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At least 469 records · Page 26

Algorithmic Patterns for $$\mathcal {H}$$-Matrices on Many-Core Processors

In this work, we consider the reformulation of hierarchical ( \(\mathcal {H}\) ) matrix algorithms for many-core processors with a model implementation on graphics processing units (GPUs). \(\mathcal {H}\) matrices approximate specific dense matrices, e.g., from discretized integral equations or kernel ridge regression, leading to log-linear time complexity in dense matrix–vector products. The parallelization of \(\mathcal {H}\) matrix operations on many-core processors is difficult due to the complex nature of the underlying algorithms. While previous algorithmic advances for many-core hardware focused on accelerating existing \(\mathcal {H}\) matrix CPU implementations by many-core processors, we here aim at totally relying on that processor type. As main contribution, we introduce the necessary parallel algorithmic patterns allowing to map the full \(\mathcal {H}\) matrix construction and the fast matrix–vector product to many-core hardware. In this work, crucial ingredients are space filling curves, parallel tree traversal and batching of linear algebra operations. The resulting model GPU implementation hmglib is the, to the best of the authors knowledge, first entirely GPU-based Open Source \(\mathcal {H}\) matrix library of this kind. We investigate application examples as present in kernel ridge regression, Gaussian Process Regression and kernel-based interpolation. In this context, an in-depth performance analysis and a comparative performance study against a standard multi-core CPU \(\mathcal {H}\) matrix library highlights profound speedups of our many-core parallel approach.

97 MATHEMATICS AND COMPUTING↗

A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma

Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. In this article, the non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. The finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. The collision operator's good weak and strong scaling behavior are shown.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Lifeline-Based Approach for Work Requesting and Parallel Particle Advection

Particle advection, a fundamental building block for many flow visualization algorithms, is very difficult to parallelize efficiently. That said, work requesting is a promising technique to improve parallel performance for particle advection. With this work, we introduce a new work requesting-based method which uses the Lifeline scheduling method. To evaluate the impact of this new algorithm, we ran 92 experiments, running at concurrencies as high as 8192 cores, data sets as large as 17 billion cells, and as many as 16 million particles, comparing against other work requesting scheduling methods. Overall, our results show that Lifeline has significantly less idle time than other approaches, since it reduces the number of failed attempts to request work.

Pugmire, Dave↗

A high-speed, high-efficiency phase controller for coherent beam combining based on SPGD algorithm

A phase controller for coherent beam combining (CBC) of fibre lasers has been designed and manufactured based on a stochastic parallel gradient descent (SPGD) algorithm and a field programmable gate array (FPGA). The theoretical analysis shows that the iteration rate is higher than 1.9 MHz, and the average compensation bandwidth of CBC for 5 or 20 channels is 50 kHz or 12.5 kHz, respectively. The tests show that the phase controller ensures reliable phase locking of lasers: When the phases of five lasers are locked by the improved control strategy with a variable gain, the energy encircled in the target is increased by 23 times than that in the single output, the phase control accuracy is better than λ/20, and the combining efficiency is 92%. (control of laser radiation parameters)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A non-intrusive parallel-in-time adjoint solver with the XBraid library

In this paper, an adjoint solver for the multigrid-in-time software library XBraid is presented. XBraid provides a non-intrusive approach for simulating unsteady dynamics on multiple processors while parallelizing not only in space but also in the time domain (XBraid: Parallel multigrid in time, http://llnl.gov/casc/xbraid). It applies an iterative multigrid reduction in time algorithm to existing spatially parallel classical time propagators and computes the unsteady solution parallel in time. Techniques from Automatic Differentiation are used to develop a consistent discrete adjoint solver which provides sensitivity information of output quantities with respect to design parameter changes. The adjoint code runs backwards through the primal XBraid actions and accumulates gradient information parallel in time. It is highly non-intrusive as existing adjoint time propagators can easily be integrated through the adjoint interface. The adjoint code is validated on advection-dominated flow with periodic upstream boundary condition. We report it provides similar strong scaling results as the primal XBraid solver and offers great potential for speeding up the overall computational costs for sensitivity analysis using multiple processors.

97 MATHEMATICS AND COMPUTING↗

A Scalable Interior‐Point Gauss–Newton Method for PDE‐Constrained Optimization With Bound Constraints

Here, we present a scalable approach to solve a class of partial differential equation (PDE)‐constrained optimization problems with bound constraints. This approach utilizes a robust full‐space interior‐point (IP)‐Gauss–Newton optimization method. To cope with the poorly‐conditioned IP‐Gauss–Newton saddle‐point linear systems that need to be solved approximately, once per optimization step, we propose two spectrally related preconditioners. These preconditioners leverage the limited informativeness of data in regularized PDE‐constrained optimization problems. A block Gauss–Seidel preconditioner is proposed for the GMRES‐based solution of the IP‐Gauss–Newton linear systems. It is shown, for a large‐class of PDE‐ and bound‐constrained optimization problems, that the spectrum of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix is asymptotically independent of discretization and is not impacted by the ill‐conditioning that notoriously plagues interior‐point methods. We exploit symmetry of the IP‐Gauss–Newton linear systems and propose a regularization and log‐barrier Hessian preconditioner for the preconditioned conjugate gradient (PCG)‐based solution of the equivalent IP‐Gauss–Newton–Schur complement linear systems. The eigenvalues of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix, that are not equal to one, are identical to the eigenvalues of the regularization and log‐barrier Hessian preconditioned Schur complement matrix. The scalability of the approach is demonstrated on two example problems. The numerical solution of these optimization problems is shown to require a discretization independent number of IP‐Gauss–Newton linear solves. Furthermore, the linear systems are solved in a discretization and IP ill‐conditioning independent number of preconditioned Krylov subspace iterations. The parallel scalability of the preconditioner, achieved via algebraic multigrid component solvers when applicable, and the aforementioned algorithmic scalability permits a parallel scalable means to compute solutions of a large class of PDE‐ and bound‐constrained problems.

PDE-constrained optimization↗

2HOT: an improved parallel hashed oct-tree n-body algorithm for cosmological simulation

We report on improvements made over the past two decades to our adaptive treecode N-body method (HOT). A mathematical and computational approach to the cosmological N-body problem is described, with performance and scalability measured up to 256k (2 18 ) processors. We present error analysis and scientific application results from a series of more than ten 69 billion (4096 3 ) particle cosmological simulations, accounting for 4 × 10 20 floating point operations. These results include the first simulations using the new constraints on the standard model of cosmology from the Planck satellite. Our simulations set a new standard for accuracy and scientific throughput, while meeting or exceeding the computational efficiency of the latest generation of hybrid TreePM N-body methods.

Computer Science↗

Scalable All-pairs Shortest Paths for Huge Graphs on Multi-GPU Clusters

We present an optimized Floyd-Warshall (Floyd-Warshall) algorithm that computes the All-pairs shortest path (APSP) for GPU accelerated clusters. The Floyd-Warshall algorithm due to its structural similarities to matrix-multiplication is well suited for highly parallel GPU architectures. To achieve high parallel efficiency, we address two key algorithmic challenges: reducing high communication overhead and addressing limited GPU memory. To reduce high communication costs, we redesign the parallel (a) to expose more parallelism, (b) aggressively overlap communication and computation with pipelined and asynchronous scheduling of operations, and (c) tailored MPI-collective. To cope with limited GPU memory, we employ an offload model, where the data resides on the host and is transferred to GPU on-demand. The proposed optimizations are supported with detailed performance models for tuning. Our optimized parallel Floyd-Warshall implementation is up to 5x faster than a strong baseline and achieves 8.1 PetaFLOPS/sec on 256~nodes of the Summit supercomputer at Oak Ridge National Laboratory. This performance represents 70% of the theoretical peak and 80% parallel efficiency. The offload algorithm can handle 2.5x larger graphs with a 20% increase in overall running time.

Sao, Piyush↗

ZettaBricks: A Language Compiler and Runtime System for Anyscale Computing

This grant supported the ZettaBricks and OpenTuner projects. ZettaBricks is a new implicitly parallel language and compiler where defining multiple implementations of multiple algorithms to solve a problem is the natural way of programming. ZettaBricks makes algorithmic choice a first class construct of the language. Choices are provided in a way that also allows our compiler to tune at a finer granularity. The ZettaBricks compiler autotunes programs by making both fine-grained as well as algorithmic choices. Choices also include different automatic parallelization techniques, data distributions, algorithmic parameters, transformations, and blocking. Additionally, ZettaBricks introduces novel techniques to autotune algorithms for different convergence criteria. When choosing between various direct and iterative methods, the ZettaBricks compiler is able to tune a program in such a way that delivers near-optimal efficiency for any desired level of accuracy. The compiler has the flexibility of utilizing different convergence criteria for the various components within a single algorithm, providing the user with accuracy choice alongside algorithmic choice. OpenTuner is a generalization of the experience gained in building an autotuner for ZettaBricks. OpenTuner is a new open source framework for building domain-specific multi-objective program autotuners. OpenTuner supports fully-customizable configuration representations, an extensible technique representation to allow for domain-specific techniques, and an easy to use interface for communicating with the program to be autotuned. A key capability inside OpenTuner is the use of ensembles of disparate search techniques simultaneously; techniques that perform well will dynamically be allocated a larger proportion of tests.

97 MATHEMATICS AND COMPUTING↗

Studies of Quark Transport and Hadronization in Nuclei

In this project, we conducted the first measurement of di‑hadron azimuthal correlations in deep inelastic scattering (DIS) off nuclei using the CLAS detector at Jefferson Lab. Using 5 GeV electron‑beam data collected on deuterium, carbon, iron, and lead targets, we extracted di‑pion correlation functions over a broad kinematic range. The results show a monotonic broadening of the correlation peak with increasing nuclear mass, along with pronounced dependencies on the pions’ kinematics. Separately, we implemented an algorithm based on the Kalman filter that achieved the first complete alignment of the CLAS12 central tracking system. In parallel, we developed simulations, algorithms, and performance studies that informed the conceptual designs of the forward hadronic calorimeter Insert and the Zero Degree Calorimeter, both of which are now included in the ePIC detector baseline for the forthcoming Electron Ion Collider.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Dynamic Network Analysis of Nuclear Science Literature for Research Influence Assessment

Analyzing nuclear science literature via data-driven methods is a critical step for assessing research influence and technology advancements. Indicators of scholarly activities may be buried in large volumes of nuclear research publications and collaboration networks over time. Mining for relevant scholarly influence trends in large volumes of text can be computationally challenging; however, open-source information on research collaborations over time can offer opportunities to extract meaningful insights. While network centrality analysis of scholarly research provides topology-based insights, additional emphasis on dynamics associated with the diffusion of information through these networks is important. Here this paper represents a step in that direction through the development of a novel dynamic network analysis framework and computational engine to identify key entities and capabilities over time within global scholarly nuclear science collaboration networks. Network theoretic, stochastic simulation, and optimization methods are leveraged to address variability in scholarly interactions, influence propagation, and collaboration patterns via network connections. A topic-aware influence maximization algorithm is developed to address the goal of identifying key influential authors in diverse research topics over time. Efficient parallelized implementation of the algorithm is applied to reduce computational costs. A proof-of-concept case study using open-source Scopus data with 33,517 published nuclear research papers from 2000-2019 is presented and representative analytic insights are generated. Broad implications of these insights are discussed and future research directions are also identified.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

GAtor: A First-Principles Genetic Algorithm for Molecular Crystal Structure Prediction

We present the implementation of GAtor, a massively parallel, first-principles genetic algorithm (GA) for molecular crystal structure prediction. GAtor is written in Python and currently interfaces with the FHI-aims code to perform local optimizations and energy evaluations using dispersion-inclusive density functional theory (DFT). GAtor offers a variety of fitness evaluation, selection, crossover, and mutation schemes. Breeding operators designed specifically for molecular crystals provide a balance between exploration and exploitation. Evolutionary niching is implemented in GAtor by using machine learning to cluster the dynamically updated population by structural similarity and then employing a cluster-based fitness function. Evolutionary niching promotes uniform sampling of the potential energy surface by evolving several subpopulations, which helps overcome initial pool biases and selection biases (genetic drift). The various settings offered by GAtor increase the likelihood of locating numerous low-energy minima, including those located in disconnected, hard to reach regions of the potential energy landscape. The best structures generated are re-relaxed and re ranked using a hierarchy of increasingly accurate DFT functionals and dispersion methods. GAtor is applied to a chemically diverse set of four past blind test targets, characterized by different types of intermolecular interactions. Furthermore, the experimentally observed structures and other low-energy structures are found for all four targets. In particular, for Target II, 5-cyano-3-hydroxythiophene, the top ranked putative crystal structure is a Z' = 2 structure with PT symmetry and a scaffold packing motif, which has not been reported previously.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dynamic Data Repartitioning for Load-Balanced Parallel Particle Tracing

We present a novel dynamic load-balancing algorithm based on data repartitioning for parallel particle tracing in flow visualization. Instead of static data assignment, we dynamically repartition the data into blocks and reassign the blocks to processes to balance the workload distribution among the processes. Block repartitioning is performed based on a dynamic workload estimation method that predicts the workload in the flow field on the fly as the input. In our approach, we allow data duplication in the repartitioning, enabling the same data blocks to be assigned to multiple processes. Load balance is achieved by regularly exchanging the blocks (together with the particles in the blocks) among processes according to the output of the data repartitioning. Compared with other load-balancing algorithms, our approach does not need any preprocessing on the raw data and does not require any dedicated process for work scheduling, while it has the capability to balance uneven workload efficiently. Results show improved load balance and high efficiency of our method on tracing particles in both steady and unsteady flow.

data repartitioning↗

GPU-Based Static Data-Flow Analysis for Fast and Scalable Android App Vetting

Many popular vetting tools for Android applications use static code analysis techniques. In particular, Interprocedural Data-Flow Graph (IDFG) construction is the computation at the core of Android static data-flow analysis and consumes most of the analysis time. Many analysis tools use a worklist algorithm, an iterative fixed-point approach, to construct the IDFG. In this paper, we observe that a straightforward GPU parallelization of the worklist algorithm leads to significant underutilization of the GPU resources. We identify four performance bottlenecks, namely, frequent dynamic memory allocations, high branch divergence, workload imbalance, and irregular memory access patterns. Accordingly, we propose GDroid, a GPU-based worklist algorithm implementation with multiple fine-grained optimizations tailored to common characteristics of Android applications. The optimizations considered are: matrix-based data structure, memory access-based node grouping, and worklist merging. Our experimental evaluation, performed on 1000 Android applications, shows that the proposed optimizations are beneficial to performance, and GDroid can achieve up to 128X speedups against a plain GPU implementation.

Android security↗

Partitioning and Communication Strategies for Sparse Non-negative Matrix Factorization

Non-negative matrix factorization (NMF), the problem of finding two non-negative low-rank factors whose product approximates an input matrix, is a useful tool for many data mining and scientific applications such as topic modeling in text mining and unmixing in microscopy. In this paper, we focus on scaling algorithms for NMF to very large sparse datasets and massively parallel machines by employing effective algorithms, communication patterns, and partitioning schemes that leverage the sparsity of the input matrix. We consider two previous works developed for related problems, one that uses a fine-grained partitioning strategy using a point-to-point communication pattern and one that uses a Cartesian, or checkerboard, partitioning strategy using a collective-based communication pattern. We show that a combination of the previous approaches balances the demands of the various computations within NMF algorithms and achieves high efficiency and scalability. From the experiments, we see that our proposed strategy runs up to 10x faster than the state of the art on real-world datasets.

Kaya, Oguz↗

Multiresolution molecular mechanics: Implementation and efficiency

Atomistic/continuum coupling methods combine accurate atomistic methods and efficient continuum methods to simulate the behavior of highly ordered crystalline systems. Coupled methods utilize the advantages of both approaches to simulate systems at a lower computational cost, while retaining the accuracy associated with atomistic methods. Many concurrent atomistic/continuum coupling methods have been proposed in the past; however, their true computational efficiency has not been demonstrated. The present work presents an efficient implementation of a concurrent coupling method called the Multiresolution Molecular Mechanics (MMM) for serial, parallel, and adaptive analysis. First, we present the features of the software implemented along with the associated technologies. The scalability of the software implementation is demonstrated, and the competing effects of multiscale modeling and parallelization are discussed. Then, the algorithms contributing to the efficiency of the software are presented. These include algorithms for eliminating latent ghost atoms from calculations and measurement-based dynamic balancing of parallel workload. The efficiency improvements made by these algorithms are demonstrated by benchmark tests. The efficiency of the software is found to be on par with LAMMPS, a state-of-the-art Molecular Dynamics (MD) simulation code, when performing full atomistic simulations. Speed-up of the MMM method is shown to be directly proportional to the reduction of the number of the atoms visited in force computation. Finally, an adaptive MMM analysis on a nanoindentation problem, containing over a million atoms, is performed, yielding an improvement of 6.3–8.5 times in efficiency, over the full atomistic MD method. For the first time, the efficiency of a concurrent atomistic/continuum coupling method is comprehensively investigated and demonstrated.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Efficient Parallel Sparse Symmetric Tucker Decomposition for High-Order Tensors

Tensor based methods are receiving renewed attention in recent years due to their prevalence in diverse real-world applications. There is considerable literature on tensor representations and algorithms for tensor decompositions, both for dense and sparse tensors. Many applications in hypergraph analytics, machine learning, psychometry, and signal processing result in tensors that are both sparse and symmetric, making it an important class for further study. Similar to the critical Tensor Times Matrix chain operation (TTMc) in general sparse tensors, the Sparse Symmetric Tensor Times Same Matrix chain (S3TTMc) operation is compute and memory intensive due to high tensor order and the associated factorial explosion in the number of non-zeros. In this work, we present a novel compressed storage format CSS for sparse symmetric tensors, along with an efficient parallel algorithm for the S3TTMc operation. We theoretically establish that S3TTMc on CSS achieves a better memory versus run-time trade-off compared to state-of-the-art implementations. We demonstrate experimental findings that confirm these results and achieve up to 2.9× speedup on synthetic and real datasets.

Shivakumar, Shruti↗

Time Series Discord Detection in Medical Data using a Parallel Relational Database [PowerPoint]

Recent advances in sensor technology have made continuous real-time health monitoring available in both hospital and non-hospital settings. Since data collected from high frequency medical sensors includes a huge amount of data, storing and processing continuous medical data is an emerging big data area. Especially detecting anomaly in real time is important for patients’ emergency detection and prevention. A time series discord indicates a subsequence that has the maximum difference to the rest of the time series subsequences, meaning that it has abnormal or unusual data trends. In this study, we implemented two versions of time series discord detection algorithms on a high performance parallel database management system (DBMS) and applied them to 240 Hz waveform data collected from 9,723 patients. The initial brute force version of the discord detection algorithm takes each possible subsequence and calculates a distance to the nearest non-self match to find the biggest discords in time series. For the heuristic version of the algorithm, a combination of an array and a trie structure was applied to order time series data for enhancing time efficiency. The study results showed efficient data loading, decoding and discord searches in a large amount of data, benefiting from the time series discord detection algorithm and the architectural characteristics of the parallel DBMS including data compression, data pipe-lining, and task scheduling.

47 OTHER INSTRUMENTATION↗