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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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A Sparse Tableau Formulation for Node-Breaker Representations in Security-Constrained Optimal Power Flow

Realistic representations of contingencies in AC optimal power flow (ACOPF) often challenge traditional bus-branch network models. Derived from nodal analysis, such approaches represent network constraints in terms of the familiar bus admittance matrix, Ybus. A fixed Ybus is unable to represent common circuit breaker actions such as bus splitting. Work-arounds for Ybus-based analysis typically rely on topology processing, switching between different Ybus matrices depending on breaker settings. In this paper, we propose a very general node-breaker approach, employing multi-port element models and using a sparse tableau formulation (STF) for network constraints. Instead of treating breaker action as altering network topology, and hence changing the structure of Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL) equations, this approach represents a breaker’s position as impacting only constraints associated with a single component, thereby maintaining fixed structure in the KVL and KCL constraints. While larger numbers of variables are required, STF proves sparser than Ybus formulations. Numerical case studies herein demonstrate that STF provides computational efficiency comparable to a Ybus-based ACOPF at the scale of several hundred buses, and lower computational cost in an example of over one thousand buses.

Park, Byungkwon (ORCID:000000033189816X)↗
DOE OSTI2019

Benefits of Sparse Tableau Over Nodal Admittance Formulation for Power-Flow Studies

Assembly of power-flow equations has traditionally begun from a nodal analysis formulation of the underlying transmission circuit's behavior. Most power-flow formulations encapsulate network constraints in the bus admittance matrix, Y bus . From a circuit perspective, this admittance representation restricts the network elements to be voltage controlled; resulting drawbacks treating zero-impedance branches in such applications as state estimation have long been recognized. This paper explores the advantages of the alternatives to Y bus -based formulations in power flow. It proposes a sparse tableau formulation (STF), and it demonstrates its computational efficiency, robustness, and generality in detailed comparison to traditional Y bus -based solution algorithms. In the examples of power networks ranging from 1888 to 82 000 buses, computational case studies indicate that STF provides comparable computational speed, while allowing simple treatment of zero-impedance branches and more reliably converging to solutions in many cases for which Y bus -based Newton algorithms diverge.

42 ENGINEERING↗
DOE OSTI2018

Quickest Detection for Changes in Maximal kNN Coherence of Random Matrices

This paper addresses the problem of quickest detection of a change in the maximal coherence between columns of a n p random matrix based on a sequence of matrix observations having a single unknown change point. The random matrix is assumed to have identically distributed rows and the maximal coherence is defined as the largest of the ( 2 p) correlation coefficients associated with any row. Likewise the κ nearest neighbor (kNN) coherence is defined as the κ-th largest of these correlation coefficients. The forms of the preand postchange distributions of the observed matrices are assumed to belong to the family of elliptically contoured densities with sparse dispersion matrices but are otherwise unknown. A nonparametric stopping rule is proposed that is based on the maximal kNN sample coherence between columns of each observed random matrix. This is a summary statistic that is related to a test of existence of a hub vertex in a sample correlation graph having degree at least κ. Performance bounds on the delay and false alarm performance of the proposed stopping rule are obtained in the purely high-dimensional regime where p → ∞ and n is fixed. When the prechange dispersion matrix is diagonal it is shown that, among all functions of the proposed summary statistic, the proposed stopping rule is asymptotically optimal under a minimax quickest change detection model as the stopping threshold approaches infinity. Furthermore, the theory developed also applies to sequential hypothesis testing and fixed sample size tests.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2018

Domain decomposition approaches for accelerating contour integration eigenvalue solvers for symmetric eigenvalue problems

This work discusses techniques for computing a few selected eigenvalue–eigenvector pairs of large and sparse symmetric matrices. A recently developed class of techniques to solve this type of problems is based on integrating the matrix resolvent operator along a complex contour that encloses the interval containing the eigenvalues of interest. This paper considers such contour integration techniques from a domain decomposition viewpoint and proposes two schemes. The first scheme can be seen as an extension of domain decomposition linear system solvers in the framework of contour integration methods for eigenvalue problems, such as FEAST. The second scheme focuses on integrating the resolvent operator primarily along the interface region defined by adjacent subdomains. A parallel implementation of the proposed schemes is described, and results on distributed computing environments are reported. These results show that domain decomposition approaches can lead to reduced run times and improved scalability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

MFiX: Fractional-Step Method Implementation

A comprehensive, multiphase computational fluid dynamics (CFD) simulation solves several coupled transport equations including continuity, momentum, species, and energy. Chemical reactions further couple these equations through heats of reaction and rates of formation of products and rates of destruction of reactants. A fractional-step method separates changes attributed to chemical reactions from transport phenomena like convection and diffusion. When the governing equations are split into the transport and reacting components, efficient and independent methodologies can be exploited to solve the different systems. Specifically, discretization of field variable transport equations results in large, sparse matrices which are loosely coupled. These systems are solved in succession using iterative techniques that take advantage of the matrix structure. In contrast, chemical reactions tightly couple field variables locally within the domain (e.g., within a single computational cell) resulting in low dimensional but dense, nonlinear systems that are better solved using direct integration techniques.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Explicit Quantum Circuits for Block Encodings of Certain Sparse Matrices

Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding embeds a properly scaled matrix of interest A in a larger unitary transformation U that can be decomposed into a product of simpler unitaries and implemented efficiently on a quantum computer. Although quantum algorithms can potentially achieve exponential speedup in solving linear algebra problems compared to the best classical algorithm, such a gain in efficiency ultimately hinges on our ability to construct an efficient quantum circuit for the block encoding of A, which is difficult in general, and not trivial even for well structured sparse matrices. Here, in this paper, we give a few examples on how efficient quantum circuits can be explicitly constructed for some well structured sparse matrices and discuss a few strategies used in these constructions. We also provide implementations of these quantum circuits in MATLAB.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Magnetic leverage effects in amorphous SmCo/CoAlZr heterostructures

Although magnetic heterostructures are the basis of many magnetic technologies, the mechanisms involved in magnetization reversals in such structures are not fully understood, especially in amorphous multilayers. Here, we report on the SmCo/CoAlZr system and exploit resonant magnetic x-ray scattering to probe the element specific magnetization reversals. When combined into a tri-layer structure, two different switching fields and reversal mechanisms are observed for the Sm and Co sub-lattices. We argue that the decoupling of the sub-lattices arises from the local distribution of atomic species within the amorphous matrix leading to a strong magnetic leverage effect and exchange pinning. The decoupling arises due to strong interactions between regions of high Co density which span the interface. The relatively sparse interactions between Sm and Co induce a localized pinning of the Co-rich areas, resulting in an exchange bias in minor loops and an enhanced coercivity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Monaural Music Source Separation using Convolutional Sparse Coding

We present a comprehensive performance study of a new time-domain approach for estimating the components of an observed monaural audio mixture. Unlike existing time-frequency approaches that use the product of a set of spectral templates and their corresponding activation patterns to approximate the spectrogram of the mixture, the proposed approach uses the sum of a set of convolutions of estimated activations with prelearned dictionary filters to approximate the audio mixture directly in the time domain. The approximation problem can be solved by an efficient convolutional sparse coding algorithm. The effectiveness of this approach for source separation of musical audio has been demonstrated in our prior work, but under rather restricted and controlled conditions, requiring the musical score of the mixture being informed a priori and little mismatch between the dictionary filters and the source signals. In this paper, we report an evaluation that considers wider, and more practical, experimental settings. This includes the use of an audio-based multipitch estimation algorithm to replace the musical score, and an external dataset of audio single notes to construct the dictionary filters. Here, our result shows that the proposed approach remains effective with a larger dictionary, and compares favorably with the state-of-the-art nonnegative matrix factorization approach. However, in the absence of the score and in the case of a small dictionary, our approach may not be better.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Structural and electrical characterization of CoTiN metal gates

As the gate size continues to decrease in nanoscale transistors, having metal gates with amorphous or near amorphous structures can potentially reduce grain-induced work function variation. Furthermore, amorphous materials are known to have superior diffusion barrier properties, which can help prevent work function change due to the diffusion of metals in contact with the gate. In this work we show that with the addition of cobalt, thin films of polycrystalline TiN become more amorphous with a smaller grain size. Co{sub x}(TiN){sub 1-x} films, where x = 60–80%, appear to consist of nanocrystals embedded in an amorphous matrix, and are thermally stable with no significant crystallization up to an annealing temperature of at least 600 °C. Reducing the nitrogen gas flow ratio during sputter deposition from 9% to 2.5% further decreases the films' crystallinity, which is apparent by more sparse and even smaller nanocrystals. In addition to being partially amorphous, these CoTiN films also exhibit good thermal stability, low resistivity, low roughness, and have the potential for atomic layer deposition compatibility. Even though these materials are not completely amorphous, their small crystal size and amorphous matrix can potentially reduce work function variation and improve their diffusion barrier property. These properties make CoTiN a good candidate as a gate material for future nanoelectronic devices and technology.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

A GPU-based compressible combustion solver for applications exhibiting disparate space and time scales

High-speed chemically active flows pose significant computational challenges due to their disparate space and time scales, with stiff chemistry often dominating simulation time. While modern scientific computing programs achieve exascale performance by leveraging graphics processing units (GPUs), existing GPU-based compressible combustion solvers face critical limitations in memory management, load balancing, and handling the highly localized nature of chemical reactions. To this end, we present a high-performance compressible reacting flow solver built on the AMReX framework and optimized for multi-GPU settings. Here, our approach addresses three GPU performance bottlenecks: memory access patterns through column-major storage optimization, computational workload variability via a bulk-sparse integration strategy for chemical kinetics, and multi-GPU load distribution for adaptive mesh refinement applications. The solver adapts existing matrix-based chemical kinetics formulations to multi-grid contexts. Using representative combustion applications, including 2D and 3D detonations and a 3D jet-in-crossflow configuration, we demonstrate 1.4–5× performance improvements over initial implementations on an in-house cluster of NVIDIA H100 GPUs, and near-ideal weak scaling on the Frontier supercomputer (Oak Ridge Leadership Computing Facility) with up to 1024 AMD Instinct MI250X GPUs. Roofline analysis reveals substantial improvements in arithmetic intensity for both convection (∼ 10 ×) and chemistry (∼ 4 ×) routines, confirming efficient utilization of GPU memory bandwidth and computational resources.

42 ENGINEERING↗
DOE OSTI2019

O(N) Quantum Molecular Dynamics (QMD) Algorithms, Code Requirements, Release Notes, and Library Deployment

The Exascale Computing Project (ECP) Co-design Center for Particle Applications (CoPA) is addressing the challenges for particle applications to run on upcoming exascale computing architectures. This includes short- and long-range molecular dynamics (MD), particle-in-cell (PIC), and quantum molecular dynamics (QMD). This document addresses $\mathcal{O}(N)$ QMD. The goal of this CoPA team is to develop $\mathcal{O}(N)$ linear scaling methods for QMD optimized for new and next generation architectures. This will provide the capability to simulate larger systems and run for longer timeframes than is possible today. Focus is initially on the density matrix construction. This requires efficient matrix formats and linear algebra operations for distributed architectures. A significant reduction in the wallclock time for an MD timestep is necessary to achieve practical large scale QMD. Equally challenging is to develop scalable distributed implementations. This requires the exploration of efficient data formats (dense, sparse, etc.), data decomposition and distribution across compute nodes using block- and graph-based methods. Traditional programming models such as MPI/OpenMP, hybrid MPI/OpenMP/Accelerator, as well as asynchronous task-based models will be explored to achieve maximum parallelism. Parallelism at the level of a matrix operation, solver, and/or application needs to be explored to gain the most benefit on new and emerging architectures. This report serves as a “living document” of the additions and enhancements throughout the ECP CoPA project for $\mathcal{O}(N)$ QMD. The following sections address the applications we are working with, the quantum chemistry libraries (BML and PROGRESS), and our co-design exploration through the use of a proxy application.

36 MATERIALS SCIENCE↗
DOE OSTI2024

MAGMA: Enabling exascale performance with accelerated BLAS and LAPACK for diverse GPU architectures

MAGMA (Matrix Algebra for GPU and Multicore Architectures) is a pivotal open-source library in the landscape of GPU-enabled dense and sparse linear algebra computations. With a repertoire of approximately 750 numerical routines across four precisions, MAGMA is deeply ingrained in the DOE software stack, playing a crucial role in high-performance computing. Notable projects such as ExaConstit, HiOP, MARBL, and STRUMPACK, among others, directly harness the capabilities of MAGMA. In addition, the MAGMA development team has been acknowledged multiple times for contributing to the vendors’ numerical software stacks. Looking back over the time of the Exascale Computing Project (ECP), we highlight how MAGMA has adapted to recent changes in modern HPC systems, especially the growing gap between CPU and GPU compute capabilities, as well as the introduction of low precision arithmetic in modern GPUs. We also describe MAGMA’s direct impact on several ECP projects. Maintaining portable performance across NVIDIA and AMD GPUs, and with current efforts toward supporting Intel GPUs, MAGMA ensures its adaptability and relevance in the ever-evolving landscape of GPU architectures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

On the Strong Convergence of Forward-Backward Splitting in Reconstructing Jointly Sparse Signals

We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work (Daubechies et al., Pure Appl. Math. 57(11), 1413–1457, 2004), where the single vector signal can be infinite-dimensional, and (Fornasier and Rauhut, SIAM J. Numer. Anal. 46(2), 577613, 2008), which extends the aforementioned work to the joint sparse recovery of finite number of infinite-dimensional vectors. In our case, to take account of the joint sparsity and promote the coupling of nonvanishing components, we employ a convex relaxation approach with mixed norm penalty ℓ 2,1 . This paper discusses the computation of the solutions of linear inverse problems with such relaxation by a forward-backward splitting algorithm. However, since the solution matrix possesses infinitely many columns, the arguments of Daubechies et al. (Pure Appl. Math. 57(11), 1413–1457, 2004) no longer apply. As such, we establish new strong convergence results for the algorithm, in particular when the set of jointly sparse vectors is infinite.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Large-Scale Optimization with Linear Equality Constraints Using Reduced Compact Representation

For optimization problems with linear equality constraints, we prove that the (1,1) block of the inverse KKT matrix remains unchanged when projected onto the nullspace of the constraint matrix. In this work, we develop reduced compact representations of the limited-memory inverse BFGS Hessian to compute search directions efficiently when the constraint Jacobian is sparse. Orthogonal projections are implemented by a sparse QR factorization or a preconditioned LSQR iteration. In numerical experiments two proposed trust-region algorithms improve in computation times, often significantly, compared to previous implementations of related algorithms and compared to IPOPT.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Exploration with Scalable Gaussian Process Reinforcement Learning

Exploration is a challenging problem in reinforcement learning (RL), especially in environments with sparse rewards. Quantifying and utilizing the parametric uncertainty has been shown to be paramount for successful exploration [Osband et al., 2018]. Bayesian, or approximately Bayesian, methods present a principled means of estimating the parametric uncertainty in RL problems. Gaussian processes, nonparametric Bayesian models, are often impractical due to poor scalability and computational bottlenecks. We introduce a scalable Gaussian process RL (GPRL) method which directly induces sparsity in the covariance matrix to facilitate faster computation. This is a departure from previous GPRL methods which instead rely on data reduction and subsampling. We compare various covariance-based exploration techniques (Thompson sampling, upper confidence bound, and probabilistic maximum variance) which leverage our scalable GP framework in sparse reward environments. Finally, we show favorable comparison against the bootstrapped deep Q-Network.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On LPMHSS-based iteration methods for a class of weakly nonlinear systems

In this paper, for a class of the large sparse system of weakly nonlinear equations, combining separable property of the linear and nonlinear terms with the lopsided Hermitian and skew-Hermitian splitting (LHSS) of the coefficient matrix, the Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are presented. Theoretical analysis shows that these methods are locally convergent under suitable conditions. Numerical results show that both Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are feasible and effective for the large-scale system of weakly nonlinear equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

An Algebraic Multilevel Preconditioner with Low-Rank Corrections for Sparse Symmetric Matrices

In this work, we describe a multilevel preconditioning technique for solving sparse symmetric linear systems of equations. This “Multilevel Schur Low-Rank” (MSLR) preconditioner first builds a tree structure $\mathcal{T}$ based on a hierarchical decomposition of the matrix and then computes an approximate inverse of the original matrix level by level. Unlike classical direct solvers, the construction of the MSLR preconditioner follows a top-down traversal of $\mathcal{T}$ and exploits a low-rank property that is satisfied by the difference between the inverses of the local Schur complements and specific blocks of the original matrix. A few steps of the generalized Lanczos tridiagonalization procedure are applied to capture most of this difference. Numerical results are reported to illustrate the efficiency and robustness of the MSLR preconditioner with both two- and three-dimensional discretized PDE problems and with publicly available test problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Sparse, iterative simulation methods for one-dimensional laminar flames

Sparse, iterative simulation methods for one-dimensional laminar flames are proposed. The resulting steady and unsteady flame solvers exploit approximate Jacobians to greatly reduce the computational cost associated with matrix operations. The constant, non-unity Lewis number assumption is introduced to further reduce the computational cost. The solvers are also parallelized to reduce time-to-solution on distributed memory computer systems. Computed laminar flame speeds and species profiles for a range of chemical mechanisms (from 10 to 2878 species) are compared against a well-validated commercial code and are found to be consistent within solver tolerances. The computation times of both the unsteady and steady solutions increase only linearly with the number of species, which is a significant improvement over the quadratic or cubic scaling of existing steady-state flame solvers. For the largest mechanism tested, the steady-state flame solver is two orders of magnitude faster than commonly-used codes. The use of an approximate Jacobian is shown to reduce the rate of convergence for the steady-state solver, but does not significantly affect the domain of convergence. The steady-state solver with approximate Jacobian is thus well suited for computationally efficient laminar flame speed sweeps with large kinetic mechanisms.

42 ENGINEERING↗