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At least 469 records · Page 26

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↗

Streaming Solutions for Fine-Grained Network Traffic Measurements and Analysis

Online network traffic measurements and analysis is critical for detecting and preventing any real-time anomalies in the network. We propose, implement, and evaluate an online, adaptive measurement platform, which utilizes real-time traffic analysis results to refine subsequent traffic measurements. Central to our solution is the concept of Multi-Resolution Tiling (MRT), a heuristic approach that performs sequential analysis of traffic data to zoom into traffic subregions of interest. However, MRT is sensitive to transient traffic spikes. In this paper, we propose three novel traffic streaming algorithms that overcome the limitations of MRT and can cater to varying degrees of computational and storage budgets, detection latency, and accuracy of query response. We evaluate our streaming algorithms on a highly parallel and programmable hardware as well as a traditional software-based platforms. The algorithms demonstrate significant accuracy improvement over MRT in detecting anomalies consisting of synthetic hard-to-track elephant flows and global icebergs. Our proposed algorithms maintain the worst-case complexities of the MRT while incurring only a moderate increase in average resource utilization.

97 MATHEMATICS AND COMPUTING↗

Calculating potential energy curves with fixed-node diffusion Monte Carlo: CO and N 2

This study reports on the prospect for the routine use of Quantum Monte Carlo (QMC) for the electronic structure problem, applying fixed-node Diffusion Monte Carlo (DMC) to generate highly accurate Born-Oppenheimer potential energy curves (PECs) for small molecular systems. The singlet ground electronic states of CO and N 2 were used as test cases. The PECs obtained by DMC employing multiconfigurational trial wavefunctions were compared with those obtained by conventional high-accuracy electronic structure methods such as multireference configuration interaction and/or the best available empirical spectroscopic curves. The goal was to test whether a straightforward procedure using available QMC codes could be applied robustly and reliably. Results obtained with DMC codes were found to be in close agreement with the benchmark PECs, and the n 3 scaling with the number of electrons (compared with n 7 or worse for conventional high-accuracy quantum chemistry) could be advantageous depending on the system size. Due to a large pre-factor in the scaling, for the small systems tested here, it is currently still much more computationally intensive to compute PECs with QMC. Nevertheless, QMC algorithms are particularly well-suited to large-scale parallelization and are therefore likely to become more relevant for future massively parallel hardware architectures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Distributed Multi-GPU Community Detection on Exascale Computing Platforms

Community detection is a fundamental operation in graph mining, and by uncovering hidden structures and patterns within complex systems it helps solve fundamental problems pertaining to social networks, such as information diffusion, epidemics, and recommender systems. Scaling graph algorithms for massive networks becomes challenging on modern distributed-memory multi-GPU (Graphics Processing Unit) systems due to limitations such as irregular memory access patterns, load imbalances, higher communication-computation ratios, and cross-platform support. We present a novel algorithm HiPDPL-GPU (distributed parallel Louvain) to address these challenges. We conduct experiments involving different partitioning techniques to achieve optimized performance of HiPDPL-GPU on the two largest supercomputers: Frontier and Summit. Remarkably, HiPDPL-GPU processes a graph with 4.2 billion edges in less than 3 minutes using 1024 GPUs. Qualitatively performance of HiPDPL-GPU is similar or better compared to other state-of-the-art CPU- and GPU-based implementations. While prior GPU implementations have predominantly employed CUDA, our first-of-its-kind implementation for community detection is cross-platform, accommodating both AMD and NVIDIA GPUs.

graph algorithms, high performance comptuing↗

Chance-Constrained Energy Management System for Power Grids With High Proliferation of Renewables and Electric Vehicles

This paper proposes a two-stage energy management system (EMS) for power grids with massive integration of electric vehicles (EVs) and renewable energy resources. The first stage economic dispatch determines the optimal operating points of charging stations and battery swapping stations (BSS) for EVs under plug-in and battery swapping modes, respectively. The proposed stochastic model predictive control (SMPC) problem in this stage is characterized through a chance-constrained optimization formulation that can effectively capture the system and the forecast uncertainties. A distributed algorithm, the alternating direction method of multipliers (ADMM), is applied to accelerate the optimization computation through parallel computing. The second stage is aimed in coordinating the EV charging mechanisms to continuously follow the first-stage solutions, i.e., the target operating points, and meeting the EV customers' charging demands captured via the Advanced Metering Infrastructure (AMI). In this work, the proposed solution offers a holistic control strategy for large-scale centralized power grids in which the aggregated individual parameters are predictable and the system dynamics do not vary sharply within a short time-interval.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Polynomial Preconditioned Arnoldi with Stability Control

Polynomial preconditioning can improve the convergence of the Arnoldi method for computing eigenvalues. Such preconditioning significantly reduces the cost of orthogonalization; for difficult problems, it can also reduce the number of matrix-vector products. Parallel computations can particularly benefit from the reduction of communication-intensive operations. Additoinally, the GMRES algorithm provides a simple and effective way of generating the preconditioning polynomial. For some problems high degree polynomials are especially effective, but they can lead to stability problems that must be mitigated. A two-level “double polynomial preconditioning” strategy provides an effective way to generate high-degree preconditioners.

97 MATHEMATICS AND COMPUTING↗

PyBioNetFit

Systems biology models written in the BioNetGen language often contain parameters that must be fit based on experimental data. PyBioNetFit is a software tool designed to fit parameters of BioNetGen models. The user is expected to provide a BioNetGen model that contains unknown parameters, along with one or more text files containing experimental data. PyBioNetFit will perform a series of calls to the BioNetGen simulator using different parameter sets, to identify the parameter set that best fits the data. The parameter search is dictated by the user's choice of one of several metaheuristic optimization algorithms, including differential evolution, particle swarm optimization, scatter search, and simulated annealing. The software supports parallelized computing on multi-core computers and on computing clusters. We expect this software to be a useful tool for researchers designing BioNetGen models in collaboration with experimentalists.

Mitra, Eshan↗

Distributed Multi-GPU Community Detection on Exascale Computing Platforms

Community detection is a fundamental operation in graph mining, and by uncovering hidden structures and patterns within complex systems it helps solve fundamental problems pertaining to social networks, such as information diffusion, epidemics, and recommender systems. Scaling graph algorithms for massive networks becomes challenging on modern distributed-memory multi-GPU (Graphics Processing Unit) systems due to limitations such as irregular memory access patterns, load imbalances, higher communication-computation ratios, and cross-platform support. We present a novel algorithm HiPDPL-GPU (Distributed Parallel Louvain) to address these challenges. We conduct experiments involving different partitioning techniques to achieve an optimized performance of HiPDPL-GPU on the two largest supercomputers: Frontier and Summit. Remarkably, HiPDPL-GPU processes a graph with 4.2 billion edges in less than 3 minutes using 1024 GPUs. Qualitatively, the performance of HiPDPL-GPU is similar or better compared to other state-of-the-art CPU- and GPU-based implementations. While prior GPU implementations have predominantly employed CUDA, our first-of-its-kind implementation for community detection is cross-platform, accommodating both AMD and NVIDIA GPUs.

Sattar, Naw Safrin↗

A Length Adaptive Algorithm-Hardware Co-design of Transformer on FPGA Through Sparse Attention and Dynamic Pipelining

Transformers are considered one of the most important deep learning models since 2018, in part because it establishes state-of-the-art (SOTA) records and could potentially replace existing Deep Neural Networks (DNNs). Despite the remarkable triumphs, the prolonged turnaround time of Transformer models is a widely recognized roadblock. The variety of sequence lengths imposes additional computing overhead where inputs need to be zero-padded to the maximum sentence length in the batch to accommodate the parallel computing platforms. This paper targets the field-programmable gate array (FPGA) and proposes a coherent sequence length adaptive algorithm–hardware co-design for Transformer acceleration. Particularly, we develop a hardware-friendly sparse attention operator and a length-aware hardware resource scheduling algorithm. The proposed sparse attention operator brings the complexity of attention-based models down to linear complexity and alleviates the off-chip memory traffic. The proposed length-aware resource hardware scheduling algorithm dynamically allocates the hardware resources to fill up the pipeline slots and eliminates bubbles for NLP tasks. Experiments show that our design has very small accuracy loss and has 80.2 × and 2.6 × speedup compared to CPU and GPU implementation, and 4 × higher energy efficiency than state-of-the-art GPU accelerator optimized via CUBLAS GEMM.

Peng, Hongwu↗

Performance of GeantV EM Physics Models

The recent progress in parallel hardware architectures with deeper vector pipelines or many-cores technologies brings opportunities for HEP experiments to take advantage of SIMD and SIMT computing models. Launched in 2013, the GeantV project studies performance gains in propagating multiple particles in parallel, improving instruction throughput and data locality in HEP event simulation on modern parallel hardware architecture. Due to the complexity of geometry description and physics algorithms of a typical HEP application, performance analysis is indispensable in identifying factors limiting parallel execution. In this report, we will present design considerations and preliminary computing performance of GeantV physics models on coprocessors (Intel Xeon Phi and NVidia GPUs) as well as on mainstream CPUs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

High-fidelity kinetic modeling of plasmas in Z-pinch and pulsed power configurations (18-ERD-048)

Plasma dynamics can be strongly influenced by fine-scale kinetic physics, which is not captured by standard fluid treatments, is challenging to simulate, and is poorly understood. The aim of this research was to investigate the fundamental fine-scale properties of collisionless plasmas in Z-pinch and pulsed power configurations by deploying novel noisefree high-accuracy computational algorithms. Significant advances were achieved through the development of robust numerical capabilities to exploit axisymmetry in kinetic simulations, the development of new methodologies to construct kinetic equilibria, and the theoretical and computational study of kinetic sheared-flow-driven transport in pulsed power systems. These new capabilities shed light on the anisotropies that can develop in Z-pinches and the transport processes that can lead to parasitic currents in pulsed power inertial confinement fusion experiments. The use of cutting-edge massively-parallel numerical algorithms to address outstanding scientific questions in plasma physics advances the mission of Lawrence Livermore National Laboratory in the areas of high energy density science and high performance computing. By bringing together kinetic theory, high-order numerical methods, high performance computing, and experimental applications, this research advances the state of the art in plasma physics modeling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Multigrid methods with space–time concurrency

Here, we consider the comparison of multigrid methods for parabolic partial differential equations that allow space–time concurrency. With current trends in computer architectures leading towards systems with more, but not faster, processors, space–time concurrency is crucial for speeding up time-integration simulations. In contrast, traditional time-integration techniques impose serious limitations on parallel performance due to the sequential nature of the time-stepping approach, allowing spatial concurrency only. This paper considers the three basic options of multigrid algorithms on space–time grids that allow parallelism in space and time: coarsening in space and time, semicoarsening in the spatial dimensions, and semicoarsening in the temporal dimension. We develop parallel software and performance models to study the three methods at scales of up to 16K cores and introduce an extension of one of them for handling multistep time integration. We then discuss advantages and disadvantages of the different approaches and their benefit compared to traditional space-parallel algorithms with sequential time stepping on modern architectures.

97 MATHEMATICS AND COMPUTING↗

Parallel computing for power system climate resiliency: Solving a large-scale stochastic capacity expansion problem with mpi-sppy

Here we propose a nodal stochastic generation and transmission expansion planning model that incorporates the output from high-resolution global climate models through load and generation availability scenarios. We implement our model in Pyomo and perform computational studies on a realistically-sized test case of the California electric grid in a high performance computing environment. We propose model reformulations and algorithm tuning to efficiently solve this large problem using a variant of the Progressive Hedging Algorithm. We utilize the parallelization capabilities and overall versatility of mpi-sppy, exploiting its hub-and-spoke architecture to concurrently obtain inner and outer bounds on an optimal expansion plan. Initial results show that instances with 360 representative days on a system with over 8,000 buses can be solved to within 5% of optimality in under 4 h of wall clock time, a first step towards solving a large-scale power system expansion planning problem across a wide range of climate-informed operational scenarios.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A supernodal all-pairs shortest path algorithm

We show how to exploit graph sparsity in the Floyd-Warshall algorithm for the all-pairs shortest path (Apsp) problem. Floyd-Warshall is an attractive choice for Apsp on high-performing systems due to its structural similarity to solving dense linear systems and matrix multiplication. However, if sparsity of the input graph is not properly exploited, Floyd-Warshall will perform unnecessary asymptotic work and thus may not be a suitable choice for many input graphs. To overcome this limitation, the key idea in our approach is to use the known algebraic relationship between Floyd-Warshall and Gaussian elimination, and import several algorithmic techniques from sparse Cholesky factorization, namely, fill-in reducing ordering, symbolic analysis, supernodal traversal, and elimination tree parallelism. When combined, these techniques reduce computation, improve locality and enhance parallelism. We implement these ideas in an efficient shared memory parallel prototype that is orders of magnitude faster than an efficient multi-threaded baseline Floyd-Warshall that does not exploit sparsity. Our experiments suggest that the Floyd-Warshall algorithm can compete with Dijkstra's algorithm (the algorithmic core of Johnson's algorithm) for several classes sparse graphs.

Sao, Piyush↗

Exploring Heterogeneous Multicore Architectures for Advanced Embedded Uncertainty Quantification

We explore rearrangements of classical uncertainty quantification methods with the aim of achieving higher aggregate performance for uncertainty quantification calculations on emerging multicore and many core architectures. We show a rearrangement of the stochastic Galerkin method leads to improved performance and scalability on several computational architectures whereby uncertainty information is propagated at the lowest levels of the simulation code improving memory access patterns, exposing new dimensions of fine grained parallelism, and reducing communication. We also develop a general framework for implementing such rearrangements for a diverse set of uncertainty quantification algorithms as well as computational simulation codes to which they are applied.

97 MATHEMATICS AND COMPUTING↗

Neuromorphic Graph Algorithms: Cycle Detection, Odd Cycle Detection, and Max Flow

Neuromorphic computing is poised to become a promising computing paradigm in the post Moore’s law era due to its extremely low power usage and inherent parallelism. Spiking neural networks are the traditional use case for neuromorphic systems, and have proven to be highly effective at machine learning tasks such as control problems. More recently, neuromorphic systems have been applied outside of the arena of machine learning, primarily in the field of graph algorithms. Neuromorphic systems have been shown to perform graph algorithms faster and with lower power consumption than their traditional (GPU/CPU) counterparts, and are hence an attractive option for a co-processing unit in future high performance computing systems, where graph algorithms play a critical role. In this paper, we present a neuromorphic implementation of cycle detection, odd cycle detection, and the Ford-Fulkerson max-flow algorithm. We further evaluate the performance of these implementations using the NEST neuromorphic simulator by using spike counts and simulation time as proxies for energy consumption and run time. In addition to gains inherent in neuromorphic systems, we show that within the neuromorphic implementations early stopping criteria can be implemented to further improve performance.

Kay, Bill↗

Hyperspectral Image Classification Using Graph Clustering Methods

Hyperspectral imagery is a challenging modality due to the dimension of the pixels which can range from hundreds to over a thousand frequencies depending on the sensor. Most methods in the literature reduce the dimension of the data using a method such as principal component analysis, however this procedure can lose information. More recently methods have been developed to address classification of large datasets in high dimensions. This paper presents two classes of graph-based classification methods for hyperspectral imagery. Using the full dimensionality of the data, we consider a similarity graph based on pairwise comparisons of pixels. The graph is segmented using a pseudospectral algorithm for graph clustering that requires information about the eigenfunctions of the graph Laplacian but does not require computation of the full graph. We develop a parallel version of the Nyström extension method to randomly sample the graph to construct a low rank approximation of the graph Laplacian. With at most a few hundred eigenfunctions, we can implement the clustering method designed to solve a variational problem for a graph-cut-based semi-supervised or unsupervised classification problem. We implement OpenMP directive-based parallelism in our algorithms and show performance improvement and strong, almost ideal, scaling behavior. The method can handle very large datasets including a video sequence with over a million pixels, and the problem of segmenting a data set into a pre-determined number of classes.

47 OTHER INSTRUMENTATION↗

MOOSE ProbML: Parallelized probabilistic machine learning and uncertainty quantification for computational energy applications

Here, this paper presents the development and demonstration of massively parallel probabilistic machine learning (ML) and uncertainty quantification (UQ) capabilities within the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source computational platform for parallel finite element and finite volume analyses. In addressing the computational expense and uncertainties inherent in complex multiphysics simulations, this paper integrates Gaussian process (GP) variants, active learning, Bayesian inverse UQ, adaptive forward UQ, Bayesian optimization, evolutionary optimization, and Markov chain Monte Carlo (MCMC) within MOOSE. It also elaborates on the interaction among key MOOSE systems — Sampler, MultiApp, Reporter, and Surrogate — in enabling these capabilities. The modularity offered by these systems enables development of a multitude of probabilistic ML and UQ algorithms in MOOSE. Example code demonstrations include parallel active learning and parallel Bayesian inference via active learning. The impact of these developments is illustrated through five applications relevant to computational energy applications: UQ of nuclear fuel fission product release, using parallel active learning Bayesian inference; very rare events analysis in nuclear microreactors using active learning; advanced manufacturing process modeling using multi-output GPs (MOGPs) and dimensionality reduction; fluid flow using deep GPs (DGPs); and tritium transport model parameter optimization for fusion energy, using batch Bayesian optimization. These capabilities are part of the MOOSE framework.

97 - MATHEMATICS AND COMPUTING↗