Search NASA⌕ Search

SEARCH · Search NASA

Results for “decomposition algorithms”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Block-oriented modeling of superstructure optimization problems

We present a novel software framework for modeling large-scale engineered systems as mathematical optimization problems. A key motivating feature in such systems is their hierarchical, highly structured topology. Existing mathematical optimization modeling environments do not facilitate the natural expression and manipulation of hierarchically structured systems. Rather, the modeler is forced to "flatten" the system description, hiding structure that may be exploited by solvers, and obfuscating the system that the modeling environment is attempting to represent. To correct this deficiency, we propose a Python-based "block-oriented" modeling approach for representing the discrete components within the system. Our approach is an extension of the Pyomo library for specifying mathematical optimization problems. Through the use of a modeling components library, the block-oriented approach facilitates a clean separation of system superstructure from the details of individual components. This approach also naturally lends itself to expressing design and operational decisions as disjunctive expressions over the component blocks. By expressing a mathematical optimization problem in a block-oriented manner, inherent structure (e.g., multiple scenarios) is preserved for potential exploitation by solvers. In particular, we show that block-structured mathematical optimization problems can be straightforwardly manipulated by decomposition-based multi-scenario algorithmic strategies, specifically in the context of the PySP stochastic programming library. We illustrate our block-oriented modeling approach using a case study drawn from the electricity grid operations domain: unit commitment with transmission switching and N - 1 reliability constraints. Finally, we demonstrate that the overhead associated with block-oriented modeling only minimally increases model instantiation times, and need not adversely impact solver behavior. (C) 2013 Elsevier Ltd. All rights reserved.

Friedman, Z↗
DOE OSTI2019

Accelerating and Parallelizing Lagrangian Simulations of Mixing-Limited Reactive Transport

Recent advances in random walk particle tracking have enabled direct simulation of mixing and reactions by allowing the particles to interact with each other using a multipoint mass transfer scheme. The mass transfer scheme allows separation of mixing and spreading processes, among other advantages, but it is computationally expensive because its speed depends on the number of interacting particle pairs. This note explores methods for relieving the computational bottleneck caused by the mass transfer step, and we use these algorithms to develop a new parallel, interacting particle model. The new model is a combination of a sparse search algorithm and a novel domain decomposition scheme, both of which offer significant speedup relative to the reference case—even when they are executed serially. We combine the strengths of these methods to create a parallel particle scheme that is highly accurate and efficient with run times that scale as 1/P for a fixed number of particles, where P is the number of computational cores (equivalently, subdomains, in this work) being used. Here, the new parallel model is a significant advance because it enables efficient simulation of large particle ensembles that are needed for environmental simulations and also because it can naturally pair with parallel geochemical solvers to create a practical Lagrangian tool for simulating mixing and reactions in complex chemical systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Three-dimensional reconstruction of neutron, gamma-ray, and x-ray sources using spherical harmonic decomposition

Neutron, gamma-ray, and x-ray imaging are important diagnostic tools at the National Ignition Facility (NIF) for measuring the two-dimensional (2D) size and shape of the neutron producing region, for probing the remaining ablator and measuring the extent of the DT plasmas during the stagnation phase of Inertial Confinement Fusion implosions. Due to the difficulty and expense of building these imagers, at most only a few two-dimensional projections images will be available to reconstruct the three-dimensional (3D) sources. In this work, we present a technique that has been developed for the 3D reconstruction of neutron, gamma-ray, and x-ray sources from a minimal number of 2D projections using spherical harmonics decomposition. We present the detailed algorithms used for this characterization and the results of reconstructed sources from experimental neutron and x-ray data collected at OMEGA and NIF.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Communication-Avoiding Parallel Sparse-Dense Matrix-Matrix Multiplication

Multiplication of a sparse matrix with a dense matrix is a building block of an increasing number of applications in many areas such as machine learning and graph algorithms. However, most previous work on parallel matrix multiplication considered only both dense or both sparse matrix operands. This paper analyzes the communication lower bounds and compares the communication costs of various classic parallel algorithms in the context of sparse-dense matrix-matrix multiplication. We also present new communication-avoiding algorithms based on a 1D decomposition, called 1.5D, which - while suboptimal in dense-dense and sparse-sparse cases - outperform the 2D and 3D variants both theoretically and in practice for sparse-dense multiplication. Our analysis separates one-time costs from per iteration costs in an iterative machine learning context. Experiments demonstrate speedups up to 100x over a baseline 3D SUMMA implementation and show parallel scaling over 10 thousand cores.

Koanantakool, Penporn↗
DOE OSTI2024

Beam correction for multi-pass arcs in FFA@CEBAF: status update

This work examines the multi-pass steering of six electron beams in an FFA arc ranging from approximately 10.5 GeV to 22 GeV. Shown here is an algorithm based on singular value decomposition (SVD) to successfully steer all six beams through the arc given precise knowledge of all beam positions at each of one hundred and one diagnostic locations with one hundred individual corrector magnets: that is successive application of SVD to different 100 × 101 response matrices—one for each beam energy. Further, a machine learning scheme is developed which only requires knowledge of the energy-averaged beam position at each location to provide equivalent steering. Extension of this scheme to other beam optics quantities as well as transverse and longitudinal coupling is explored.

Accelerator Physics↗
DOE OSTI2021

True Load Balancing for Matricized Tensor Times Khatri-Rao Product

MTTKRP is the bottleneck operation in algorithms used to compute the CP tensor decomposition. For sparse tensors, utilizing the compressed sparse fibers (CSF) storage format and the CSF-oriented MTTKRP algorithms is important for both memory and computational efficiency on distributed-memory architectures. Existing intelligent tensor partitioning models assume the computational cost of MTTKRP to be proportional to the total number of nonzeros in the tensor. However, this is not the case for the CSF-oriented MTTKRP on distributed-memory architectures. We outline two deficiencies of nonzero-based intelligent partitioning models when CSF-oriented MTTKRP operations are performed locally: failure to encode processors' computational loads and increase in total computation due to fiber fragmentation. We focus on existing fine-grain hypergraph model and propose a novel vertex weighting scheme that enables this model encode correct computational loads of processors. We also propose to augment the fine-grain model by fiber nets for reducing the increase in total computational load via minimizing fiber fragmentation. In this way, the proposed model encodes minimizing the load of the bottleneck processor. In conclusion, parallel experiments with real-world sparse tensors on up to 1024 processors prove the validity of the outlined deficiencies and demonstrate the merit of our proposed improvements in terms of parallel runtimes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Event-Based Parareal: A data-flow based implementation of parareal

Parareal is an iterative algorithm that, in effect, achieves temporal decomposition for a time-dependent system of differential or partial differential equations. A solution is obtained in a shorter wall-clock time, but at the expense of increased compute cycles. The algorithm combines a fine solver that solves the system to acceptable accuracy with an approximate coarse solver. The critical task for the successful implementation of parareal on any system is the development of a coarse solver that leads to convergence in a small number of iterations compared to the number of time slices in the full time interval, and is, at the same time, much faster than the fine solver. Fast coarse solvers may not lead to sufficiently rapid convergence, and slow coarse solvers may not lead to significant gains even if the number of iterations to convergence is satisfactory. We find that the difficulty of meeting these conflicting demands can be substantially eased by using a data-driven, event-based implementation of parareal instead of the conventional algorithm where solver tasks are executed sequentially. For given convergence properties, the event-based approach relaxes the speed requirements on the coarse solver by a factor of , where is the number of iterations required for a converged solution. This may, for many problems, lead to an efficient parareal implementation that would otherwise not be possible or would require substantial coarse solver development.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Exploring the Interplay of Resilience and Energy Consumption for a Task-Based Partial Differential Equations Preconditioner

We discuss algorithm-based resilience to silent data corruption (SDC) in a task- based domain-decomposition preconditioner for partial differential equations (PDEs). The algorithm exploits a reformulation of the PDE as a sampling problem, followed by a solution update through data manipulation that is resilient to SDC. The implementation is based on a server-client model where all state information is held by the servers, while clients are designed solely as computational units. Scalability tests run up to ~ 51 K cores show a parallel efficiency greater than 90%. We use a 2D elliptic PDE and a fault model based on random single bit-flip to demonstrate the resilience of the application to synthetically injected SDC. We discuss two fault scenarios: one based on the corruption of all data of a target task, and the other involving the corruption of a single data point. We show that for our application, given the test problem considered, a four-fold increase in the number of faults only yields a 2% change in the overhead to overcome their presence, from 7% to 9%. We then discuss potential savings in energy consumption via dynamics voltage/frequency scaling, and its interplay with fault-rates, and application overhead.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

MatRIS: Addressing the Challenges for Portability and Heterogeneity Using Tasking for Matrix Decomposition (Cholesky)

The ubiquitous in-node heterogeneity of HPC and cloud computing platforms makes software portability and performance optimization extremely challenging. Described here, the MatRIS multilevel math library abstraction framework employs tasking to alleviate these difficulties. MatRIS includes the IRIS task-based runtime on the bottom level and exposes different layers of abstraction to render algorithms architecturally agnostic. MatRIS ensures the decomposition and creation of tasks that represent the necessary encapsulation of the optimized kernels from both vendor and open-source math libraries. Once built, MatRIS can select different combinations of accelerators at runtime, making it portable even on diverse heterogeneous architectures. By leveraging the IRIS runtime’s features for managing heterogeneity, MatRIS deploys algorithms that remove the need to specify orchestration and data transfer. This study describes how the serial task abstraction of a tiled Cholesky factorization is made portable and scalable in the case of multi-device and multi-vendor heterogeneity on a node with NVIDIA and AMD GPUs by using MatRIS. First, we demonstrate that Cholesky in MatRIS provides multi-GPU scalability that offers competitive performance versus cuSolverMG. Then, we present the challenges and opportunities for heterogeneous execution.

Monil, M. A. H.↗
DOE OSTI2017

Exploring the interplay of resilience and energy consumption for a task-based partial differential equations preconditioner

Here, we discuss algorithm-based resilience to silent data corruptions (SDCs) in a task-based domain-decomposition preconditioner for partial differential equations (PDEs). The algorithm exploits a reformulation of the PDE as a sampling problem, followed by a solution update through data manipulation that is resilient to SDCs. The implementation is based on a server-client model where all state information is held by the servers, while clients are designed solely as computational units. Scalability tests run up to ~51K cores show a parallel efficiency greater than 90%. We use a 2D elliptic PDE and a fault model based on random single and double bit-flip to demonstrate the resilience of the application to synthetically injected SDC. We discuss two fault scenarios: one based on the corruption of all data of a target task, and the other involving the corruption of a single data point. We show that for our application, given the test problem considered, a four-fold increase in the number of faults only yields a 2% change in the overhead to overcome their presence, from 7% to 9%. We then discuss potential savings in energy consumption via dynamic voltage/frequency scaling, and its interplay with fault-rates, and application overhead.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Lifting MGARD: Construction of (pre)wavelets on the interval using polynomial predictors of arbitrary order

MGARD (MultiGrid Adaptive Reduction of Data) is an algorithm for compressing and refactoring scientific data, based on the theory of multigrid methods. The core algorithm is built around stable multilevel decompositions of conforming piecewise linear $C^0$ finite element spaces, enabling accurate error control in various norms and derived quantities of interest. In this work, we extend this construction to arbitrary order Lagrange finite elements $\mathbb{Q}_p$, $p \geq 0$, and propose a reformulation of the algorithm as a lifting scheme with polynomial predictors of arbitrary order. Additionally, a new formulation using a compactly supported wavelet basis is discussed, and an explicit construction of the proposed wavelet transform for uniform dyadic grids is described.

Reshniak, Viktor [Oak Ridge National Laboratory (O↗
DOE OSTI2011

A generalized implicit algorithm for multi-dimensional particle-in-cell simulations in Cartesian geometry

An implicit multi-dimensional particle-in-cell (PIC) code is developed to study the interaction of ultrashort pulse lasers with matter. The algorithm is based on current density decomposition and is only marginally more complicated compared to explicit PIC codes, but it completely eliminates grid heating and possesses good energy conserving properties with relaxed time step and grid resolution. This is demonstrated in a test case study, in which high-energy protons are generated from a thin carbon foil at solid density using linear and circular polarizations. The grid heating rate is estimated to be 1-10 eV/ps.

36 MATERIALS SCIENCE↗
DOE OSTI2011

Efficient decomposition of cosmic microwave background polarization maps into pure E, pure B, and ambiguous components

Separation of the B component of a cosmic microwave background (CMB) polarization map from the much larger E component is an essential step in CMB polarimetry. For a map with incomplete sky coverage, this separation is necessarily hampered by the presence of ambiguous modes which could be either E or B modes. I present an efficient pixel-space algorithm for removing the ambiguous modes and separating the map into pure E and B components. The method, which works for arbitrary geometries, does not involve generating a complete basis of such modes and scales the cube of the number of pixels on the boundary of the map.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

A Cyber-Physical Anomaly Detection for Wide-Area Protection Using Machine Learning

Wide-area protection scheme (WAPS) provides system-wide protection by detecting and mitigating small and large-scale disturbances that are difficult to resolve using local protection schemes. As this protection scheme is evolving from a substation-based distributed remedial action scheme (DRAS) to the control center-based centralized RAS (CRAS), it presents severe challenges to their cybersecurity because of its heavy reliance on an insecure grid communication, and its compromise would lead to system failure. This article presents an architecture and methodology for developing a cyber-physical anomaly detection system (CPADS) that utilizes synchrophasor measurements and properties of network packets to detect data integrity and communication failure attacks on measurement and control signals in CRAS. The proposed machine leaning-based methodology applies a rules-based approach to select relevant input features, utilizes variational mode decomposition (VMD) and decision tree (DT) algorithms to develop multiple classification models, and performs final event identification using a rules-based decision logic. Here, we have evaluated the proposed methodology of CPADS using the IEEE 39 bus system for several performance measures (accuracy, recall, precision, and F-measure) in a cyber-physical testbed environment. Furthermore, our experimental results reveal that the proposed algorithm (VMD-DT) of CPADS outperforms the existing machine learning classifiers during noisy and noise-free measurements while incurring an acceptable processing overhead.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Wide ranging equation of state with Tartarus: A hybrid Green’s function/orbital based average atom code

Average atom models are widely used to make equation of state tables and for calculating other properties of materials over a wide range of conditions, from zero temperature isolated atom to fully ionized free electron gases. The numerical challenge of making these density functional theory based models work for any temperature, density or nuclear species is formidable. Here we present in detail a hybrid Green’s function/orbital based approach that has proved to be stable and accurate for wide ranging conditions. Algorithmic strategies are discussed. In particular the decomposition of the electron density into numerically advantageous parts is presented and a robust and rapid self consistent field method based on a quasi-Newton algorithm is given. Example application to the equation of state of lutetium (Z = 71) is explored in detail, including the effect of relativity, finite temperature exchange and correlation, and a comparison to a less approximate method. Furthermore, the hybrid scheme is found to be numerically stable and accurate for lutetium over at least 6 orders of magnitude in density and 5 orders of magnitude in temperature.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

Combined iterative reconstruction and image-domain decomposition for dual energy CT using total-variation regularization

Purpose: Dual-energy CT (DECT) is being increasingly used for its capability of material decomposition and energy-selective imaging. A generic problem of DECT, however, is that the decomposition process is unstable in the sense that the relative magnitude of decomposed signals is reduced due to signal cancellation while the image noise is accumulating from the two CT images of independent scans. Direct image decomposition, therefore, leads to severe degradation of signal-to-noise ratio on the resultant images. Existing noise suppression techniques are typically implemented in DECT with the procedures of reconstruction and decomposition performed independently, which do not explore the statistical properties of decomposed images during the reconstruction for noise reduction. In this work, the authors propose an iterative approach that combines the reconstruction and the signal decomposition procedures to minimize the DECT image noise without noticeable loss of resolution. Methods: The proposed algorithm is formulated as an optimization problem, which balances the data fidelity and total variation of decomposed images in one framework, and the decomposition step is carried out iteratively together with reconstruction. The noise in the CT images from the proposed algorithm becomes well correlated even though the noise of the raw projections is independent on the two CT scans. Due to this feature, the proposed algorithm avoids noise accumulation during the decomposition process. The authors evaluate the method performance on noise suppression and spatial resolution using phantom studies and compare the algorithm with conventional denoising approaches as well as combined iterative reconstruction methods with different forms of regularization. Results: On the Catphan©600 phantom, the proposed method outperforms the existing denoising methods on preserving spatial resolution at the same level of noise suppression, i.e., a reduction of noise standard deviation by one order of magnitude. This improvement is mainly attributed to the high noise correlation in the CT images reconstructed by the proposed algorithm. Iterative reconstruction using different regularization, including quadratic orq-generalized Gaussian Markov random field regularization, achieves similar noise suppression from high noise correlation. However, the proposed TV regularization obtains a better edge preserving performance. Studies of electron density measurement also show that our method reduces the average estimation error from 9.5% to 7.1%. On the anthropomorphic head phantom, the proposed method suppresses the noise standard deviation of the decomposed images by a factor of ∼14 without blurring the fine structures in the sinus area. Conclusions: The authors propose a practical method for DECT imaging reconstruction, which combines the image reconstruction and material decomposition into one optimization framework. Compared to the existing approaches, our method achieves a superior performance on DECT imaging with respect to decomposition accuracy, noise reduction, and spatial resolution.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2022

A Lagrangian dual method for two-stage robust optimization with binary uncertainties

This report presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably Benders decomposition and column-and-constraint generation, compute worst-case parameter realizations by solving mixed-integer bilinear optimization subproblems. However, their numerical solution can be computationally expensive not only due to their resulting large size after reformulating the bilinear terms, but also because decision-independent bounds on their variables are typically unknown. We propose an alternative Lagrangian dual method that circumvents these difficulties and is readily integrated in either algorithm. We specialize the method to problems where the binary parameters switch on or off constraints as these are commonly encountered in applications, and discuss extensions to problems that lack relatively complete recourse and to those with integer recourse. Numerical experiments provide evidence of significant computational improvements over existing methods.

42 ENGINEERING↗