Kokkos? Multidimensional Array and future directions for std::array_ref.
Abstract not provided.
Edwards, Harold C.↗
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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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Inferring Missing Data in Multidimensional Arrays using Tensor Completion Algorithms.
Abstract not provided.
Coon, Joshua Jeremiah↗
Scalable and Energy-Efficient Methods for Interactive Exploration of Scientific Data
The main scientific contributions of this project are the following novel concepts for multidimensional arrays: shape-based similarity join (SIGMOD 2016), incremental view maintenance (SIGMOD 2017), user-defined stencil functions (HPDC 2017), and distributed caching for in-situ processing (SSDBM 2018). Building on our collaboration with the astrophysics group at LBNL, we applied these techniques to the data generated in the Palomar Transient Factory (PTF) astronomical survey. They played a pivotal role in the first-ever observation of a neutron star merger, which produces gravitational waves and turns out to be the origin of heavy elements, including gold. This has lead to a Science magazine article that has received extensive media coverage on ACM TechNews, Slashdot, FiveThirtyEight, and Quanta Magazine, among others. Additionally, two other articles detailing related aspects of the same discovery have been published in the Astrophysical Journal Letters journal. These publications have more than 3,000 citations according to Google Scholar (as of February 2022). This cross-disciplinary collaboration provided very good opportunities to apply database techniques to real-life scientific problems. The fact that they facilitated major discoveries in astrophysics proves the importance of our research. In addition to the work on multidimensional array databases, this project has also developed stochastic gradient descent (SGD) optimization algorithms for training large scale machine learning models, methods for querying in-situ data, and a database query optimizer based on sketch synopses.
79 ASTRONOMY AND ASTROPHYSICS↗
A simple json format for storing and exchanging code calculation and experimental results
Calculation codes and code systems give their results in a plethora of different formats and/or files. For instance, MCNP gives a user the MCNP specific output file, the mctal file, the ptrac file, etc. while PARTISN has a PARTISN specific output file and a number of binary files with various kinds of information about the calculation. However, the results we are interested in are always the same. These can be single values such as the effective multiplication factor k eff or the effective delayed neutron fraction β eff . It can be histogram data (such as particle spectra, reaction rates, sensitivity profiles, etc.) or even pointwise data (for example the nuclide composition as a function of time, etc.). It is also worthwhile to note that this would also apply to experimental data that we may wish to compare with as well. Calculation and experimental results can basically be split into two components: attributes (or metadata) and the actual result itself. Attributes represent information about the result that are not necessarily required for its’ interpretation but that are still good to have. Often, these attributes are what we will want to filter results on. This means that these attributes are often the answer to specific questions we may have about the result. The following is a non exhaustive list of such basic questions: what type of result is it: e.g. the effective multiplication factor k eff , the effective delayed neutron fraction β eff , etc.; which case does it relate to: e.g. a specific ICSBEP case such as PU-MET-FAST-001-001; which code and version produced this result: e.g. MCNP 6.2, etc.; which nuclear data library was used to obtain the result: e.g. ENDF/B-VIII.0 or JEFF 3.3; which nuclide and reaction does it apply to (for reaction rates and sensitivity profiles); which volume in the geometry was it calculated in? The second component of the calculation or experimental result is the actual numerical data of the result. It is this data that we want to compare, exchange, plot, interpret, etc. It consists of values with optional uncertainties and units. It also includes the underlying structure (if any structure is required to interpret the result). Depending on the type of result, it may be a single value (e.g. the effective multiplication factor), an array of values (e.g. a reaction rate or particle spectrum) or even a multidimensional array. In order to exchange results between different organisations, for instance for benchmarking, people often resort to spreadsheets or custom text files that need to be filled out. While this approach works well if little information is to be exchanged, it can become cumbersome when dealing with large amounts of data (like for instance particle spectra for thousands of cases). In addition, such an approach does not always capture the metadata we may be interested in to allow for automated processing of these files. The purpose of this report is to propose a standardised json structure to store any type of result and present an associated python interface to interact with these results directly. For such a structure to be useful, it must fulfill a specific set of functional requirements that we try to meet with this proposal. The format must allow for the calculation result to stand by itself. This means that we should not have to look in multiple places to be able to understand it. For example, if the result relates to a particle spectrum, the group structure in which the result is given should be stored with it. The format should be code agnostic. This means that we do not need to know where it came from to understand it. The format should be result type agnostic. This means that the format must be generic enough so that we can even use it for results we have not thought of yet. The format should be relatively easy to interact with through different scripting or programming languages (i.e. the machine interface) while still providing a clean structure that can be used directly by any human.
97 MATHEMATICS AND COMPUTING↗
ZFP: A compressed array representation for numerical computations
HPC trends favor algorithms and implementations that reduce data motion relative to FLOPS. We investigate the use of lossy compressed data arrays in place of traditional IEEE floating point arrays to store the primary data of calculations. Simulation is fundamentally an exercise in controlled approximation, and error introduced by finite-precision arithmetic (or lossy compression) is just one of several sources of error that need to be managed to ensure sufficient accuracy in a computed result. We describe ZFP, a compressed numerical format designed for in-memory storage of multidimensional arrays, and summarize theoretical results that demonstrate that the error of repeated lossy compression can be bounded and controlled. Furthermore, we establish a relationship between grid resolution and compression-induced errors and show that, contrary to conventional floating point, ZFP reduces finite-difference errors with finer grids. We present example calculations that demonstrate data reduction by 4x or more with negligible impact on solution accuracy. Our results further demonstrate several orders-of-magnitude increase in accuracy using ZFP over IEEE floating point and Posits for the same storage budget.
Lindstrom, Peter↗
The tensor t‐function: A definition for functions of third‐order tensors
Summary A definition for functions of multidimensional arrays is presented. The definition is valid for third‐order tensors in the tensor t‐product formalism, which regards third‐order tensors as block circulant matrices. The tensor function definition is shown to have similar properties as standard matrix function definitions in fundamental scenarios. To demonstrate the definition's potential in applications, the notion of network communicability is generalized to third‐order tensors and computed for a small‐scale example via block Krylov subspace methods for matrix functions. A complexity analysis for these methods in the context of tensors is also provided.
Lund, Kathryn↗
Nonnegative canonical tensor decomposition with linear constraints: nnCANDELINC
Abstract There is an emerging interest for tensor factorization applications in big‐data analytics and machine learning. To speed up the factorization of extra‐large datasets, organized in multidimensional arrays (also known as tensors), easy to compute compression‐based tensor representations, such as, Tucker and tensor train formats, are used to approximate the initial large‐tensor. Further, tensor factorization is used to extract latent features that can facilitate discoveries of new mechanisms and signatures hidden in the data, where the explainability of the latent features is of principal importance. Nonnegative tensor factorization extracts latent features that are naturally sparse and parts of the data, which makes them easily interpretable. However, to take into account available domain knowledge and subject matter expertise, often additional constraints need to be imposed, which lead us to canonical decomposition with linear constraints (CANDELINC), a canonical polyadic decomposition with rank deficient factors. In CANDELINC, Tucker compression is used as a preprocessing step, which lead to a larger residual error but to more explainable latent features. Here, we propose a nonnegative CANDELINC (nnCANDELINC) accomplished via a specific nonnegative Tucker decomposition; we refer to as minimal or canonical nonnegative Tucker. We derive several results required to understand the specificity of nnCANDELINC, focusing on the difficulties of preserving the nonnegative rank of a tensor to its Tucker core and comparing the real valued to nonnegative case. Finally, we demonstrate nnCANDELINC performance on synthetic and real‐world examples.
97 MATHEMATICS AND COMPUTING↗
An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU
An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (multidimensional arrays) and is based on the optimization of cache utilization on x86 CPU and the use of shared memory on NVidia GPU. From the applied side, the ultimate goal is to minimize the overhead encountered in the transformation of tensor contractions into matrix multiplications in computer implementations of advanced methods of quantum many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional tensors that typically appear in the so-called multireference correlated methods of electronic structure theory. Depending on tensor dimensionality, the presented optimized algorithms can achieve an order of magnitude speedup on x86 CPUs and 2-3 times speedup on NVidia Tesla K20X GPU with respect to the na ve scattering algorithm (no memory access optimization). Furthermore, the tensor transpose routines developed in this work have been incorporated into a general-purpose tensor algebra library (TAL-SH).
97 MATHEMATICS AND COMPUTING↗
A Hartree-Fock Application Using UPC++ and the New DArray Library
The Hartree-Fock (HF) method is the fundamental first step for incorporating quantum mechanics into many-electron simulations of atoms and molecules, and it is an important component of computational chemistry toolkits like NWChem. The GTFock code is an HF implementation that, while it does not have all the features in NWChem, represents crucial algorithmic advances that reduce communication and improve load balance by doing an up-front static partitioning of tasks, followed by work stealing whenever necessary. To enable innovations in algorithms and exploit next generation exascale systems, it is crucial to support quantum chemistry codes using expressive and convenient programming models and runtime systems that are also efficient and scalable. Here, this paper presents an HF implementation similar to GTFock using UPC++, a partitioned global address space model that includes flexible communication, asynchronous remote computation, and a powerful multidimensional array library. UPC++ offers runtime features that are useful for HF such as active messages, a rich calculus for array operations, hardware-supported fetch-and-add, and functions for ensuring asynchronous runtime progress. We present a new distributed array abstraction, DArray, that is convenient for the kinds of random-access array updates and linear algebra operations on block-distributed arrays with irregular data ownership. Finally, we analyze the performance of atomic fetch-and-add operations (relevant for load balancing) and runtime attentiveness, then compare various techniques and optimizations for each. Our optimized implementation of HF using UPC++ and the DArrays library shows up to 20% improvement over GTFock with Global Arrays at scales up to 24,000 cores.
97 MATHEMATICS AND COMPUTING↗
OpenACC offloading of the MFC compressible multiphase flow solver on AMD and NVIDIA GPUs
GPUs are the heart of the latest generations of supercomputers. We efficiently accelerate a compressible multiphase flow solver via OpenACC on NVIDIA and AMD Instinct GPUs. Optimization is accomplished by specifying the directive clauses gang vector and collapse. Further speedups of six and ten times are achieved by packing user-defined types into coalesced multidimensional arrays and manual inlining via metaprogramming. Additional optimizations yield seven-times speedup of array packing and thirty-times speedup of select kernels on Frontier. Weak scaling efficiencies of 97% and 95% are observed when scaling to 50% of Summit and 87% of Frontier. Strong scaling efficiencies of 84% and 81% are observed when increasing the device count by a factor of 8 and 16 on V100 and MI250X hardware. The strong scaling efficiency of AMD’s MI250X increases to 92% when increasing the device count by a factor of 16 when GPU-aware MPI is used for communication.
Wilfong, Benjamin↗
TuckerMPI: A Parallel C++/MPI Software Package for Large-scale Data Compression via the Tucker Tensor Decomposition
With this study, our goal is compression of massive-scale grid-structured data, such as the multi-terabyte output of a high-fidelity computational simulation. For such data sets, we have developed a new software package called TuckerMPI, a parallel C++/MPI software package for compressing distributed data. The approach is based on treating the data as a tensor, i.e., a multidimensional array, and computing its truncated Tucker decomposition, a higher-order analogue to the truncated singular value decomposition of a matrix. The result is a low-rank approximation of the original tensor-structured data. Compression efficiency is achieved by detecting latent global structure within the data, which we contrast to most compression methods that are focused on local structure. In this work, we describe TuckerMPI, our implementation of the truncated Tucker decomposition, including details of the data distribution and in-memory layouts, the parallel and serial implementations of the key kernels, and analysis of the storage, communication, and computational costs. We test the software on 4.5 and 6.7 terabyte data sets distributed across 100 s of nodes (1,000 s of MPI processes), achieving compression ratios between 100 and 200,000×, which equates to 99--99.999% compression (depending on the desired accuracy) in substantially less time than it would take to even read the same dataset from a parallel file system. Moreover, we show that our method also allows for reconstruction of partial or down-sampled data on a single node, without a parallel computer so long as the reconstructed portion is small enough to fit on a single machine, e.g., in the instance of reconstructing/visualizing a single down-sampled time step or computing summary statistics. The code is available at https://gitlab.com/tensors/TuckerMPI.
97 MATHEMATICS AND COMPUTING↗
Kokkos Version 2.0
The Kokkos library implements thread-parallel execution policies and shared-memory multidimensional array data structures that enable applications and domain libraries to develop computational kernels that are performance portable across multicore-CPU and manycore-accelerator (e.g. GPU) computing architectures.
SciDAC↗
Tensor Toolbox for MATLAB v. 3.0
Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors using MATLAB's object-oriented features. It also provides algorithms for tensor decomposition and factorization, algorithms for computing tensor eigenvalues, and methods for visualization of results.
Kolda, Tamara↗
Genten: Software for Generalized Tensor Decompositions v. 1.0.0
Tensors, or multidimensional arrays, are a powerful mathematical means of describing multiway data. This software provides computational means for decomposing or approximating a given tensor in terms of smaller tensors of lower dimension, focusing on decomposition of large, sparse tensors. These techniques have applications in many scientific areas, including signal processing, linear algebra, computer vision, numerical analysis, data mining, graph analysis, neuroscience and more. The software is designed to take advantage of parallelism present emerging computer architectures such has multi-core CPUs, many-core accelerators such as the Intel Xeon Phi, and computation-oriented GPUs to enable efficient processing of large tensors.
Phipps, EricT.↗
TabVar: Tabulated Variables
TabVar: A Python library for manipulating datasets in the form of tabulated variables. Tables in tabvar contain many columns representing independent variables, but exactly one distinguished column for the dependent variable. Having a single distinguished column allows a natural lifting of arithmetic operators to tables, much (and in fact fully generalizing) multidimensional array arithmetic. The convenient syntax of whole-table arithmetic, along with the usual operations of filtering and aggregation, and all in the setting of python's interactive REPL allows for rapid exploration of datasets.
Bachan, John↗
A Brief Summary on Formalizing Parallel Tensor Distributions, Redistributions, and Algorithm Derivations
Large-scale datasets in computational chemistry typically require distributed-memory parallel methods to perform a special operation known as tensor contraction. Tensors are multidimensional arrays, and a tensor contraction is akin to matrix multiplication with special types of permutations. Creating an efficient algorithm and optimized implementation in this domain is complex, tedious, and error-prone. To address this, we develop a notation to express data distributions so that we can apply use automated methods to find optimized implementations for tensor contractions. We consider the spin-adapted coupled cluster singles and doubles method from computational chemistry and use our methodology to produce an efficient implementation. Experiments per- formed on the IBM Blue Gene/Q and Cray XC30 demonstrate impact both improved performance and reduced memory consumption.
97 MATHEMATICS AND COMPUTING↗
The Average Spectrum Norm and Near-Optimal Tensor Completion
We propose the average spectrum norm to study the minimum number of measurements required to approximate a multidimensional array (i.e., sample complexity) via low-rank tensor recovery. Our focus is on the tensor completion problem, where the aim is to estimate a multiway array using a subset of tensor entries corrupted by noise. Our average spectrum norm-based analysis provides near-optimal sample complexities, exhibiting dependence on the ambient dimensions and rank that do not suffer from exponential scaling as the order increases.
97 MATHEMATICS AND COMPUTING↗
HOMMEXX 1.0: a performance-portable atmospheric dynamical core for the Energy Exascale Earth System Model
Abstract. We present an architecture-portable and performant implementation of the atmospheric dynamical core (High-Order Methods Modeling Environment, HOMME) of the Energy Exascale Earth System Model (E3SM). The original Fortran implementation is highly performant and scalable on conventional architectures using the Message Passing Interface(MPI) and Open MultiProcessor (OpenMP) programming models.We rewrite the model in C++ and use the Kokkos library to express on-node parallelism in a largely architecture-independent implementation. Kokkos provides an abstraction of a compute node or device,layout-polymorphic multidimensional arrays, and parallel execution constructs. The new implementation achieves the same or better performance on conventional multicore computers and is portable to GPUs. We present performance data for the original and new implementations on multiple platforms, on up to 5400 compute nodes, and study several aspects of the single- and multi-node performance characteristics of the new implementation on conventional CPU (e.g., Intel Xeon), many core CPU (e.g., Intel Xeon Phi Knights Landing),and Nvidia V100 GPU.
58 GEOSCIENCES↗