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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Applying Technology Ranking and Systems Engineering in Advanced Life Support

According to the Advanced Life Support (ALS) Program Plan, the Systems Modeling and Analysis Project (SMAP) has two important tasks: 1) prioritizing investments in ALS Research and Technology Development (R&TD), and 2) guiding the evolution of ALS systems. Investments could be prioritized simply by independently ranking different technologies, but we should also consider a technology's impact on system design. Guiding future ALS systems will require SMAP to consider many aspects of systems engineering. R&TD investments can be prioritized using familiar methods for ranking technology. The first step is gathering data on technology performance, safety, readiness level, and cost. Then the technologies are ranked using metrics or by decision analysis using net present economic value. The R&TD portfolio can be optimized to provide the maximum expected payoff in the face of uncertain future events. But more is needed. The optimum ALS system can not be designed simply by selecting the best technology for each predefined subsystem. Incorporating a new technology, such as food plants, can change the specifications of other subsystems, such as air regeneration. Systems must be designed top-down starting from system objectives, not bottom-up from selected technologies. The familiar top-down systems engineering process includes defining mission objectives, mission design, system specification, technology analysis, preliminary design, and detail design. Technology selection is only one part of systems analysis and engineering, and it is strongly related to the subsystem definitions. ALS systems should be designed using top-down systems engineering. R&TD technology selection should consider how the technology affects ALS system design. Technology ranking is useful but it is only a small part of systems engineering.

Jones, Harry↗
DOE OSTI2023

Computing rank‐revealing factorizations of matrices stored out‐of‐core

This paper describes efficient algorithms for computing rank-revealing factorizations of matrices that are too large to fit in main memory (RAM), and must instead be stored on slow external memory devices such as disks (out-of-core or out-of-memory). Traditional algorithms for computing rank-revealing factorizations (such as the column pivoted QR factorization and the singular value decomposition) are very communication intensive as they require many vector-vector and matrix-vector operations, which become prohibitively expensive when data is not in RAM. Randomization allows to reformulate new methods so that large contiguous blocks of the matrix are processed in bulk. The paper describes two distinct methods. The first is a blocked version of column pivoted Householder QR, organized as a “left-looking” method to minimize the number of the expensive write operations. The second method results employs a UTV factorization. It is organized as an algorithm-by-blocks to overlap computations and I/O operations. As it incorporates power iterations, it is much better at revealing the numerical rank. Numerical experiments on several computers demonstrate that the new algorithms are almost as fast when processing data stored on slow memory devices as traditional algorithms are for data stored in RAM.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Bayesian tensorized neural networks with automatic rank selection

Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is a challenging task due to the difficulty of choosing a proper tensor rank. In order to address this challenge, this paper proposes a low-rank Bayesian tensorized neural network. Our Bayesian method performs automatic model compression via an adaptive tensor rank determination. We also present approaches for posterior density calculation and maximum a posteriori (MAP) estimation for the end-to-end training of our tensorized neural network. Here, we provide experimental validation on a two-layer fully connected neural network, a 6-layer CNN and a 110-layer residual neural network where our work produces 7.4x to 137x more compact neural networks directly from the training while achieving high prediction accuracy.

Low-rank tensor↗
DOE OSTI2022

A low-rank power iteration scheme for neutron transport criticality problems

Computing effective eigenvalues for neutron transport often requires a fine numerical resolution. Here, the main challenge of such computations is the high memory effort of classical solvers, which limits the accuracy of chosen discretizations. In this work, we derive a method for the computation of effective eigenvalues when the underlying solution has a low-rank structure. This is accomplished by utilizing dynamical low-rank approximation (DLRA), which is an efficient strategy to derive time evolution equations for low-rank solution representations. The main idea is to interpret the iterates of the classical inverse power iteration as pseudo-time steps and apply the DLRA concepts in this framework. In our numerical experiment, we demonstrate that our method significantly reduces memory requirements while achieving the desired accuracy. Analytic investigations show that the proposed iteration scheme inherits the convergence speed of the inverse power iteration, at least for a simplified setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Incorporating uncertainty for enhanced leaderboard scoring and ranking in data competitions

Data competitions have become a popular and cost-effective approach for crowdsourcing versatile solutions from diverse expertise. Current practice relies on the simple leaderboard scoring based on a given set of competition data for ranking competitors and distributing the prize. However, a disadvantage of this practice in many competitions is that a slight difference in the scores due to the natural variability of the observed data could result in a much larger difference in the prize amounts. In this article, we propose a new strategy to quantify the uncertainty in the rankings and scores from using different data sets that share common characteristics with the provided competition data. By using a bootstrap approach to generate many comparable data sets, the new method has four advantages over current practice. Furthermore, during the competition, it provides a mechanism for competitors to get feedback about the uncertainty in their relative ranking. After the competition, it allows the host to gain a deeper understanding of the algorithm performance and their robustness across representative data sets. It also offers a transparent mechanism for prize distribution to reward the competitors more fairly with superior and robust performance. Finally, it has the additional advantage of being able to explore what results might have looked like if competition goals evolved from their original choices. The implementation of the strategy is illustrated with a real data competition hosted by Topcoder on urban radiation search.

42 ENGINEERING↗
DOE OSTI2022

Factorization of Binary Matrices: Rank Relations, Uniqueness and Model Selection of Boolean Decomposition

The application of binary matrices are numerous. Representing a matrix as a mixture of a small collection of latent vectors via low-rank decomposition is often seen as an advantageous method to interpret and analyze data. In this work, we examine the factorizations of binary matrices using standard arithmetic (real and nonnegative) and logical operations (Boolean and $\mathbb{Z}$ 2 ). We examine the relationships between the different ranks, and discuss when factorization is unique. In particular, we characterize when a Boolean factorization X = W$\land$H has a unique W, a unique H (for a fixed W), and when both W and H are unique, given a rank constraint. We introduce a method for robust Boolean model selection, called BMFk, and show on numerical examples that BMFk not only accurately determines the correct number of Boolean latent features but reconstruct the pre-determined factors accurately.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2021

Seasonal Disorder in Urban Traffic Patterns: A Low Rank Analysis

This article proposes several advances to sparse nonnegative matrix factorization (SNMF) as a way to identify large-scale patterns in urban traffic data. The input to our model is traffic counts organized by time and location. Nonnegative matrix factorization additively decomposes this information, organized as a matrix, into a linear sum of temporal signatures. Penalty terms encourage this factorization to concentrate on only a few temporal signatures, with weights which are not too large. Our interest here is to quantify and compare the regularity of traffic behavior, particularly across different broad temporal windows. In addition to the rank and error, we adapt a measure introduced by Hoyer to quantify sparsity in the representation. Combining these, we construct several curves which quantify error as a function of rank (the number of possible signatures) and sparsity; as rank goes up and sparsity goes down, the approximation can be better and the error should decreases. Plots of several such curves corresponding to different time windows leads to a way to compare disorder/order at different time scalewindows. In this paper, we apply our algorithms and procedures to study a taxi traffic dataset from New York City. In this dataset, we find weekly periodicity in the signatures, which allows us an extra framework for identifying outliers as significant deviations from weekly medians. We then apply our seasonal disorder analysis to the New York City traffic data and seasonal (spring, summer, winter, fall) time windows. We do find seasonal differences in traffic order.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A ranking methodology for the coupling of pressurized water nuclear reactors and molten salt thermal energy storage

Thermal energy storage (TES) systems are a proposed solution to electricity market demand fluctuations and can be coupled to nuclear power plants to enable load following. Here, this work focuses on developing a methodology for evaluating potential designs for integrating a TES system into an existing pressurized water nuclear power plant. The proposed ranking methodology allows a group of experts to postulate and weigh designs based on ranking criteria derived from literature. The methodology developed in this study can aid in the final selection of a TES design for an existing nuclear power plant. The same process could be used to analyze other TES and nuclear reactor designs. The determined optimum design from this methodology was to place the TES system after the steam generator and to utilize the steam generated from the nuclear power plant to heat a molten salt TES unit. Another conclusion of this research was that human bias is prevalent during design selection, and actions such as standardized ranking criteria and large groups of experts should be used to minimize this error.

25 ENERGY STORAGE↗
DOE OSTI2021

A Ranked-Orbital Approach to Select Active Spaces for High-Throughput Multireference Computation

The past decade has seen a great increase in the application of high-throughput computation to a variety of important problems in chemistry. However, one area which has been resistant to the high-throughput approach is multireference wave function methods, in large part due to the technicalities of setting up these calculations and in particular the not always intuitive challenge of active space selection. As we look toward a future of applying high-throughput computation to all areas of chemistry, it is important to prepare these methods for large-scale automation. Here, we propose a ranked-orbital approach to select active spaces with the goal of standardizing multireference methods for high-throughput computation. This method allows for the meaningful comparison of different active space selection schemes and orbital localizations, and we demonstrate the utility of this approach across 1120 multireference calculations for the excitation energies of small molecules. Our results reveal that it is helpful to distinguish the method used to generate orbitals from the method of ranking orbitals in terms of importance for the active space. Additionally, we propose our own orbital ranking scheme that estimates the importance of an orbital for the active space through a pair-interaction framework from orbital energies and features of the Hartree–Fock exchange matrix. Here, we call this new scheme the “approximate pair coefficient” (APC) method and we show that it performs quite well for the test systems presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Low-rank Sachdev-Ye-Kitaev models

Motivated by recent proposals of experimental realization of fast scramblers, we study a family of solvable variants of the ($\textit{q}$ = 4) Sachdev-Ye-Kitaev model in which the rank and eigenvalue distribution of the coupling matrix $J_{ ij,kl}$ are tuneable. When the rank is proportional to the number of fermions, the low temperature behavior is sensitive to the eigenvalue distribution. We obtain a complete classification of the possible non-Fermi liquid quantum phases. These include two previously studied phases whose fermion scaling dimension depends continuously on the rank; we show that they are maximally chaotic, but necessitate an extensively degenerate or negative semidefinite coupling matrix. In this work, more generic distributions give rise to “almost Fermi liquids” with a scaling dimension Δ = 1/2, but which differ from a genuine Fermi liquid in quasiparticle decay rate, quantum Lyapunov exponent, and/or specific heat.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

PLANC: Parallel Low-rank Approximation with Nonnegativity Constraints

In this work, we consider the problem of low-rank approximation of massive dense nonnegative tensor data, for example, to discover latent patterns in video and imaging applications. As the size of data sets grows, single workstations are hitting bottlenecks in both computation time and available memory. We propose a distributed-memory parallel computing solution to handle massive data sets, loading the input data across the memories of multiple nodes, and performing efficient and scalable parallel algorithms to compute the low-rank approximation. We present a software package called Parallel Low-rank Approximation with Nonnegativity Constraints, which implements our solution and allows for extension in terms of data (dense or sparse, matrices or tensors of any order), algorithm (e.g., from multiplicative updating techniques to alternating direction method of multipliers), and architecture (we exploit GPUs to accelerate the computation in this work). We describe our parallel distributions and algorithms, which are careful to avoid unnecessary communication and computation, show how to extend the software to include new algorithms and/or constraints, and report efficiency and scalability results for both synthetic and real-world data sets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Sampling-based Sublinear Low-rank Matrix Arithmetic Framework for Dequantizing Quantum Machine Learning

We present an algorithmic framework for quantum-inspired classical algorithms on close-to-low-rank matrices, generalizing the series of results started by Tang’s breakthrough quantum-inspired algorithm for recommendation systems [STOC’19]. Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gilyén et al. [STOC’19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions. Our results give compelling evidence that in the corresponding QRAM data structure input model, quantum SVT does not yield exponential quantum speedups. Since the quantum SVT framework generalizes essentially all known techniques for quantum linear algebra, our results, combined with sampling lemmas from previous work, suffice to generalize all prior results about dequantizing quantum machine learning algorithms. In particular, our classical SVT framework recovers and often improves the dequantization results on recommendation systems, principal component analysis, supervised clustering, support vector machines, low-rank regression, and semidefinite program solving. We also give additional dequantization results on low-rank Hamiltonian simulation and discriminant analysis. Our improvements come from identifying the key feature of the quantum-inspired input model that is at the core of all prior quantum-inspired results: ℓ 2 -norm sampling can approximate matrix products in time independent of their dimension. We reduce all our main results to this fact, making our exposition concise, self-contained, and intuitive.

Computer Science↗
DOE OSTI2025

Evaluation of data driven low-rank matrix factorization for accelerated solutions of the Vlasov equation

Low-rank methods have shown success in accelerating simulations of a collisionless plasma described by the Vlasov equation, but still rely on computationally costly linear algebra every time step. We propose a data-driven factorization method using artificial neural networks, specifically with convolutional layer architecture, that trains on existing simulation data. At inference time, the model outputs a low-rank decomposition of the distribution field of the charged particles, and we demonstrate that this step is faster than the standard linear algebra technique. Numerical experiments show that the method achieves comparable reconstruction accuracy for interpolation tasks, generalizing to unseen test data in a manner beyond just memorizing training data; patterns in factorization also inherently followed the same numerical trend as those within algebraic methods (e.g., truncated singular-value decomposition). However, when training on the first 70% of a time-series data and testing on the remaining 30%, the method fails to meaningfully extrapolate. Despite this limiting result, the technique may have benefits for simulations in a statistical steady-state or otherwise showing temporal stability. These results suggest that while the model offers a computationally efficient alternative for datasets with temporal stability, its current formulation is best suited for interpolation rather than for predicting future states in time-evolving systems. This study thus lays the groundwork for further refinement of neural network-based approaches to low-rank matrix factorization in high-dimensional plasma simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry

We propose nonabelian higher-rank gauge theories in 2+1D and 3+1D. The gauge group is constructed from the volume-preserving diffeomorphisms of space. We show that the intriguing physics of the lowest Landau level (LLL) limit can be interpreted as the consequences of the symmetry. We derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term within our formalism. Using the gauge symmetry in 2+1D, we derive the LLL effective action of vortex crystal in rotating Bose gas as well as Wigner crystal of electron in an applied magnetic field. We show that the nonlinear sigma models of ferromagnets in 2+1D and 3+1D exhibit the higher-rank gauge symmetries that we introduce in this paper. We interpret the fractonic behavior of the excitations on the lowest Landau level and of skyrmions in ferromagnets as the consequence of the higher-rank gauge symmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Quality Ranking of Unary Fluoride Salt Property Data in MSTDB-TP

Molten salt reactor developers rely on thermal property data to design, license and operate the reactors they are developing. The Molten Salt Thermal Database-Thermophysical Properties (MSTDB-TP) is being developed under the DOE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program and managed by Oak Ridge National Laboratory. The MSTDB-TP is intended to serve as a single source of measured thermophysical property values for a wide variety of molten salt systems available to researchers, molten salt reactor developers, and regulators. These properties include melting and boiling points, heat capacity, density, viscosity and thermal diffusivity and conductivity. Published measurements of molten salt properties are lacking for many salts and the data that are available are often inconsistent. This creates a challenge for MSR developers in determining which property values to select when designing their reactors. The MSDTDB-TP collects all available property data and down-selects to preferred data sets or correlations. It is the purpose of this work to apply a recently developed ranking system that indicates the quality of property values listed in the database to inform decisions about how to use the available data. Quality assessments and rankings are being applied to data in MSTDB-TP to provide an indication of the quality of the data available. A previous report detailed the ranking system that was followed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1972

Methods of computing vocabulary size for the two-parameter rank distribution

A summation method is described for computing the vocabulary size for given parameter values in the 1- and 2-parameter rank distributions. Two methods of determining the asymptotes for the family of 2-parameter rank-distribution curves are also described. Tables are computed and graphs are drawn relating paris of parameter values to the vocabulary size. The partial product formula for the Riemann zeta function is investigated as an approximation to the partial sum formula for the Riemann zeta function. An error bound is established that indicates that the partial product should not be used to approximate the partial sum in calculating the vocabulary size for the 2-parameter rank distribution.

Edmundson, H. P.↗
NASA NTRS1983

First-ranked galaxies in groups

A statistical analysis of five group catalogs shows that the B(0) magnitudes of first-ranked group members are consistent with a statistical model in which the luminosities of all group members are drawn from the same distribution. As in the Hickson compact groups, indications are that first-ranked group members are only rarely the products of distinctive evolutionary processes. Distance-dependent selection effects can introduce spurious correlations among group parameters which may appear to support environment-dependent evolution of the first-ranked group members.

Geller, M. J.↗