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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 631 records · Page 35
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NASA NTRSDate not supplied

Application of an Affine Nonlinear Galerkin Reduced-order Model to Compressible Fluid Flows

Galerkin reduced-order models (ROMs) often struggle to accurately capture multiscale fluid physics in challenging flow regimes such as flows experiencing compressibility effects. This in part stems from the global nature of both the basis construction problem and the spectral formulation itself. In this work, a multi-basis ROM is developed in an affine space based on proper orthogonal decomposition (POD) by projecting the full Navier-Stokes equations expressed in terms of the specific volume, velocity, and pressure primitive variables. The model is applied to high-fidelity numerical simulation datasets obtained for a canonical compressible flow configuration: the flow over a backward facing step at different subsonic Mach numbers. It is observed that application of an eigenvalue reassignment (ER) stabilization method is required to avoid early divergence of the ROM predictions for this configuration in the three Mach numbers tested. The sensitivity of the POD-ROM results to the choice of parameters in the stabilization algorithm is discussed.

reduced-order model↗
DOE OSTI2024

Computing Sparse Tensor Decompositions via Chapel and C++/MPI Interoperability without Intermediate I/O

We extend an existing approach for efficient use of shared mapped memory across Chapel and C++ for graph data stored as 1-D arrays to sparse tensor data stored using a combination of 2-D and 1-D arrays. We describe the specific extensions that provide use of shared mapped memory tensor data for a particular C++ tensor decomposition tool called GentenMPI. We then demonstrate our approach on several real-world datasets, providing timing results that illustrate minimal overhead incurred using this approach. Finally, we extend our work to improve memory usage and provide convenient random access to sparse shared mapped memory tensor elements in Chapel, while still being capable of leveraging high performance implementations of tensor algorithms in C++.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Bayesian Tensor Decompositions for Scalable Supervised Learning of Scientific Data (Final Report)

In this document we highlight the detailed accomplishments and progress that we have made in this period. This progress seeks to address the three main objectives to provide new algorithms for quantifying uncertainty in low-multilinear-rank models and to leverage them for data analysis. These include: (1) develop probabilistic models for low-multilinear-rank functions; (2) develop a suite of Bayesian learning approaches to learn the probabilistic models from data; (3) apply the techniques on challenging problems arising in DOE-relevant applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Globally Optimizing QAOA Circuit Depth for Constrained Optimization Problems

We develop a global variable substitution method that reduces n-variable monomials in combinatorial optimization problems to equivalent instances with monomials in fewer variables. We apply this technique to 3-SAT and analyze the optimal quantum unitary circuit depth needed to solve the reduced problem using the quantum approximate optimization algorithm. For benchmark 3-SAT problems, we find that the upper bound of the unitary circuit depth is smaller when the problem is formulated as a product and uses the substitution method to decompose gates than when the problem is written in the linear formulation, which requires no decomposition.

3-SAT↗
DOE OSTI2023

Stochastic quantum Krylov protocol with double-factorized Hamiltonians

Here we propose a class of randomized quantum Krylov diagonalization (rQKD) algorithms capable of solving the eigenstate estimation problem with modest quantum resource requirements. Compared to previous real-time evolution quantum Krylov subspace methods, our approach expresses the time evolution operator e –i$\widehat{H}$$\tau$ as a linear combination of unitaries and subsequently uses a stochastic sampling procedure to reduce circuit depth requirements. While our methodology applies to any Hamiltonian with fast-forwardable subcomponents, we focus on its application to the explicitly double-factorized electronic-structure Hamiltonian. To demonstrate the potential of the proposed rQKD algorithm on near-term quantum devices, we provide numerical benchmarks for a variety of molecular systems with circuit-based state-vector simulators including the effects of sampling noise, achieving ground-state energy errors of less than 1 kcal mol -1 with circuit depths orders of magnitude shallower than those required for low-rank deterministic Trotter-Suzuki decompositions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1988

Parallel algorithms for mapping pipelined and parallel computations

Many computational problems in image processing, signal processing, and scientific computing are naturally structured for either pipelined or parallel computation. When mapping such problems onto a parallel architecture it is often necessary to aggregate an obvious problem decomposition. Even in this context the general mapping problem is known to be computationally intractable, but recent advances have been made in identifying classes of problems and architectures for which optimal solutions can be found in polynomial time. Among these, the mapping of pipelined or parallel computations onto linear array, shared memory, and host-satellite systems figures prominently. This paper extends that work first by showing how to improve existing serial mapping algorithms. These improvements have significantly lower time and space complexities: in one case a published O(nm sup 3) time algorithm for mapping m modules onto n processors is reduced to an O(nm log m) time complexity, and its space requirements reduced from O(nm sup 2) to O(m). Run time complexity is further reduced with parallel mapping algorithms based on these improvements, which run on the architecture for which they create the mappings.

Nicol, David M.↗
DOE OSTI2019

Scalable Extended Dynamic Mode Decomposition Using Random Kernel Approximation

The Koopman operator is a linear, infinite-dimensional operator that governs the dynamics of system observables; extended dynamic mode decomposition (EDMD) is a data-driven method for approximating the Koopman operator using functions (features) of the system state snapshots. This paper investigates an approach to EDMD in which the features used provide random approximations to a particular kernel function. The objective of this is computational economy for large data sets: EDMD is generally ill-suited for problems with large state dimension, and its dual kernel formulation (KDMD) is well-suited for such problems only if the number of data snapshots is relatively small. We discuss two specific methods for generating features: random Fourier features and the Nÿstrom method. The first method is a data-independent method for translation-invariant kernels only and involves random sampling in feature space; the second method is a data-dependent empirical method that may be used for any kernel and involves random sampling of data. We first discuss how these ideas may be applied in an EDMD context, as well as a means for adaptively adding random Fourier features. As a result, we demonstrate these methods on two example problems and conclude with an analysis of the relative benefits and drawbacks of each method.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Development of Building Design Optimization Methodology: Residential Building Applications

Building design optimization is a highly complex problem, requiring long computational running processes because of the many options that exist when a building is being designed. This paper introduces an integrated approach through which to perform this optimization within an acceptable time frame. The approach includes the methods of variable selection, model simplification, and a sequential optimization process. Using singular value decomposition, a large number of design variables is reduced to a smaller subset that can be solved more quickly through the optimization algorithm. To expedite the variable selection process, a modeling approach that quickly simulates annual energy consumption was developed to replace full annual energy simulations. The developed methodology was applied to two residential buildings in the US, and the results are discussed herein. To assess the accuracy of the integrated optimization methodology, the optimized life cycle costs are compaa variables demonstrating the strongest contributions in the optimization study were identified. The proposed methodology significantly shortened the time requirements for the optimization processes of the two case studies by 74% and 84%; the optimized life cycle costs were within 0.05% and 0.06%, respectively, of the optimum point.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2013

RUSHMAPS: Real-Time Uploadable Spherical Harmonic Moment Analysis for Particle Spectrometers

RUSHMAPS is a new onboard data reduction scheme that gives real-time access to key science parameters (e.g. moments) of a class of heliophysics science and/or solar system exploration investigation that includes plasma particle spectrometers (PPS), but requires moments reporting (density, bulk-velocity, temperature, pressure, etc.) of higher-level quality, and tolerates a lowpass (variable quality) spectral representation of the corresponding particle velocity distributions, such that telemetry use is minimized. The proposed methodology trades access to the full-resolution velocity distribution data, saving on telemetry, for real-time access to both the moments and an adjustable-quality (increasing quality increases volume) spectral representation of distribution functions. Traditional onboard data storage and downlink bandwidth constraints severely limit PPS system functionality and drive cost, which, as a consequence, drives a limited data collection and lower angular energy and time resolution. This prototypical system exploit, using high-performance processing technology at GSFC (Goddard Space Flight Center), uses a SpaceCube and/or Maestro-type platform for processing. These processing platforms are currently being used on the International Space Station as a technology demonstration, and work is currently ongoing in a new onboard computation system for the Earth Science missions, but they have never been implemented in heliospheric science or solar system exploration missions. Preliminary analysis confirms that the targeted processor platforms possess the processing resources required for realtime application of these algorithms to the spectrometer data. SpaceCube platforms demonstrate that the target architecture possesses the sort of compact, low-mass/power, radiation-tolerant characteristics needed for flight. These high-performing hybrid systems embed unprecedented amounts of onboard processing power in the CPU (central processing unit), FPGAs (field programmable gate arrays), and DSP (digital signal processing) elements. The fundamental computational algorithm de constructs 3D velocity distributions in terms of spherical harmonic spectral coefficients (which are analogous to a Fourier sine-cosine decomposition), but uses instead spherical harmonics Legendre polynomial orthogonal functions as a basis for the expansion, portraying each 2D angular distribution at every energy or, geometrically, spherical speed-shell swept by the particle spectrometer. Optionally, these spherical harmonic spectral coefficients may be telemetered to the ground. These will provide a smoothed description of the velocity distribution function whose quality will depend on the number of coefficients determined. Successfully implemented on the GSFC-developed processor, the capability to integrate the proposed methodology with both heritage and anticipated future plasma particle spectrometer designs is demonstrated (with sufficiently detailed design analysis to advance TRL) to show specific science relevancy with future HSD (Heliophysics Science Division) solar-interplanetary, planetary missions, sounding rockets and/or CubeSat missions.

Figueroa-Vinas, Adolfo↗
DOE OSTI2018

Benchmarking treewidth as a practical component of tensor network simulations

Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on the tensor ranks and the order in which they are contracted. Unfortunately, computing optimal contraction sequences (orderings) in general is known to be a computationally difficult (NP-complete) task. In 2005, Markov and Shi showed that optimal contraction sequences correspond to optimal (minimum width) tree decompositions of a tensor network’s line graph, relating the contraction sequence problem to a rich literature in structural graph theory. While treewidth-based methods have largely been ignored in favor of dataset-specific algorithms in the prior tensor networks literature, we demonstrate their practical relevance for problems arising from two distinct methods used in quantum simulation: multi-scale entanglement renormalization ansatz (MERA) datasets and quantum circuits generated by the quantum approximate optimization algorithm (QAOA). We exhibit multiple regimes where treewidth-based algorithms outperform domain-specific algorithms, while demonstrating that the optimal choice of algorithm has a complex dependence on the network density, expected contraction complexity, and user run time requirements. We further provide an open source software framework designed with an emphasis on accessibility and extendability, enabling replicable experimental evaluations and future exploration of competing methods by practitioners.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Consistent coupling algorithms for coupled core-edge simulations of plasma turbulence

Two schemes for coupling gyrokinetic simulations of microturbulence in tokamaks are proposed. The first scheme is based on an additive Schwarz domain decomposition. In this work, we show that, because the goal of turbulence is long-time averages of the dynamics rather than temporal accuracy, the iteration to self-consistency across domains, which is typically required by Schwarz schemes, can be avoided, thereby accelerating the computation. Second, we propose a coupling scheme that relies entirely on the addition of source terms, leaving the boundary conditions arbitrary. The practical motivations for such a scheme are discussed, and forms of the source terms that ensure consistency and stability are derived. The schemes are tested on a nonlinear, one-dimensional model problem, and the first scheme is further tested on the Hasegawa–Wakatani model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory

With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple (bosonic and fermionic) quantum numbers with non-trivial functional coefficients. In particular, we analyze diagonalization of Hamiltonian terms using a singular-value decomposition technique, and discuss how the achieved diagonal unitaries in the digitized time-evolution operator can be implemented. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions, for which a complete quantum-resource analysis within different computational models is presented. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories. The example chosen further demonstrates the importance of adopting efficient theoretical formulations: it is shown that an explicitly gauge-invariant formulation using loop, string, and hadron degrees of freedom simplifies the algorithms and lowers the cost compared with the standard formulations based on angular-momentum as well as the Schwinger-boson degrees of freedom. The loop-string-hadron formulation further retains the non-Abelian gauge symmetry despite the inexactness of the digitized simulation, without the need for costly controlled operations. Such theoretical and algorithmic considerations are likely to be essential in quantumly simulating other complex theories of relevance to nature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Toward the Minimal Floating Operation Count Cholesky Decomposition of Electron Repulsion Integrals

As quantum chemistry calculations deal with molecular systems of increasing size, the memory requirement to store electron-repulsion integrals (ERIs) greatly outpaces the physical memory available in computing hardware. Here, the Cholesky decomposition of ERIs provides a convenient yet accurate technique to reduce the storage requirement of integrals. Recent developments of a two-step algorithm have drastically reduced the memory operation (MOP) count, leaving the floating operation (FLOP) count as the last frontier of cost reduction in the Cholesky ERI algorithm. In this report, we introduce a dynamic integral tracking, reusing, and compression/elimination protocol embedded in the two-step Cholesky ERI method. Benchmark studies suggest that this technique becomes particularly advantageous when the basis set consists of many computationally expensive high-angular-momentum basis functions. With this dynamic ERI improvement, the Cholesky ERI approach proves to be a highly efficient algorithm with minimal FLOP and MOP count.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2000

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Shu, Chi-Wang↗
DOE OSTI2021

Multi-Area Model-Free State Estimation via Distributed Tensor Decomposition

This paper proposes a model-free method for distribution system state estimation based on tensor completion using canonical polyadic decomposition. In particular, we consider a setting where the network is divided into multiple areas. The measured physical quantities at buses located in the same area are processed by an area controller. A third-order tensor is constructed to collect these measured quantities. The measurements are analyzed locally to recover the full state information of the network. A closed-form iterative algorithm based on the alternating direction method of multipliers is developed to obtain the low-rank factors of the whole network state tensor where information exchange happens only between neighboring areas. To demonstrate the efficacy of the developed algorithm, numerical simulations are carried out using an IEEE test system.

alternating direction method of multipliers↗
NASA NTRS1992

Sub-band/transform compression of video sequences

The progress on compression of video sequences is discussed. The overall goal of the research was the development of data compression algorithms for high-definition television (HDTV) sequences, but most of our research is general enough to be applicable to much more general problems. We have concentrated on coding algorithms based on both sub-band and transform approaches. Two very fundamental issues arise in designing a sub-band coder. First, the form of the signal decomposition must be chosen to yield band-pass images with characteristics favorable to efficient coding. A second basic consideration, whether coding is to be done in two or three dimensions, is the form of the coders to be applied to each sub-band. Computational simplicity is of essence. We review the first portion of the year, during which we improved and extended some of the previous grant period's results. The pyramid nonrectangular sub-band coder limited to intra-frame application is discussed. Perhaps the most critical component of the sub-band structure is the design of bandsplitting filters. We apply very simple recursive filters, which operate at alternating levels on rectangularly sampled, and quincunx sampled images. We will also cover the techniques we have studied for the coding of the resulting bandpass signals. We discuss adaptive three-dimensional coding which takes advantage of the detection algorithm developed last year. To this point, all the work on this project has been done without the benefit of motion compensation (MC). Motion compensation is included in many proposed codecs, but adds significant computational burden and hardware expense. We have sought to find a lower-cost alternative featuring a simple adaptation to motion in the form of the codec. In sequences of high spatial detail and zooming or panning, it appears that MC will likely be necessary for the proposed quality and bit rates.

Sauer, Ken↗
DOE OSTI2021

Examination of Semi-Analytical Solution Methods in the Coarse Operator of Parareal Algorithm for Power System Simulation

With continuing advances in high-performance parallel computing platforms, parallel algorithms have become powerful tools for development of faster than real-time power system dynamic simulations. In particular, it has been demonstrated in recent years that parallel-in-time (Parareal) algorithms have the potential to achieve such an ambitious goal. Here, the selection of a fast and reasonably accurate coarse operator of the Parareal algorithm is crucial for its effective utilization and performance. This paper examines semi-analytical solution (SAS) methods as the coarse operators of the Parareal algorithm and explores performance of the SAS methods to the standard numerical time integration methods. Two promising time-power series-based SAS methods were considered; Adomian decomposition method and Homotopy analysis method with a windowing approach for improving the convergence. Numerical performance case studies on 10-generator 39-bus system and 327-generator 2383-bus system were performed for these coarse operators over different disturbances, evaluating the number of Parareal iterations, computational time, and stability of convergence. All the coarse operators tested with different scenarios have converged to the same corresponding true solution (if they are convergent) and the SAS methods provide comparable computational speed, while having more stable convergence to the true solution in many cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Quantified Differentiation of Surface Topography for Nano-materials As-Obtained from Atomic Force Microscopy Images

Surface texture is an important issue to realize the nature (crest and trough) of surfaces. Atomic force microscopy (AFM) image is a key analysis for surface topography. However, in nano-scale, the nature (i.e., deflection or crack) as well as quantification (i.e., height or depth) of deposited layers is essential information for material scientist. In this paper, a gradient-based K-means algorithm is used to differentiate the layered surfaces depending on their color contrast of as-obtained from AFM images. A transformation using wavelet decomposition is initiated to extract the information about deflection or crack on the material surfaces from the same images. Z-axis depth analysis from wavelet coefficients provides information about the crack present in the material. Using the above method corresponding surface information for the material is obtained. In addition, the Gaussian filter is applied to remove the unwanted lines, which occurred during AFM scanning. Few known samples are taken as input, and validity of the above approaches is shown.

77 NANOSCIENCE AND NANOTECHNOLOGY↗