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Register a new userScalable Multigrid-based Hierarchical Scientific Data Refactoring on GPUs
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Added by
Jieyang Chen
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Rapid growth in scientific data and a widening gap between computational speed and I/O bandwidth makes it increasingly infeasible to store and share all data produced by scientific simulations. Instead, we need methods for reducing data volumes: ideally, methods that can scale data volumes adaptively so as to enable negotiation of performance and fidelity tradeoffs in different situations. Multigrid-based hierarchical data representations hold promise as a solution to this problem, allowing for flexible conversion between different fidelities so that, for example, data can be created at high fidelity and then transferred or stored at lower fidelity via logically simple and mathematically sound operations. However, the effective use of such representations has been hindered until now by the relatively high costs of creating, accessing, reducing, and otherwise operating on such representations. We describe here highly optimized data refactoring kernels for GPU accelerators that enable efficient creation and manipulation of data in multigrid-based hierarchical forms. We demonstrate that our optimized design can achieve up to 264 TB/s aggregated data refactoring throughput -- 92% of theoretical peak -- on 1024 nodes of the Summit supercomputer. We showcase our optimized design by applying it to a large-scale scientific visualization workflow and the MGARD lossy compression software.
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Rapid growth in scientific data and a widening gap between computational speed and I/O bandwidth make it increasingly infeasible to store and share all data produced by scientific simulations. Instead, we need methods for reducing data volumes: ideally, methods that can scale data volumes adaptively so as to enable negotiation of performance and fidelity tradeoffs in different situations. Multigrid-based hierarchical data representations hold promise as a solution to this problem, allowing for flexible conversion between different fidelities so that, for example, data can be created at high fidelity and then transferred or stored at lower fidelity via logically simple and mathematically sound operations. However, the effective use of such representations has been hindered until now by the relatively high costs of creating, accessing, reducing, and otherwise operating on such representations. We describe here highly optimized data refactoring kernels for GPU accelerators that enable efficient creation and manipulation of data in multigrid-based hierarchical forms. We demonstrate that our optimized design can achieve up to 250 TB/s aggregated data refactoring throughput -- 83% of theoretical peak -- on 1024 nodes of the Summit supercomputer. We showcase our optimized design by applying it to a large-scale scientific visualization workflow and the MGARD lossy compression software.
Error-bounded lossy compression is a critical technique for significantly reducing scientific data volumes. With ever-emerging heterogeneous high-performance computing (HPC) architecture, GPU-accelerated error-bounded compressors (such as cuSZ+ and cuZFP) have been developed. However, they suffer from either low performance or low compression ratios. To this end, we propose cuSZ+ to target both high compression ratios and throughputs. We identify that data sparsity and data smoothness are key factors for high compression throughputs. Our key contributions in this work are fourfold: (1) We propose an efficient compression workflow to adaptively perform run-length encoding and/or variable-length encoding. (2) We derive Lorenzo reconstruction in decompression as multidimensional partial-sum computation and propose a fine-grained Lorenzo reconstruction algorithm for GPU architectures. (3) We carefully optimize each of cuSZ+ kernels by leveraging state-of-the-art CUDA parallel primitives. (4) We evaluate cuSZ+ using seven real-world HPC application datasets on V100 and A100 GPUs. Experiments show cuSZ+ improves the compression throughputs and ratios by up to 18.4X and 5.3X, respectively, over cuSZ on the tested datasets.
LDA is a statistical approach for topic modeling with a wide range of applications. However, there exist very few attempts to accelerate LDA on GPUs which come with exceptional computing and memory throughput capabilities. To this end, we introduce EZLDA which achieves efficient and scalable LDA training on GPUs with the following three contributions: First, EZLDA introduces three-branch sampling method which takes advantage of the convergence heterogeneity of various tokens to reduce the redundant sampling task. Second, to enable sparsity-aware format for both D and W on GPUs with fast sampling and updating, we introduce hybrid format for W along with corresponding token partition to T and inverted index designs. Third, we design a hierarchical workload balancing solution to address the extremely skewed workload imbalance problem on GPU and scaleEZLDA across multiple GPUs. Taken together, EZLDA achieves superior performance over the state-of-the-art attempts with lower memory consumption.
Decomposing matrix A into a lower matrix L and an upper matrix U, which is also known as LU decomposition, is an essential operation in numerical linear algebra. For a sparse matrix, LU decomposition often introduces more nonzero entries in the L and U factors than in the original matrix. A symbolic factorization step is needed to identify the nonzero structures of L and U matrices. Attracted by the enormous potentials of the Graphics Processing Units (GPUs), an array of efforts have surged to deploy various LU factorization steps except for the symbolic factorization, to the best of our knowledge, on GPUs. This paper introduces gSoFa, the first GPU-based Symbolic factorization design with the following three optimizations to enable scalable LU symbolic factorization for nonsymmetric pattern sparse matrices on GPUs. First, we introduce a novel fine-grained parallel symbolic factorization algorithm that is well suited for the Single Instruction Multiple Thread (SIMT) architecture of GPUs. Second, we tailor supernode detection into a SIMT friendly process and strive to balance the workload, minimize the communication and saturate the GPU computing resources during supernode detection. Third, we introduce a three-pronged optimization to reduce the excessive space consumption problem faced by multi-source concurrent symbolic factorization. Taken together, gSoFa achieves up to 31x speedup from 1 to 44 Summit nodes (6 to 264 GPUs) and outperforms the state-of-the-art CPU project, on average, by 5x. Notably, gSoFa also achieves {up to 47%} of the peak memory throughput of a V100 GPU in Summit.
In this paper, we propose a novel method to compute triangle counting on GPUs. Unlike previous formulations of graph matching, our approach is BFS-based by traversing the graph in an all-source-BFS manner and thus can be mapped onto GPUs in a massively parallel fashion. Our implementation uses the Gunrock programming model and we evaluate our implementation in runtime and memory consumption compared with previous state-of-the-art work. We sustain a peak traversed-edges-per-second (TEPS) rate of nearly 10 GTEPS. Our algorithm is the most scalable and parallel among all existing GPU implementations and also outperforms all existing CPU distributed implementations. This work specifically focuses on leveraging our implementation on the triangle counting problem for the Subgraph Isomorphism Graph Challenge 2019, demonstrating a geometric mean speedup over the 2018 champion of 3.84x.
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