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Results for “Dense and Sparse Storage”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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7 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

MATAR: A performance portability and productivity implementation of data-oriented design with Kokkos

There is a need for simple, fast, and memory-efficient multidimensional data structures for dense and sparse storage that arise with numerical methods and in software applications. The data structures must perform equally well across multiple computer architectures, including CPUs and GPUs. For this purpose, we developed MATAR, a C++ software library that allows for simple creation and use of intricate data structures that is also portable across disparate architectures using Kokkos. Here, the performance aspect is achieved by forcing contiguous memory layout (or as close to contiguous as possible) for multidimensional and multi-size dense or sparse MATrix and ARray (hence, MATAR) types. Our results show that MATAR has the capability to improve memory utilization, performance, and programmer productivity in scientific computing. This is achieved by fitting more work into the available memory, minimizing memory loads required, and by loading memory in the most efficient order. This document describes the purpose of the work, the implementation of each of the data types, and the resulting performance both in some simple baseline test cases and in an application code.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A High Performance Sparse Tensor Algebra Compiler in MLIR

Sparse tensor algebra is widely used in many applications, including scientific computing, machine learning, and data analytics. The performance of sparse tensor algebra kernels strongly depends on the intrinsic characteristics of the input tensors, hence many storage formats are designed for tensors to achieve optimal performance for particular applications/architectures, which makes it challenging to implement and optimize every tensor operation of interest on a given architecture. We propose a tensor algebra domain-specific language (DSL) and compiler framework to automatically generate kernels for mixed sparse-dense tensor algebra operations. The proposed DSL provides high-level programming abstractions that resemble the familiar Einstein notation to represent tensor algebra operations. The compiler introduces a new Sparse Tensor Algebra dialect built on top of LLVM's extensible MLIR compiler infrastructure for efficient code generation while covering a wide range of tensor storage formats. Our compiler also leverages input-dependent code optimization to enhance data locality for better performance. Our results show that the performance of automatically generated kernels outperforms the state-of-the-art sparse tensor algebra compiler, with up to 20.92x, 6.39x, and 13.9x performance improvement over state-of-the-art tensor algebra compilers, for parallel SpMV, SpMM, and TTM, respectively.

Tian, Ruiqin↗
DOE OSTI2022

Bit-GraphBLAS: Bit-Level Optimizations of Matrix-Centric Graph Processing on GPU

In the graph data structure like adjacency matrix, the connectivity of two nodes can be sufficiently represented using only 1 bit, but they are generally treated as 32-bit full-precision in state-of-the-art graph frameworks to adopt common sparse format such as CSR. Meanwhile, bit-level parallelism has recently be explored to have high-performance potential and low storage requirement on GPUs with dense bit-tiles. To fill the gap, our solution is a hierarchical storage format that contains the bit-indexing base and dense bit-tile units. Inherently, the granularity of the bit-tile is an essential factor in achieving both storage compression and GPU parallelism. How to find a sweet spot that trades off between avoiding sparsity and exploiting is comprehensively researched in this work. In the experiment, we evaluate the proposed storage format and algorithms on modern generation GPUs, including Pascal and Volta, to figure out critical software co-designs in conjunction with existing hardware-specific optimization.

Chen, Jou-An↗
DOE OSTI2023

3D-Printed Graded Electrode with Ultrahigh MnO 2 Loading for Non-Aqueous Electrochemical Energy Storage

Electrolytic manganese dioxide is one of the promising cathode candidates for electrochemical energy storage devices due to its high redox capacity and ease of synthesis. Yet, high-loading MnO 2 often suffers from sluggish reaction kinetics, especially in non-aqueous electrolytes. The non-uniform deposition of MnO 2 on a porous current collectors also makes it difficult to fully utilize the active materials at high mass loading. Here, a 3D printed graded graphene aerogel (3D GA) that contains sparsely separated exterior ligaments is developed to create large open channels for mass transport as well as densely arranged interior ligaments providing large ion-accessible active surface. The unique structural design homogenizes the thickness of electro deposited MnO 2 even at an ultrahigh mass loading of ≈70 mg cm -2 . The electrode achieves a remarkable volumetric capacity of 29.1 mA h cm -3 in the non-aqueous electrolyte. A Li-ion hybrid capacitor device assembled with a graded 3D GA/MnO2 cathode and graded 3D GA/VO x anode exhibits a wide voltage window of 0–4 V and a superior volumetric energy density of 20.2 W h L -1 . The findings offer guidance on 3D printed electrode design for supporting ultrahigh loading of active materials and developments of high energy density energy storage devices.

electrochemical energy storage↗
DOE OSTI2021

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↗
DOE OSTI2023

Sparse Symmetric Format for Tucker Decomposition

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 them an important class for further study. Similar to the critical Tensor Times Matrix chain operation (TTM c ) in general sparse tensors, the $\underline{S}$ parse $\underline{S}$ ymmetric $\underline{T}$ ensor $\underline{T}$ imes $\underline{S}$ ame $\underline{M}$ atrix $\underline{c}$ hain (S 3 TTM c ) operation is compute and memory intensive due to high tensor order and the associated factorial explosion in the number of non-zeros. We present the novel Compressed Sparse Symmetric (CSS) format for sparse symmetric tensors, along with an efficient parallel algorithm for the S 3 TTM c operation. We theoretically establish that S 3 TTM c on CSS achieves a better memory versus run-time trade-off compared to state-of-the-art implementations, and visualize the variation of the performance gap over the parameter space. We demonstrate experimental findings that confirm these results and achieve up to 2.72× speedup on synthetic and real datasets. The scaling of the algorithm on different test architectures is also showcased to highlight the effect of machine characteristics on algorithm performance.

42 ENGINEERING↗
DOE OSTI2020

Towards real-time monitoring: data assimilated time-lapse full waveform inversion for seismic velocity and uncertainty estimation

SUMMARY Rapid development of time-lapse seismic monitoring instrumentations has made it possible to collect dense time-lapse data for tomographically retrieving time-lapse (even continuous) images of subsurface changes. While traditional time-lapse full waveform inversion (TLFWI) algorithms are designed for sparse time-lapse surveys, they lack of effective temporal constraint on time-lapse data, and, more importantly, lack of the uncertainty estimation of the TLFWI results that is critical for further interpretation. Here, we propose a new data assimilation TLFWI method, using hierarchical matrix powered extended Kalman filter (HiEKF) to quantify the image uncertainty. Compared to existing Kalman filter algorithms, HiEKF allows to store and update a data-sparse representation of the cross-covariance matrices and propagate model errors without expensive operations involving covariance matrices. Hence, HiEKF is computationally efficient and applicable to 3-D TLFWI problems. Then, we reformulate TLFWI in the framework of HiEKF (termed hereafter as TLFWI-HiEKF) to predict time-lapse images of subsurface spatiotemporal velocity changes and simultaneously quantify the uncertainty of the inverted velocity changes over time. We demonstrate the validity and applicability of TLFWI–HiEKF with two realistic CO2 monitoring models derived from Frio-II and Cranfield CO2 injection sites, respectively. In both 2-D and 3-D examples, the inverted high-resolution time-lapse velocity results clearly reveal a continuous velocity reduction due to the injection of CO2. Moreover, the accuracy of the model is increasing over time by assimilating more time-lapse data while the standard deviation is decreasing over lapsed time. We expect TLFWI-HiEKF to be equipped with real-time seismic monitoring systems for continuously imaging the distribution of subsurface gas and fluids in the future large-scale CO2 sequestration experiments and reservoir management.

58 GEOSCIENCES↗