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Results for “Sparse Coding”

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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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Prediction and compression of lattice QCD data using machine learning algorithms on quantum annealer

We present regression and compression algorithms for lattice QCD data utilizing the efficient binary optimization ability of quantum annealers. In the regression algorithm, we encode the correlation between the input and output variables into a sparse coding machine learning algorithm. The trained correlation pattern is used to predict lattice QCD observables of unseen lattice configurations from other observables measured on the lattice. In the compression algorithm, we define a mapping from lattice QCD data of floating-point numbers to the binary coefficients that closely reconstruct the input data from a set of basis vectors. Since the reconstruction is not exact, the mapping defines a lossy compression, but, a reasonably small number of binary coefficients are able to reconstruct the input vector of lattice QCD data with the reconstruction error much smaller than the statistical fluctuation. In both applications, we use D-Wave quantum annealers to solve the NP-hard binary optimization problems of the machine learning algorithms.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2010

The Spatial Vision Tree: A Generic Pattern Recognition Engine- Scientific Foundations, Design Principles, and Preliminary Tree Design

New foundational ideas are used to define a novel approach to generic visual pattern recognition. These ideas proceed from the starting point of the intrinsic equivalence of noise reduction and pattern recognition when noise reduction is taken to its theoretical limit of explicit matched filtering. This led us to think of the logical extension of sparse coding using basis function transforms for both de-noising and pattern recognition to the full pattern specificity of a lexicon of matched filter pattern templates. A key hypothesis is that such a lexicon can be constructed and is, in fact, a generic visual alphabet of spatial vision. Hence it provides a tractable solution for the design of a generic pattern recognition engine. Here we present the key scientific ideas, the basic design principles which emerge from these ideas, and a preliminary design of the Spatial Vision Tree (SVT). The latter is based upon a cryptographic approach whereby we measure a large aggregate estimate of the frequency of occurrence (FOO) for each pattern. These distributions are employed together with Hamming distance criteria to design a two-tier tree. Then using information theory, these same FOO distributions are used to define a precise method for pattern representation. Finally the experimental performance of the preliminary SVT on computer generated test images and complex natural images is assessed.

Rahman, Zia-ur↗
DOE OSTI2023

symPACK: A GPU-Capable Fan-Out Sparse Cholesky Solver

Sparse symmetric positive definite systems of equations are ubiquitous in scientific workloads and applications. Parallel sparse Cholesky factorization is the method of choice for solving such linear systems. Therefore, the development of parallel sparse Cholesky codes that can efficiently run on today’s large-scale heterogeneous distributed-memory platforms is of vital importance. Modern supercomputers offer nodes that contain a mix of CPUs and GPUs. To fully utilize the computing power of these nodes, scientific codes must be adapted to offload expensive computations to GPUs. We present symPACK, a GPU-capable parallel sparse Cholesky solver that uses one-sided communication primitives and remote procedure calls provided by the UPC++ library. We also utilize the UPC++ "memory kinds" feature to enable efficient communication of GPU-resident data. We show that on a number of large problems, symPACK outperforms comparable state-of-the-art GPU-capable Cholesky factorization codes by up to 14x on the NERSC Perlmutter supercomputer.

Bellavita, Julian↗
DOE OSTI2024

Diversity of visual inputs to Kenyon cells of the Drosophila mushroom body

The arthropod mushroom body is well-studied as an expansion layer representing olfactory stimuli and linking them to contingent events. However, 8% of mushroom body Kenyon cells in Drosophila melanogaster receive predominantly visual input, and their function remains unclear. Here, we identify inputs to visual Kenyon cells using the FlyWire adult whole-brain connectome. Input repertoires are similar across hemispheres and connectomes with certain inputs highly overrepresented. Many visual neurons presynaptic to Kenyon cells have large receptive fields, while interneuron inputs receive spatially restricted signals that may be tuned to specific visual features. Individual visual Kenyon cells randomly sample sparse inputs from combinations of visual channels, including multiple optic lobe neuropils. These connectivity patterns suggest that visual coding in the mushroom body, like olfactory coding, is sparse, distributed, and combinatorial. However, the specific input repertoire to the smaller population of visual Kenyon cells suggests a constrained encoding of visual stimuli.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Performance of an Astrophysical Radiation Hydrodynamics Code under Scalable Vector Extension Optimization

We present results of a performance study of an astrophysical radiation hydrodynamics code, V2D, on the Arm-based A64FX processor developed by Fujitsu. The code solves sparse linear systems, a task for which the A64FX architecture should be well suited. Here, we performed the performance analysis study on Ookami, an Apollo 80 platform utilizing the A64FX processor. We explored several compilers and performance anal-ysis packages and found the code did not perform as expected under scalable vector extension optimization, suggesting that a “deeper dive” into analyzing the code is worthwhile. However, a simple driver program that exercised basic sparse linear algebra routines used by V2D did show significant speedup with the use of the scalable vector extension optimization. We present the initial results from the study which used V2D on a relatively simple test problem that emphasized the repeated solution of sparse linear systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

On the Information in Spike Timing: Neural Codes Derived from Polychronous Groups

There is growing evidence regarding the importance of spike timing in neural information processing, with even a small number of spikes carrying information, but computational models lag significantly behind those for rate coding. Experimental evidence on neuronal behavior is consistent with the dynamical and state dependent behavior provided by recurrent connections. This motivates the minimalistic abstraction investigated in this paper, aimed at providing insight into information encoding in spike timing via recurrent connections. We employ information-theoretic techniques for a simple reservoir model which encodes input spatiotemporal patterns into a sparse neural code, translating the polychronous groups introduced by Izhike-vich into codewords on which we can perform standard vector operations. Finally, we show that the distance properties of the code are similar to those for (optimal) random codes. In particular, the code meets benchmarks associated with both linear classification and capacity, with the latter scaling exponentially with reservoir size.

computational modeling↗
NASA NTRS1990

A manual for PARTI runtime primitives

Primitives are presented that are designed to help users efficiently program irregular problems (e.g., unstructured mesh sweeps, sparse matrix codes, adaptive mesh partial differential equations solvers) on distributed memory machines. These primitives are also designed for use in compilers for distributed memory multiprocessors. Communications patterns are captured at runtime, and the appropriate send and receive messages are automatically generated.

Berryman, Harry↗
NASA NTRS1991

A manual for PARTI runtime primitives, revision 1

Primitives are presented that are designed to help users efficiently program irregular problems (e.g., unstructured mesh sweeps, sparse matrix codes, adaptive mesh partial differential equations solvers) on distributed memory machines. These primitives are also designed for use in compilers for distributed memory multiprocessors. Communications patterns are captured at runtime, and the appropriate send and receive messages are automatically generated.

Das, Raja↗
DOE OSTI2016

The Improved Simple Corner Balance Method and Efforts to Enhance its Computational Performance

The diamond difference (DD) spatial discretization has long been a work horse of the neutron transport community. For nearly as long as DD has been used in neutron transport, it has been observed that DD produces undamped, non-physical angular fluxes in spatially under resolved problems and can fail in the thick diffusion limit. A long list of alternative spatial discretizations, all with better physics properties: accuracy, robustness, and/or preservation of the thick diffusion limit, have been proposed as alternatives to DD. Unfortunately, these alternative spatial discretizations also require significantly more floating point operations (FLOPs) per unknown compared to DD. Historically, neutron transport problems of interest have been able to be resolved sufficiently that DD is accurate enough and FLOPs have been the computational performance bottleneck controlling time to solution. Thus, in practice DD has been and remains a preferred spatial discretization for neutron transport simulations. Trends in computing architecture are leading to a new paradigm where data movement, not FLOPs will control time to solution. This presents an opportunity to improve neutron transport physics by reconsidering more FLOP intensive spatial discretization than DD without incurring a time to solution penalty. In this work, we consider the improved simple corner balance (ISCB) spatial discretization, a unique alternative to DD that has the same memory footprint as DD, and detail efforts to improve its computational performance. The ISCB spatial discretization is a more FLOP intensive spatial discretization than DD with the same memory footprint as DD. Though designed to maximize FLOP intensity, third party libraries such as LAPACK are not tuned for the unique, frequent, small linear algebra needs of neutron transport problems. While hand coding a sparse Gauss elimination is likely to be faster than a dense matrix solve (CM vs. HGE), were LAPACK suitable for small linear algebra problems, we would not have seen a performance increase with decreased numbers of LAPACK calls for the Schur complement solve (SC4 vs. SC1). Significant effort has reduced the relative compute time of ISCB to DD, but on current computer architectures DD is still faster than ISCB. Future work comparing the overall efficiency of ISCB to DD may reveal that while ISCB is slower than DD on current computers, ISCB is more accurate than DD by a factor greater than the compute time slowdown. As new computer architectures become available, we will test our hypothesis that neutron transport simulations will be bandwidth limited, ideally rendering the additional FLOPs required by ISCB to be 'free' [in terms of time to solution]. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1990

Using a multifrontal sparse solver in a high performance, finite element code

We consider the performance of the finite element method on a vector supercomputer. The computationally intensive parts of the finite element method are typically the individual element forms and the solution of the global stiffness matrix both of which are vectorized in high performance codes. To further increase throughput, new algorithms are needed. We compare a multifrontal sparse solver to a traditional skyline solver in a finite element code on a vector supercomputer. The multifrontal solver uses the Multiple-Minimum Degree reordering heuristic to reduce the number of operations required to factor a sparse matrix and full matrix computational kernels (e.g., BLAS3) to enhance vector performance. The net result in an order-of-magnitude reduction in run time for a finite element application on one processor of a Cray X-MP.

King, Scott D.↗
DOE OSTI2021

SBIR Phase I Final Report, TACO: Distributed and Heterogeneous Sparse Compiler

Tensor algebra is a powerful tool for computing, but writing optimized codes that operate on sparse tensors can be very complex. This project enables a Tensor Algebra Compiler (TACO) that simplifies this task from man-years to man-days and extends TACO to support complex and large distributed systems. This report details the hypotheses, approaches used, and findings in this project.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Adaptive Sparse Grid Discretization (ASGarD)

This code solves the Vlasov-Poisson equations in 6-dimensions without approximation. It uses sparse grid discretization to solve the high-dimensional PDEs. The code functions as a discontinuous Galerkin finite element solver. Advantages/benefits include no approximations, supports high-dimensionality, leadership-scale capability, and implicit time advance.

Hahn, Steven [Oak Ridge National Laboratory (ORNL)↗
DOE OSTI2024

Milestone 49 Report: Batched Sparse LA Phase 5 Implementation

Batched sparse linear algebra operations in general, and solvers in particular, have become the major algorithmic development activity and foremost performance engineering effort in the numerical software libraries work on modern hardware with accelerators such as GPUs. Many applications, ECP and non-ECP alike, require simultaneous solutions of many small linear systems of equations that are structurally sparse in one form or another. In order to move towards high hardware utilization levels, it is important to provide these applications with appropriate interface designs to be both functionally efficient and performance portable and give full access to the appropriate batched sparse solvers running on modern hardware accelerators prevalent across DOE supercomputing sites since the inception of ECP. To this end, we present here a summary of recent advances on the interface designs in use by HPC software libraries supporting batched sparse linear algebra and the development of sparse batched kernel codes for solvers and preconditioners. We also address the potential interoperability opportunities to keep the corresponding software portable between the major hardware accelerators from AMD, Intel, and NVIDIA, while maintaining the appropriate disclosure levels conforming to the active NDA agreements. The presented interface specifications include a mix of batched band, sparse iterative, and sparse direct solvers with their accompanying functionality that is already required by the application codes or we anticipated to be needed in the near future. This report summarizes progress in Kokkos Kernels and the xSDK libraries MAGMA, Ginkgo, hypre, PETSc, and SuperLU.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Batched Sparse Linear Algebra (Final Report for Subcontract B648960)

This report finalizes design specifications for developing batched kernels for small tensor operations for unassembled matrix-free iterative solvers, batched solvers for partially assembled operators, and batched solvers with support for various sparse formats. The outcome of the project milestones is a set of interfaces to Batched Sparse LA solvers running on hardware accelerators for use in ECP Libraries and Applications. It is part of the development of sparse batched kernels, solvers/preconditioners as well as creating interoperability in xSDK libraries with sparse and dense batched functions to benefit ECP applications. The participants included representatives from ECP libraries (not limited to the xSDK project), applications, and vendors (AMD, Intel, and NVIDIA). Batched sparse linear algebra solvers form the new frontier for algorithmic development and performance engineering. Many applications (ECP and non-ECP alike) require simultaneous solutions of small linear systems of equations that are structurally sparse. To move towards high hardware utilization, it is important to provide these applications with appropriate interfaces to efficient batched sparse solvers running on modern hardware accelerators. We present interface designs in use by HPC software libraries supporting batched sparse linear algebra and the development of sparse batched kernel codes for solvers and preconditioners. We also address the potential interoperability opportunities to keep the software portable between the major hardware accelerators from AMD, Intel, and NVIDIA. The presented interface specifications includes batched band, sparse iterative, and sparse direct solvers. This report summarizes progress in Kokkos Kernels and the xSDK libraries MAGMA, Ginkgo, hypre, SUNDIALS, and SuperLU_dist.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

A Shifted Block Lanczos Algorithm 1: The Block Recurrence

In this paper we describe a block Lanczos algorithm that is used as the key building block of a software package for the extraction of eigenvalues and eigenvectors of large sparse symmetric generalized eigenproblems. The software package comprises: a version of the block Lanczos algorithm specialized for spectrally transformed eigenproblems; an adaptive strategy for choosing shifts, and efficient codes for factoring large sparse symmetric indefinite matrices. This paper describes the algorithmic details of our block Lanczos recurrence. This uses a novel combination of block generalizations of several features that have only been investigated independently in the past. In particular new forms of partial reorthogonalization, selective reorthogonalization and local reorthogonalization are used, as is a new algorithm for obtaining the M-orthogonal factorization of a matrix. The heuristic shifting strategy, the integration with sparse linear equation solvers and numerical experience with the code are described in a companion paper.

Grimes, Roger G.↗