Scalable Generation of Graphs for Benchmarking HPC Community-Detection Algorithms.
Abstract not provided.
Slota, George M.↗
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Large-Scale Parallel Viscous Flow Computations using an Unstructured Multigrid Algorithm
The development and testing of a parallel unstructured agglomeration multigrid algorithm for steady-state aerodynamic flows is discussed. The agglomeration multigrid strategy uses a graph algorithm to construct the coarse multigrid levels from the given fine grid, similar to an algebraic multigrid approach, but operates directly on the non-linear system using the FAS (Full Approximation Scheme) approach. The scalability and convergence rate of the multigrid algorithm are examined on the SGI Origin 2000 and the Cray T3E. An argument is given which indicates that the asymptotic scalability of the multigrid algorithm should be similar to that of its underlying single grid smoothing scheme. For medium size problems involving several million grid points, near perfect scalability is obtained for the single grid algorithm, while only a slight drop-off in parallel efficiency is observed for the multigrid V- and W-cycles, using up to 128 processors on the SGI Origin 2000, and up to 512 processors on the Cray T3E. For a large problem using 25 million grid points, good scalability is observed for the multigrid algorithm using up to 1450 processors on a Cray T3E, even when the coarsest grid level contains fewer points than the total number of processors.
Mavriplis, Dimitri J.↗
pnnl/NWGraph
NWGraph aims to fill the role of a reusable library of generic graph algorithms for C++, similar to the algorithms available in the standard template library (STL) in C++. The library draws lessons learned from Boost Graph Library (BGL) and other libraries (PBGL, Galois, Gunrock, GraphX etc.), the evolution of the C++ language, and the evolution of C++ practice over the last 20 years.
Lumsdaine, Andrew↗
Augmenting Graph Convolution with Distance Preserving Embedding for Improved Learning
Graph convolution incorporates topological information of a graph into learning. Message passing corresponds to traversal of a local neighborhood in classical graph algorithms. We show that incorporating additional global structures, such as shortest paths, through distance preserving embedding can improve performance. Our approach, Gavotte, significantly improves the performance of a range of popular graph neu-ral networks such as GCN, GA T,Graph SAGE, and GCNII for transductive learning. Gavotte also improves the performance of graph neural networks for full-supervised tasks, albeit to a smaller degree. As high-quality embeddings are generated by Gavotte as a by-product, we leverage clustering algorithms on these embed dings to augment the training set and introduce Gavotte+. Our results of Gavotte+ on datasets with very few labels demonstrate the advantage of augmenting graph convolution with distance preserving embedding.
Cong, Guojing↗
FGRAAL: Technical documentation
Implementation of FGRAAL, a FORTRAN-extended graph algorithmic language for the Univac 1108 is described. The report contains the description of the implemented data structures for sets, lists and graphs. It summarizes the changes made for the RALPH compiler to accommodate the special statements of FGRAAL; gives the calling sequences generated by the changed compiler; and describes the object time subroutine package.
Mesztenyi, C. K.↗
I/O-Efficient Scientific Computation Using TPIE
In recent years, input/output (I/O)-efficient algorithms for a wide variety of problems have appeared in the literature. However, systems specifically designed to assist programmers in implementing such algorithms have remained scarce. TPIE is a system designed to support I/O-efficient paradigms for problems from a variety of domains, including computational geometry, graph algorithms, and scientific computation. The TPIE interface frees programmers from having to deal not only with explicit read and write calls, but also the complex memory management that must be performed for I/O-efficient computation. In this paper we discuss applications of TPIE to problems in scientific computation. We discuss algorithmic issues underlying the design and implementation of the relevant components of TPIE and present performance results of programs written to solve a series of benchmark problems using our current TPIE prototype. Some of the benchmarks we present are based on the NAS parallel benchmarks while others are of our own creation. We demonstrate that the central processing unit (CPU) overhead required to manage I/O is small and that even with just a single disk, the I/O overhead of I/O-efficient computation ranges from negligible to the same order of magnitude as CPU time. We conjecture that if we use a number of disks in parallel this overhead can be all but eliminated.
Vengroff, Darren Erik↗
Scaling and Quality of Modularity Optimization Methods for Graph Clustering
Real-world graphs exhibit structures known as “communities” or “clusters” consisting of a group of vertices with relatively high connectivity between them, as compared to the rest of the vertices in the network. Graph clustering or community detection is a fundamental graph operation used to analyze real-world graphs occurring in the areas of computational biology, cybersecurity, electrical grids, etc. Similar to other graph algorithms, owing to irregular memory accesses and inherently sequential nature, current algorithms for community detection are challenging to parallelize. However, in order to analyze large networks, it is important to develop scalable parallel implementations of graph clustering that are capable of exploiting the architectural features of modern supercomputers. In response to the 2019 Streaming Graph Challenge, we present quality and performance analysis of our distributed- memory community detection using Vite, which is our distributed memory implementation of the popular Louvain method, on the ALCF Theta supercomputer. Clustering methods such as Louvain that rely on modularity maximization are known to suffer from the resolution limit problem, preventing identification of clusters of certain sizes. Hence, we also include quality analysis of our shared-memory implementation of the Fast-tracking Resistance method, in comparison with Louvain on the challenge datasets. Furthermore, we introduce an edge-balanced graph distribution for our distributed memory implementation, that significantly reduces communication, offering up to 80% improvement in the overall execution time. In addition to performance/quality analysis, we also include details on the power/energy consumption, and memory traffic of the distributed-memory clustering implementation using real-world graphs with over a billion edges.
Ghosh, Sayan↗
Performance optimization, modeling and analysis of sparse matrix-matrix products on multi-core and many-core processors
Sparse matrix-matrix multiplication (SpGEMM) is a computational primitive that is widely used in areas ranging from traditional numerical applications to recent big data analysis and machine learning. Although many SpGEMM algorithms have been proposed, hardware specific optimizations for multi- and many-core processors are lacking and a detailed analysis of their performance under various use cases and matrices is not available. In this work, we firstly identify and mitigate multiple bottlenecks with memory management and thread scheduling on Intel Xeon Phi (Knights Landing or KNL). Specifically targeting many-core processors, we develop a hash-table-based algorithm and optimize a heap-based shared-memory SpGEMM algorithm. We examine their performance together with other publicly available codes. Different from the literature, our evaluation also includes use cases that are representative of real graph algorithms, such as multi-source breadth-first search or triangle counting. Our hash-table and heap-based algorithms are showing significant speedups from libraries in the majority of the cases while different algorithms dominate the other scenarios with different matrix size, sparsity, compression factor and operation type. We wrap up in-depth evaluation results and make a recipe to give the best SpGEMM algorithm for target scenario. We build the performance model for hash-table and heap-based algorithms, which supports the recipe. A critical finding is that hash-table-based SpGEMM gets a significant performance boost if the nonzeros are not required to be sorted within each row of the output matrix. Finally, we integrate our implementations into a large-scale protein clustering code named HipMCL, accelerating its SpGEMM kernel by up to 10X and achieving an overall performance boost for the whole HipMCL application by 2.6X.
97 MATHEMATICS AND COMPUTING↗
Optimizing High-Throughput Inference on Graph Neural Networks at Shared Computing Facilities with the NVIDIA Triton Inference Server
Abstract With machine learning applications now spanning a variety of computational tasks, multi-user shared computing facilities are devoting a rapidly increasing proportion of their resources to such algorithms. Graph neural networks (GNNs), for example, have provided astounding improvements in extracting complex signatures from data and are now widely used in a variety of applications, such as particle jet classification in high energy physics (HEP). However, GNNs also come with an enormous computational penalty that requires the use of GPUs to maintain reasonable throughput. At shared computing facilities, such as those used by physicists at Fermi National Accelerator Laboratory (Fermilab), methodical resource allocation and high throughput at the many-user scale are key to ensuring that resources are being used as efficiently as possible. These facilities, however, primarily provide CPU-only nodes, which proves detrimental to time-to-insight and computational throughput for workflows that include machine learning inference. In this work, we describe how a shared computing facility can use the NVIDIA Triton Inference Server to optimize its resource allocation and computing structure, recovering high throughput while scaling out to multiple users by massively parallelizing their machine learning inference. To demonstrate the effectiveness of this system in a realistic multi-user environment, we use the Fermilab Elastic Analysis Facility augmented with the Triton Inference Server to provide scalable and high-throughput access to a HEP-specific GNN and report on the outcome.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials
In brittle fracture applications, failure paths, regions where the failure occurs and damage statistics, are some of the key quantities of interest (QoI). High-fidelity models for brittle failure that accurately predict these QoI exist but are highly computationally intensive, making them infeasible to incorporate in upscaling and uncertainty quantification frameworks. The goal of this paper is to provide a fast heuristic to reasonably estimate quantities such as failure path and damage in the process of brittle failure. Towards this goal, we first present a method to predict failure paths under tensile loading conditions and low-strain rates. The method uses a k-nearest neighbors algorithm built on fracture process zone theory, and identifies the set of all possible pre-existing cracks that are likely to join early to form a large crack. The method then identifies zone of failure and failure paths using weighted graphs algorithms. We compare these failure paths to those computed with a high-fidelity fracture mechanics model called the Hybrid Optimization Software Simulation Suite (HOSS). A probabilistic evolution model for average damage in a system is also developed that is trained using 150 HOSS simulations and tested on 40 simulations. A non-parametric approach based on confidence intervals is used to determine the damage evolution over time along the dominant failure path. For upscaling, damage is the key QoI needed as an input by the continuum models. This needs to be informed accurately by the surrogate models for calculating effective moduli at continuum-scale. We show that for the proposed average damage evolution model, the prediction accuracy on the test data is more than 90%. In terms of the computational time, the proposed models are ≈ O ( 10 6 ) times faster compared to high-fidelity fracture simulations by HOSS. These aspects make the proposed surrogate model attractive for upscaling damage from micro-scale models to continuum models. We would like to emphasize that the surrogate models are not a replacement of physical understanding of fracture propagation. The proposed method in this paper is limited to tensile loading conditions at low-strain rates. This loading condition corresponds to a dominant fracture perpendicular to tensile direction. The proposed method is not applicable for in-plane shear, out-of-plane shear, and higher strain rate loading conditions.
36 MATERIALS SCIENCE↗
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↗
Quantum graph learning and algorithms applied in quantum computer sciences and image classification
Graph and network theory play a fundamental role in quantum computer sciences, including quantum information and computation. Random graphs and complex network theory are pivotal in predicting novel quantum phenomena, where entangled links are represented by edges. Quantum algorithms have been developed to enhance solutions for various network problems, giving rise to quantum graph computing and quantum graph learning (QGL). Here, in this review, we explore graph theory and graph learning methods as powerful tools for quantum computers to generate efficient solutions to problems beyond the reach of classical systems. We delve into the development of quantum complex network theory and its applications in quantum computation, materials discovery, and research. We also discuss quantum machine learning (QML) methodologies for effective image classification using qubits, quantum gates, and quantum circuits. Additionally, the paper addresses the challenges of QGL and algorithms, emphasizing the steps needed to develop flexible QGL solvers. This review presents a comprehensive overview of the fields of QGL and QML, highlights recent advancements, and identifies opportunities for future research.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Parallel, Portable Algorithms for Distance-2 Maximal Independent Set and Graph Coarsening.
Abstract not provided.
Kelley, Brian↗
Hybrid quantum-classical algorithms for approximate graph coloring
We show how to apply the recursive quantum approximate optimization algorithm (RQAOA) to MAX- k -CUT, the problem of finding an approximate k -vertex coloring of a graph. We compare this proposal to the best known classical and hybrid classical-quantum algorithms. First, we show that the standard (non-recursive) QAOA fails to solve this optimization problem for most regular bipartite graphs at any constant level p : the approximation ratio achieved by QAOA is hardly better than assigning colors to vertices at random. Second, we construct an efficient classical simulation algorithm which simulates level- 1 QAOA and level- 1 RQAOA for arbitrary graphs. In particular, these hybrid algorithms give rise to efficient classical algorithms, and no benefit arising from the use of quantum mechanics is to be expected. Nevertheless, they provide a suitable testbed for assessing the potential benefit of hybrid algorithm: We use the simulation algorithm to perform large-scale simulation of level- 1 QAOA and RQAOA with up to 300 qutrits applied to ensembles of randomly generated 3 -colorable constant-degree graphs. We find that level- 1 RQAOA is surprisingly competitive: for the ensembles considered, its approximation ratios are often higher than those achieved by the best known generic classical algorithm based on rounding an SDP relaxation. This suggests the intriguing possibility that higher-level RQAOA may be a potentially useful algorithm for NISQ devices.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
GrainGNN: A dynamic graph neural network for predicting 3D grain microstructure
We propose GrainGNN, a surrogate model for the evolution of polycrystalline grain structure under rapid solidification conditions in metal additive manufacturing. High fidelity simulations of solidification microstructures are typically performed using multicomponent partial differential equations (PDEs) with moving interfaces. The inherent randomness of the PDE initial conditions (grain seeds) necessitates ensemble simulations to predict microstructure statistics, e.g., grain size, aspect ratio, and crystallographic orientation. Here, currently such ensemble simulations are prohibitively expensive and surrogates are necessary.In GrainGNN, we use a dynamic graph to represent interface motion and topological changes due to grain coarsening. We use a reduced representation of the microstructure using hand-crafted features; we combine pattern finding and altering graph algorithms with two neural networks, a classifier (for topological changes) and a regressor (for interface motion). Both networks have an encoder-decoder architecture; the encoder has a multi-layer transformer long-short-term-memory architecture; the decoder is a single layer perceptron.We evaluate GrainGNN by comparing it to high-fidelity phase field simulations for in-distribution and out-of-distribution grain configurations for solidification under laser power bed fusion conditions. GrainGNN results in 80%–90% pointwise accuracy; and nearly identical distributions of scalar quantities of interest (QoI) between phase field and GrainGNN simulations compared using Kolmogorov-Smirnov test. GrainGNN's inference speedup (PyTorch on single x86 CPU) over a high-fidelity phase field simulation (CUDA on a single NVIDIA A100 GPU) is 150×–2000× for 100-initial grain problem. Further, using GrainGNN, we model the formation of 11,600 grains in 220 seconds on a single CPU core.
36 MATERIALS SCIENCE↗
Dynamic Nested Tracking Graphs
This work describes an approach for the interactive visual analysis of large-scale simulations, where numerous superlevel set components and their evolution are of primary interest. The approach first derives, at simulation runtime, a specialized Cinema database that consists of images of component groups, and topological abstractions. This database is processed by a novel graph operation-based nested tracking graph algorithm (GO-NTG) that dynamically computes NTGs for component groups based on size, overlap, persistence, and level thresholds. Finally, the resulting NTGs are in turn used in a feature-centered visual analytics framework to query specific database elements and update feature parameters, facilitating flexible post hoc analysis.
97 MATHEMATICS AND COMPUTING↗
Software-Hardware Co-design of Heterogeneous SmartNIC System for Recommendation Models Inference and Training
Deep Learning Recommendation Models (DLRMs) are critical applications in various domains and have evolved as one of the single largest machine learning applications. Trillions of DLRM parameters exceed the on-chip memory capacity of GPUs. Large-scale multi-node systems are required for distributed DLRM inference and training, which suffer from the all-to-all communication bottleneck, mainly limiting the scalability of ever-growing DLRMs. In recent years, SmartNICs have evolved with coupled computation and communication capabilities providing opportunities for a powerful heterogeneous device in the system. However, there isn't such a distributed system that fully leverages the abundant smartNIC resources that resolve the scalability issue of DLRMs. In this work, we proposed a software-hardware co-design of a heterogeneous smartNIC system that resolves the communication bottleneck of distributed DLRMs, mitigates the memory bandwidth pressure, and improves computation efficiency. We provide a set of smartNIC designs of cache systems (including local cache and remote cache) and smartNIC computation kernels which reduce data movement, relieve memory lookup intensity, and improve the GPU's computation efficiency. In addition, we propose a graph algorithm that improves the data locality of queries within batches which optimizes the overall system performance with higher data reuse. Our evaluation shows that our system achieves 2.1x latency speedup for inference and 1.6x throughput speedup for training.
Guo, Anqi↗
Essential Signal Simulation Enabled by Netlist Transforms (ESSENT) v1.0
Hardware simulation is an indispensable tool for designing chips as well as researching future architectures. Unfortunately, the slow rate of simulation can often bottleneck the design process, as designers must wait to see the results of a simulation before changing the design and starting a new simulation. The Essential Signal Simulation Enabled by Netlist Transforms (ESSENT) is a tool designed to accelerate hardware simulations. ESSENT takes in a design, uses graph algorithms to identify opportunities for conditional execution, and generates a simulator that leverages these opportunities. The generated simulator produces the exact same simulation results that would be returned by an unoptimized simulator, but in substantially less time. For input, ESSENT takes in designs formatted in FIRRTL (an open format).
Beamer, Scott↗