limited by their high computational complexity. Given an N x N image and a W x W window, the computational complexity of vector median filter is O((WN2)-N-4). In this paper, we design three fast and efficient parallel algorithms for vector median filtering based on the 2-norm (L-2) on the arrays with reconfigurable optical buses (AROB). For 1 less than or equal to p less than or equal to W less than or equal to q less than or equal to N, our algorithms run in O(W-4 log W/p(4)), O((WN2)-N-4/p(4)p(2) log W) and W(1) times using p(4)N(2)/log W, p(4)q(2)/log W, and W(4)N(2)log N processors, respectively. In the sense of the product of time and the number of processors used, the first two results are cost optimal and the last one is time optimal.

关键词： parallel algorithm scalable algorithm vector median filter nonlinear filter image (signal) processing reconfigurable optical bus system

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SGMiner: A Fast and scalable GPU-Based Frequent Pattern Miner on SSDs

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IEEE ACCESS 2022年 10卷 62502-62519页

作者： Chon, Kang-Wook Yi, Eunjeong Kim, Min-Soo Korea Inst Sci & Technol Informat Div Natl Supercomp Daejeon South Korea Daegu Gyeongbuk Inst Sci & Technol Dept Informat & Commun Engn Daegu South Korea Korea Adv Inst Sci & Technol Sch Comp Daejeon South Korea

Frequent itemset mining is extensively employed as an essential data mining technique. Nevertheless, as the data size grows, the applicability of this method decreases owing to the relatively poor performance of the existing methods. Though numerous efficient sequential frequent itemset mining methods have been developed, the performance that can be achieved is clearly limited by the fact that they exploit only one thread. To overcome these limitations, a number of parallel methods using multi-core central processing units (CPUs), multiple machines or many-core graphic processing units (GPU) have been proposed. However, these methods are relatively slow in performance and have low scalability, mainly owing to large memory requirements for intermediate data, significant disk I/Os, and heavy computation. In this study, to resolve the aforementioned problems, we propose SGMiner, which is a new, fast, and scalable GPU-and disk-based method on a single machine equipped with multiple graphic processing units (GPUs) and multiple solid-state drives (SSDs) for extracting frequent patterns. It is based on an algorithm similar to the Apriori algorithm and neither has intermediate data nor large disk I/O overheads owing to its exploitation of SSDs. Moreover, we propose storing transaction databases, namely bitmap transaction chunks, in SSDs, streaming the chunks to GPU device memory via the main memory with reduced I/O overhead, and performing fast support counting with GPUs based on the chunks. In addition, when exploiting multiple GPUs and SSDs, it proposes a concept of replicating bitmap transaction chunks stored in SSDs to GPUs in a streaming fashion. This could allow an almost equal workload to be distributed evenly across multiple GPUs with reduced I/O overheads. The experiments we conducted demonstrate that SGMiner outperforms the existing methods in terms of scalability and performance with enhanced robustness.

关键词： Big data frequent pattern mining parallel algorithm GPUs scalable algorithm disk-based algorithm

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Network-Flow-Based Efficient Vehicle Dispatch for City-Scale Ride-Hailing Systems

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2022年第6期23卷 5526-5538页

作者： Xu, Yuhang Wang, Wanyuan Xiong, Guangwei Liu, Xiang Wu, Weiwei Liu, Kai Southeast Univ Sch Comp Sci & Engn Nanjing 211189 Peoples R China Chongqing Univ Sch Comp Sci Chongqing 400030 Peoples R China

Ride-hailing systems (RHSs) provide passengers with convenient and flexible mobility services, have played an important role in modern urban transportation. With the limited vehicles, RHSs wish to optimize the dispatch of vehicles to requests with the objective of serving as many requests as possible. To address such a city-scale vehicle dispatch problem with thousands of vehicles and requests in each epoch, existing algorithms always take a tradeoff between effectiveness (i.e., real-time) and efficiency (i.e., service rate), such as ignoring future demands to guarantee real-time or solving a complex combinatorial optimization to improve service rate. To guarantee the service rate in a real-time fashion, this paper proposes two novel network flow-based vehicle dispatch algorithms. A network flow-based algorithm (NFBA) is provided to deal with offline scenarios. By constructing the vehicle-shareability network, a min-cost flow is built to find the optimal dispatch of vehicles to requests. To improve the request service rate in real-time, an efficient multi-sample multi-network flow-based algorithm (MNFBA) is proposed for the online scenarios. Each min-cost flow is utilized for a sample of future requests, and online vehicle dispatch policy is averaged over these flows. Extensive simulations based on real-world trip datasets in New York City are conducted. The experimental results show that compared to the benchmarks, our proposed algorithm can generate the dispatch of vehicles to requests within seconds, but can greatly increase the daily request service rate.

关键词： Real-time systems Optimization Vehicles Prediction algorithms Heuristic algorithms Dispatching Demand forecasting Urban computing ride-hailing systems network flow scalable algorithm

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A Hierarchical Space-Time Spectral Element and Moment-of-Fluid Method for Improved Capturing of Vortical Structures in Incompressible Multi-phase/Multi-material Flows

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JOURNAL OF SCIENTIFIC COMPUTING 2019年第3期81卷 1527-1566页

作者： Pei, Chaoxu Vahab, Mehdi Sussman, Mark Hussaini, M. Yousuff Florida State Univ Dept Math Tallahassee FL 32306 USA FAMU FSU Coll Engn Dept Mech Engn Tallahassee FL 32310 USA

A novel block structured adaptive space-time spectral element and moment-of-fluid method is described for computing solutions to incompressible multi-phase/multi-material flows. The new method implements a space-time spectrally accurate method in the bulk regions of a multi-phase/multi-material flow and implements the cell integrated semi-Lagrangian moment-of-fluid method in the vicinity of mixed material computational cells. In the new method, the space-time order can be prescribed to be 2 <= p(l)((x)) <= 16 (space) and 2 <= p((t)) <= 16 (time) respectively. l represents the adaptive mesh refinement level. Regardless of the space-time order, only one ghost layer of cells is communicated between neighboring grid patches that are on different compute nodes or different adaptive levels l. The new method is first tested on incompressible vortical flow benchmark tests, then the new method is tested on the following incompressible multi-phase/multi-material problems: (i) vortex shedding past a tilted cone and (ii) atomization and spray of a liquid jet in a gas cross-flow.

关键词： Space-time Multi-phase flow Multi-material flow Spectral accuracy Adaptive mesh refinement scalable algorithm

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Dynamic simulation of multibody systems using a new state-time methodology

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MULTIBODY SYSTEM DYNAMICS 2005年第1期14卷 61-80页

作者： Anderson, KS Oghbaei, M Rensselaer Polytech Inst Dept Mech Aerosp & Nucl Engn Troy NY 12180 USA

This paper presents a new methodology demonstrating the feasibility and advantages of a state-time formulation for dynamic simulation of complex multibody systems which shows potential advantages for exploiting massively parallel computing resources. This formulation allows time to be discretized and parameterized so that it can be treated as a variable in a manner similar to the system state variables. As a consequence of such a state-time discretization scheme, the system of governing equations yields to a set of loosely coupled linear-quadratic algebraic equations that is well-suited in structure for some families of nonlinear algebraic equations solvers. The goal of this work is to develop efficient multibody dynamics algorithm that is extremely scalable and better able to fully exploit anticipated immensely parallel computing machines (tera flop, peta flop and beyond) made available to it.

关键词： multibody dynamics state-time formulation scalable algorithm parallel computing

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