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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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At least 91 records · Page 5
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DOE OSTI2018

On Two Algorithms of Wavelet Decomposition for Spaces of Linear Splines

The purpose of this paper is to construct new types of wavelets for minimal splines on an irregular grid. The approach applied to construct spline-wavelet decompositions uses approximation relations as an initial structure for constructing the spaces of minimal splines. The advantages of this approach are the possibilities of using irregular grids and sufficiently arbitrary nonpolynomial spline-wavelets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Scalable algorithms for domain decomposition of Monte Carlo neutral particle transport simulations on unstructured mesh

Monte Carlo simulations are the gold standard in particle transport simulations, for shielding and nuclear reactor simulations Full core simulations can require terabytes of memory for tracking pin-resolved (up to 50k pins), nuclide (200 tracked), axial (20-200 zones) reaction rates Domain decomposition, splitting the calculation and the memory storage, among several nodes is challenging as it involves communication of particles across domain boundaries We created a new MOOSE application, MaCaw, to study this problem Algorithms developed for ray tracing in MOOSE were adapted for simulating neutral particle transport Physics and tally routines in OpenMC, dynamically linked, are called from the application

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms

The computational capabilities of near-term quantum computers are limited by the noisy execution of gate operations and a limited number of physical qubits. Hybrid variational algorithms are well-suited to near-term quantum devices because they allow for a wide range of tradeoffs between the amount of quantum and classical resources used to solve a problem. This paper investigates tradeoffs available at both the algorithmic and hardware levels by studying a specific case – applying the Quantum Approximate Optimization Algorithm (QAOA) to instances of the Maximum Independent Set (MIS) problem. We consider three variants of the QAOA which offer different tradeoffs at the algorithmic level in terms of their required number of classical parameters, quantum gates, and iterations of classical optimization needed. Since MIS is a constrained combinatorial optimization problem, the QAOA must respect the problem constraints. This can be accomplished by using many multi-controlled gate operations which must be decomposed into gates executable by the target hardware. We study the tradeoffs available at this hardware level, combining the gate fidelities and decomposition efficiencies of different native gate sets into a single metric called the gate decomposition cost .

Tomesh, Teague↗
DOE OSTI2021

Big Data For Operation and Maintenance Cost Reduction

The purpose of this research is to develop a first-of-a-kind framework for integrating Big Data capability into the daily activities of our current fleet of nuclear power plants. Big Data is traditionally defined as data sets with high volume, velocity, and heterogeneity, and the existing Big Data analytics capabilities are now widely popular in fields such as finance, weather, e-commerce, healthcare and sports. In the nuclear industry, while the volume and velocity of data may present computational challenges for existing analytics capabilities, data heterogeneity are seen to present the major challenge. This research project mainly focuses on incorporating the wide range of data heterogeneities in nuclear power plants into an integrated Big Data Analytics capability. The primary end-product of this project is a Big Data framework that is capable of dealing with the large volume and heterogeneity of the data found in nuclear power plants to extract timely and valuable information on equipment performance. The framework can generate system insights that are actionable relations between measurable impacts and the corresponding maintenance action plans and enable optimization of plant operation and maintenance based on the extracted information. The developed framework is capable of handling heterogeneous data including both image data and time-series sensor data. Specifically, this developed framework includes the following components. The first component is an overarching maintenance ontology which includes system insights required by maintenance optimization. The maintenance ontology interacts with other components in the developed framework. The second component handles Piping & Instrumentation Diagram (P&ID) data. It can be used to extract system components and their relations automatically from the P&IDs. This extracted information is stored in the first component, i.e., maintenance ontology, and is also used as input to the third component, i.e., a tool for generating the fault tree for the corresponding system. The generated fault tree in turn is stored in the ontology for assessing risk that is used as a criterion in maintenance policy optimization. The fourth component is a tool for inferring the parameters in the Markov degradation model for a nuclear system. It uses basic information from the ontology. The fifth component is a tool for assessing the degradation level using sensor measurement data, for example, pressure, flowrate. This tool can be used for determining corrective maintenance actions. The results obtained from components four and five are returned to the ontology. The sixth component of the framework is a tool for optimizing the maintenance policy for a nuclear system of interest. It takes certain basic information from the ontology, e.g., costs of maintenance actions and system failures, as input, and returns the optimal maintenance policy to the ontology. This tool can be used for determining predictive maintenance actions. A set of experiments have also been conducted to verify the algorithms developed in this project for nuclear system degradation monitoring. The experiments are based on four solenoid valves, similar to the ones used in nuclear power plants. The analyses based on the experimental data using two algorithms, i.e., the Randomized Window Decomposition (RWD) algorithm and the particle filtering algorithm, and the results are introduced in the report. The Big Data framework developed in this project can be used as a support tool in daily activities of plant operation and maintenance and will reduce current costs while maintaining or improving safety levels. Overall, the project will not only benefit existing reactors, however it will open new frontiers to realize the long overdue value of Big Data Analytics in the nuclear sphere.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

A low-communication, parallel algorithm for solving PDEs based on range decomposition

This work proposes a new, low-communication algorithm for solving PDEs on massively parallel computers. The range decomposition (RD) algorithm exposes coarse-grain parallelism by applying nested iteration and adaptive mesh refinement locally before performing a global communication step. Just a few such steps are observed to be sufficient to obtain accuracy within a small multiple of discretization error. The target applications are petascale and exascale machines, where hierarchical parallelism is required and traditional parallel numerical PDE communication patterns are costly because of message latency. The RD algorithm uses a partition of unity to equally distribute the error, and thus, the work. The computational advantages of this approach are that the decomposed problems can be solved in parallel without any communication until the partitioned solutions are summed. This offers potential advantages in the paradigm of expensive communication but very cheap computation. This paper introduces the method and explains the details of the communication step. Two performance models are developed, showing that the latency cost associated with a traditional parallel implementation of nested iteration is proportional to log(P) 2 , whereas the RD method reduces the communication latency to log(P), while maintaining similar bandwidth costs. Numerical results for two problems, Laplace and advection diffusion, demonstrate the enhanced performance, and a heuristic argument explains why the method converges quickly.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Compression of tokamak boundary plasma simulation data using a maximum volume algorithm for matrix skeleton decomposition

This report demonstrates satisfactory data compression of SOLPS-ITER simulation output ranging from 2D fields, 1D profiles, and 0D scalar variables with a novel matrix decomposition approach. The singular value decomposition (SVD) scales poorly for large matrix sizes and is unsuited to the application on high dimensional data common to fusion plasma physics simulation. In this work, we employ the columns-submatrix-rows (CUR) matrix factorization technique in order to compute a low-rank approximation up to two orders of magnitude faster than the SVD, but within a nominal L2-norm relative error of ε = 10 –2 . In addition, the CUR approach maintains the original format of the data, in its extracted columns and rows, allowing for interpretable data storage at the original resolution of the simulation. We utilize an iterative algorithm to compute the CUR decomposition of simulation output by maximizing the volume, or linearly independent information content, of a low-rank submatrix contained within the data. Experiments over $\textit{n} × \textit{n}$ randomized test matrices with embedded rank-deficient features show that this maximum volume implementation of CUR matrix approximation has reduced asymptotic computational complexity on the order of n compared to the SVD, which scales approximately as $n^3$. These results show that the CUR technique can be used to effectively select time step snapshots (columns) of over 140 SOLPS-ITER output variables and the associated discretized coordinate timeseries (rows) allowing for reconstruction of the complete simulation dynamics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

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↗
DOE OSTI2025

Randomized Algorithms for Low-Rank Matrix and Tensor Decompositions

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality reduction, such as the singular value decomposition (SVD) or interpolative (ID) and CUR decompositions. Recent advances in randomized dimensionality reduction are discussed, including new methods of fast matrix sketching and sampling techniques, which are incorporated into classical matrix algorithms for fast low-rank matrix approximations. The extension of randomized matrix algorithms to tensors is then explored for several low-rank tensor decompositions in the CP and Tucker formats, including the higher-order SVD, ID, and CUR decomposition.

Pearce, Katherine J. [The University of Texas at A↗
DOE OSTI2018

Adaptive Wavelet Decomposition of Matrix Flows

Adaptive algorithms for constructing spline-wavelet decompositions of matrix flows from a linear space of matrices over a normed field are presented. The algorithms suggested provides for an a priori prescribed estimate of the deviation of the basic flow from the initial one. Comparative bounds of the volumes of data in the basic flow for various irregularity characteristics of the initial flow are obtained in the cases of pseudo-equidistant and adaptive grids. Limit characteristics of the above-mentioned volumes are given in the cases where the initial flow is generated by differentiable functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Hierarchical Distributed Optimal Power Flow of HV and MV Distribution Networks With Continuous and Discrete Devices

With large-scale distributed photovoltaics (PVs) being integrated into distribution networks (DNs), coordinated optimal power flow (OPF) of high voltage (HV) and medium voltage (MV) DNs should be investigated to optimally dispatch the distributed PVs and other network devices. Here, this paper presents a hierarchical distributed OPF method for HV and MV DNs with on-load tap changers, reactive power compensators, feeder switches and distributed PVs. A hierarchical master-slave control architecture is applied to implement coordinated OPF of two-layer DNs. The HV master problem and MV subproblems are transformed into mixed-integer convex problems respectively with second order cone programming and LinDistFlow approximation. Since there is no efficient distributed algorithm to solve such OPF models with integer subproblems, a novel distributed algorithm is proposed in this paper to efficiently solve the hierarchical coordinated OPF model with integer subproblems in a distributed manner. In the proposed algorithm, the coordinated OPF model is solved in a branch-and-bound framework, where in each branch node generalized Benders decomposition (GBD) algorithm is applied to decompose the coordinated OPF model into a master problem and relaxed subproblems and solves them iteratively to get optimal solution. The GBD optimal and feasible cutting planes generated in a branch node are proved to be valid for its descendants. Moreover, three acceleration techniques are introduced into the proposed algorithm to improve computational efficiency. Finally, the effectiveness and accuracy of the proposed method are verified via simulation tests in Jinzhai DNs of China.

42 ENGINEERING↗
DOE OSTI2017

A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems

Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton–Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Randomized algorithms for generalized singular value decomposition with application to sensitivity analysis

The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential sensitivity analysis (HDSA), in this work we propose new randomized algorithms for computing the GSVD which use randomized subspace iteration and weighted QR factorization. Detailed error analysis is given which provides insight into the accuracy of the algorithms and the choice of the algorithmic parameters. We demonstrate the performance of our algorithms on test matrices and a large-scale model problem where HDSA is used to study subsurface flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Autonomous Polycrystalline Material Decomposition For Hyperspectral Neutron Tomography

Hyperspectral neutron tomography is an effective method for analyzing crystalline material samples with complex compositions in a non-destructive manner. Since the counts in the hyperspectral neutron radiographs directly depend on the neutron cross-sections, materials may exhibit contrasting neutron responses across wavelengths. Therefore, it is possible to extract the unique signatures associated with each material and use them to separate the crystalline phases simultaneously.We introduce an autonomous material decomposition (AMD) algorithm to automatically characterize and localize polycrystalline structures using Bragg edges with contrasting neutron responses from hyperspectral data. The algorithm estimates the linear attenuation coefficient spectra from the measured radiographs and then uses these spectra to perform polycrystalline material decomposition and reconstructs 3D material volumes to localize materials in the spatial domain. Our results demonstrate that the method can accurately estimate both the linear attenuation coefficient spectra and associated reconstructions on both simulated and experimental neutron data.

Samin nur chowdhury, Mohammad↗
DOE OSTI2015

Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme

Here, we study convergence of the integral transport matrix method (ITMM) based on a parallel block Jacobi (PBJ) iterative strategy for solving particle transport problems. The ITMM is a spatial domain decomposition method proposed for massively parallel computations. AFourier analysis of the PBJ-based iterations applied to SN diamond-difference equations in 1D slab and 2D Cartesian geometries is performed. It is carried out for infinite-medium problems with homogeneous material properties. To analyze the performance of the ITMM with the PBJ algorithm and evaluate its potential in scalability we consider a limiting case of one spatial cell per subdomain. The analysis shows that in such limit the spectral radius of the iteration method is one without regard to values of the scattering ratio and optical thickness of the spatial cells. This implies lack of convergence in infinite medium. Numerical results of finite-medium problems are presented. They demonstrate effects of finite size of spatial domain on the performance of the iteration algorithm as well as its asymptotic behavior when the extent of the spatial domain increases. Finally, these numerical experiments also show that for finite domains iterative convergence to a finite criterion is achievable in a multiple of the sum of number of cells in each dimension.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models

While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based methods that further reduce this computational complexity by approximating such terms with a much smaller dimension. The goal of this work is to introduce the points selection algorithm developed by Shin and Xiu as a hyper-reduction method. The selection algorithm was originally proposed as a stochastic collocation method for uncertainty quantification. Since the algorithm aims at maximizing a quantity $\mathcal{S}$ that measures both the column orthogonality and the determinant, we refer to the algorithm as S-OPT. Numerical examples are provided to demonstrate the performance of S-OPT and to compare its performance with a gappy proper orthogonal decomposition (POD) algorithm. Here, we found that using the S-OPT algorithm is shown to predict the full order solutions with higher accuracy than gappy POD especially when the number of sampling points is small, although we note that S-OPT shows slow asymptotic convergence with respect to the number of samples for some applications, e.g., Lagrangian hydrodynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

AUTONOMOUS GAUSSIAN DECOMPOSITION

We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.

79 ASTRONOMY AND ASTROPHYSICS↗