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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
DOE OSTI2019

Distribution System State Estimation: A Semidefinite Programming Approach

Distribution system state estimation (DSSE) is one of the vital components in the next-generation distribution management system which allows operators to monitor the entire system's operating conditions. Due to the lack of real-time measurements, DSSE has to process measurements whose quality varies significantly across different sources, which causes a convergence issue to the Gauss-Newton solver. In this paper, a semidefinite programming (SDP) framework is proposed to reformulate the DSSE problem into a rank- constrained SDP problem. One challenge of this technique is the nonconvex rank-one constraint, which is generally relaxed. However, the relaxed SDP-DSSE problem cannot guarantee a rank-one solution and hence loses optimality. Therefore, we propose two solution approaches to obtain rank-one solutions for the SDPDSSE problem: the rank reduction approach and the convex iteration approach. The model and the effectiveness of the proposed solution approaches are numerically demonstrated on the IEEE 13-bus, 34-bus, and 123-bus distribution systems.

convex iteration↗
DOE OSTI2019

Sparse low rank approximation of potential energy surfaces with applications in estimation of anharmonic zero point energies and frequencies

We introduce a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing . The method is useful for studies involving large numbers of PES evaluations, such as the search for local minima, transition states, or integration. We apply this method for estimating zero point energies and frequencies of molecules using a three step approach. In the first step, we interpret the PES as a sparse tensor on polynomial basis and determine its entries by a compressed sensing based algorithm using only a few PES evaluations. Then, we establish a rank reduction strategy to compress this tensor in a suitable low-rank canonical tensor format using standard tensor compression tools. This allows representing a high dimensional PES as a small sum of products of one dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate the product of sparse canonical low-rank representation of PES and Green’s function in the second-order diagrammatic vibrational many-body Green’s function theory (XVH2) for estimation of zero-point energies and frequencies. Numerical tests on molecules considered in this work indicate a more efficient scaling of computational cost with molecular size as compared to other methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Low rank approximation in simulations of quantum algorithms

Simulating quantum algorithms on classical computers is challenging when the system size, i.e., the number of qubits used in the quantum algorithm, is moderately large. However, some quantum algorithms and the corresponding quantum circuits can be simulated efficiently on a classical computer if the input quantum state is a low rank tensor and all intermediate states of the quantum algorithm can be represented or approximated by low rank tensors. Here, in this paper, we examine the possibility of simulating a few quantum algorithms by using low-rank canonical polyadic (CP) decomposition to represent the input and all intermediate states of these algorithms. Two rank reduction algorithms are used to enable efficient simulation. We show that some of the algorithms preserve the low rank structure of the input state and can thus be efficiently simulated on a classical computer. However, the rank of the intermediate states in other quantum algorithms can increase rapidly, making efficient simulation more difficult. To some extent, such difficulty reflects the advantage or superiority of a quantum computer over a classical computer. As a result, understanding the low rank structure of a quantum algorithm allows us to identify algorithms that can benefit significantly from quantum computers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Sparsity of the electron repulsion integral tensor using different localized virtual orbital representations in local second-order Møller–Plesset theory

Utilizing localized orbitals, local correlation theory can reduce the unphysically high system-size scaling of post-Hartree–Fock (post-HF) methods to linear scaling in insulating molecules. The sparsity of the four-index electron repulsion integral (ERI) tensor is central to achieving this reduction. For second-order Møller–Plesset theory (MP2), one of the simplest post-HF methods, only the (ia|jb) ERIs are needed, coupling occupied orbitals i, j and virtuals a, b. In this paper, we compare the numerical sparsity (called the “ragged list”) and two other approaches revealing the low-rank sparsity of the ERI. The ragged list requires only one set of (localized) virtual orbitals, and we find that the orthogonal valence virtual-hard virtual set of virtuals originally proposed by Subotnik et al. gives the sparsest ERI tensor. To further compress the ERI tensor, the pair natural orbital (PNO) type representation uses different sets of virtual orbitals for different occupied orbital pairs, while the occupied-specific virtual (OSV) approach uses different virtuals for each occupied orbital. Here, our results indicate that while the low-rank PNO representation achieves significant rank reduction, it also requires more memory than the ragged list. The OSV approach requires similar memory to that of the ragged list, but it involves greater algorithmic complexity. An approximation (called the “fixed sparsity pattern”) for solving the local MP2 equations using the numerically sparse ERI tensor is proposed and tested to be sufficiently accurate and to have highly controllable error. A low-scaling local MP2 algorithm based on the ragged list and the fixed sparsity pattern is therefore promising.

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

Fast Computational Algorithms for Partial Differential Equations and Uncertainty Quantifications

This project concerned the construction, testing and analysis of computational algorithms for solving parameterized and stochastic partial differential equations. The study and understanding of equations of this type is of fundamental importance in numerous engineering and scientific applications. Examples include simulation of plasma dynamics in models of electric propulsion and nuclear fusion, simulation of multiphase flows, such as the flow of water, gas and oil in reservoirs, and structural analysis of the dependence of structures on materials. Parametrization is used in such settings when properties of the models such as viscosity of fluids or electric resistivity of materials are not precisely understood and instead are treated as random variables. The resulting solutions are themselves random, and having such solutions will enable engineers to use probabilistic methods to assess the likelihood of events, for example, whether a pollutant in a liquid will exceed a limit, and to use such analyses to develop ways to ensure positive outcomes. Construction of accurate (high resolution) computational solutions is expensive, requiring significant computer time and computational resources, and there is need to reduce computational cost to make simulation useful and effective. The aim of the project was to construct algorithms to efficiently compute surrogate solutions to parameterized problems to allow for efficient and accurate simulation. The technical approach used focused on two related strategies, based on rank-reduction methods and reduced-order models. These methods construct surrogate solutions of parameter-dependent models by projection or interpolation into low-dimensional approximation spaces. Cost savings are achieved if the low-dimensional spaces can be identified and constructed efficiently and if the resulting low-dimensional algebraic systems can be solved cheaply. Accomplishments include: Theoretical and empirical demonstration of the effectiveness of fast multigrid solution strategies for computing low-rank representations of parameter-dependent solutions to discrete partial differential equations, including the first proof establishing so-called textbook convergence properties for low-rank methods. Development of efficient solution algorithms for solving nonlinear parameter-dependent partial differential equations used in models of fluid dynamics. Developent of efficient algorithms for low-rank representation of solutions of time-dependent simulations of fluid dynamics using multi-dimensional tensor representations of solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

TeraChem: Accelerating electronic structure and ab initio molecular dynamics with graphical processing units

Developed over the past decade, TeraChem is an electronic structure and ab initio molecular dynamics software package designed from the ground up to leverage graphics processing units (GPUs) to perform large-scale ground and excited state quantum chemistry calculations in the gas and the condensed phase. TeraChem’s speed stems from the reformulation of conventional electronic structure theories in terms of a set of individually optimized high-performance electronic structure operations (e.g., Coulomb and exchange matrix builds, one- and two-particle density matrix builds) and rank-reduction techniques (e.g., tensor hypercontraction). Recent efforts have encapsulated these core operations and provided language-agnostic interfaces. Finally, this greatly increases the accessibility and flexibility of TeraChem as a platform to develop new electronic structure methods on GPUs and provides clear optimization targets for emerging parallel computing architectures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Strong-Weak Duality via Jordan-Wigner Transformation: Using Fermionic Methods for Strongly Correlated su(2) Spin Systems

The Jordan-Wigner transformation establishes a duality between $su(2)$ and fermionic algebras. We present qualitative arguments and numerical evidence that when mapping spins to fermions, the transformation makes strong correlation weaker, as demonstrated by the Hartree-Fock approximation to the transformed Hamiltonian. This result can be rationalized in terms of rank reduction of spin shift terms when transformed to fermions. Conversely, the mapping of fermions to qubits makes strong correlation stronger, complicating its solution when one uses qubit-based correlators. The presence of string operators poses challenges to the implementation of quantum chemistry methods on classical computers, but these can be dealt with using established techniques of low computational cost. Here, our proof of principle results for XXZ and J1-J2 Heisenberg (in 1D and 2D) indicate that the JW transformed fermionic Hamiltonian has reduced complexity in key regions of their phase diagrams, and provides a better starting point for addressing challenging spin problems.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1989

Statistical retrieval of precipitation cell-top altitude using passive 118-GHz observations

A nonlinear statistical-retrieval operator for precipitation cell-top altitude using high-spatial-resolution passive 118-GHz O2 brightness spectra is demonstrated. The retrieval operator consists of a Karhunen-Loeve transformation followed by a rank reduction, a linearization, and a linear minimum mean-square-error estimator. Information from the 118-GHz data on the ambient atmospheric-temperature profile and the precipitation cell size is also incorporated into the linear stage of the retrieval operator. The rms retrieval error is 1.5 km for cumulus-stage cells with tops ranging from 1.5 to 16 km. The sensitivity of nadiral 118-GHz spectra to the cell-top altitude is predominantly due to the scattering and absorption of radiation originating from low, warm atmospheric levels by colder liquid and frozen precipitation This effect causes cold perturbations in the brightness spectrum, which typically become stronger with increasing cell-top altitude.

Gasiewski, A. J.↗
DOE OSTI2024

A Low-Rank QTT-based Finite Element Method for Elasticity Problems

We present an efficient and robust numerical algorithm for solving the linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve the linear elasticity problem on a computational domain that is more general than a square. By integrating Z-ordering and subdomain concatenation, our method substantially decreases memory usage and achieves a notable reduction in rank compared to established Finite Element implementations like the FEniCS platform. This efficiency is maintained while still guaranteeing exponential convergence with respect to the number of degrees of freedom. This performance gain, however, requires a fundamental rethinking of how core finite element operations are implemented. This includes changes to mesh discretization, node and degree of freedom ordering, stiffness matrix and internal nodal force assembly, and the execution of algebraic matrix-vector operations. In this work, we discuss all these aspects in detail and assess the method’s performance in the numerical approximation of three representative test cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A flexible class of priors for orthonormal matrices with basis function-specific structure

Statistical modeling of high-dimensional matrix-valued data motivates the use of a low-rank representation that simultaneously summarizes key characteristics of the data and enables dimension reduction. Low-rank representations commonly factor the original data into the product of orthonormal basis functions and weights, where each basis function represents an independent feature of the data. However, the basis functions in these factorizations are typically computed using algorithmic methods that cannot quantify uncertainty or account for basis function correlation structure a priori. While there exist Bayesian methods that allow for a common correlation structure across basis functions, empirical examples motivate the need for basis function-specific dependence structure. We propose a prior distribution for orthonormal matrices that can explicitly model basis function-specific structure. The prior is used within a general probabilistic model for singular value decomposition to conduct posterior inference on the basis functions while accounting for measurement error and fixed effects. We discuss how the prior specification can be used for various scenarios and demonstrate favorable model properties through synthetic data examples. Finally, we apply our method to two-meter air temperature data from the Pacific Northwest, enhancing our understanding of the Earth system’s internal variability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Efficient Application of the Factorized form of the Unitary Coupled-Cluster Ansatz for the Variational Quantum Eigensolver Algorithm by Using Linear Combination of Unitaries

The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons with relatively low-depth circuits, which are otherwise difficult to solve on classical computers. The variational eigenstate is constructed from a number of factorized unitary coupled-cluster terms applied onto an initial (single-reference) state. Current algorithms for applying one of these operators to a quantum state require a number of operations that scale exponentially with the rank of the operator. We exploit a hidden SU(2) symmetry to allow us to employ the linear combination of unitaries approach, Our Prepare subroutine uses n+2 ancilla qubits for a rank-n operator. Our Select (U) scheme uses O(n) Cnot gates. This results in a full algorithm that scales like the cube of the rank of the operator n 3 , a significant reduction in complexity for rank five or higher operators. This approach, when combined with other algorithms for lower-rank operators (when compared to the standard implementation), will make the factorized form of the unitary coupled-cluster approach much more efficient to implement on all types of quantum computers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Online randomized interpolative decomposition with a posteriori error estimator for temporal PDE data reduction

Traditional low-rank approximation is a powerful tool for compressing large data matrices that arise in simulations of partial differential equations (PDEs), but suffers from high computational cost and requires several passes over the PDE data. The compressed data may also lack interpretability thus making it difficult to identify feature patterns from the original data. Here, to address these issues, we present an online randomized algorithm to compute the interpolative decomposition (ID) of large-scale data matrices in situ. Compared to previous randomized IDs that used the QR decomposition to determine the column basis, we adopt a streaming ridge leverage score-based column subset selection algorithm that dynamically selects proper basis columns from the data and thus avoids an extra pass over the data to compute the coefficient matrix of the ID. In particular, we adopt a single-pass error estimator based on the non-adaptive Hutch++ algorithm to provide real-time error approximation for determining the best coefficients. As a result, our approach only needs a single pass over the original data and thus is suitable for large and high-dimensional matrices stored outside of core memory or generated in PDE simulations. A strategy to improve the accuracy of the reconstructed data gradient, when desired, within the ID framework is also presented. We provide numerical experiments on turbulent channel flow and ignition simulations, and on the NSTX Gas Puff Image dataset, comparing our algorithm with the offline ID algorithm to demonstrate its utility in real-world applications.

Column subset selection↗
NASA NTRS1975

Oxygen reduction of several gold alloys in 1-molar potassium hydroxide

With rotated disk-and-ring equipment, polarograms and other electrochemical measurements were made of oxygen reduction in 1-molar potassium hydroxide on an equiatomic gold-copper (Au-Cu) alloy and a Au-Cu alloy doped with either indium (In) or cobalt (Co) and on Au doped with either nickel (Ni) or platinum (Pt). The results were compared with those for pure Au and pure Pt. The two-electron reaction dominated on all Au alloys as it did on Au. The polarographic results at lower polarization potentials were compared, assuming exclusively a two-step reduction. A qualified ranking of cathodic electrocatalytic activity on the freshly polished reduced disks was indicated: anodized Au Au-Cu-In Au-Cu Au-Cu-Co is equivalent or equal to Au-Pt Au-Ni. Aging in distilled water improved the electrocatalytic efficiency of Au-Cu-Co, Au-Cu, and (to a lesser extent) Au-Cu-In.

Miller, R. O.↗
NASA NTRSDate not supplied

Using the System Complexity Metric (SCM) to Compare CO2 Reduction Systems

A fundamental cause of difficulty in large engineering projects is their inherent complexity. An impression of complexity occurs if a system is simply difficult to understand, where there is no obvious mental model that correctly predicts its behavior. Higher system complexity is usually associated with higher cost and higher failure rate. Complexity is perceived if a system has many diverse components, multiple interactions and feedback loops, transients and dynamic behavior, and unanticipated failure modes. Identifying and removing these signs of complexity should improve performance and reduce the cost and failure rate. Complexity can be directly measured by the number of components and their interactions. The System Complexity Metric (SCM) is defined as the sum of the number of parts in a system, N, plus the number of the one-way interconnections between them, I. SCM = N + I. The SCM is easily determined by direct inspection of the system block diagram. SCM can be used to compare systems and to guide their redesign to reduce cost and failure rate. Carbon dioxide reduction systems are analyzed using SCM, cost, and failure rate. As in previous work, cost is directly proportional to SCM and that failure rate increases as a power of SCM for large differences in SCM. The SCM ranking of carbon dioxide reduction systems is the same as their ranking in detailed analysis and practice.

Harry W. Jones↗
DOE OSTI2024

Random projection using random quantum circuits

The random sampling task performed by Google's Sycamore processor gave us a glimpse of the “quantum supremacy era.” This has definitely shed some light on the power of random quantum circuits in this abstract task of sampling outputs from the (pseudo)random circuits. In this paper, we explore a practical near-term use of local random quantum circuits in dimensional reduction of large low-rank data sets. We make use of the well-studied dimensionality reduction technique called the random projection method. This method has been extensively used in various applications such as image processing, logistic regression, entropy computation of low-rank matrices, etc. We prove that the matrix representations of local random quantum circuits with sufficiently shorter depths [ ∼ O ( n ) ] serve as good candidates for random projection. We demonstrate numerically that their projection abilities are not far off from the computationally expensive classical principal components analysis on MNIST and CIFAR-100 image datasets. We also benchmark the performance of quantum random projection against the commonly used classical random projection in the tasks of dimensionality reduction of image data sets and computing von Neumann entropies of large low-rank density matrices. And finally, using variational quantum singular value decomposition, we demonstrate a near-term implementation of extracting the singular vectors with dominant singular values after quantum random projecting a large low-rank matrix to lower dimensions. All such numerical experiments unequivocally demonstrate the ability of local random circuits to randomize a large Hilbert space at sufficiently shorter depths with robust retention of properties of large data sets in reduced dimensions. Published by the American Physical Society 2024

Kumaran, Keerthi (ORCID:0009000949125721)↗
NASA NTRS2000

Comparison of Pilots' Situational Awareness While Monitoring Autoland Approaches Using Conventional and Advanced Flight Display Formats

A simulation experiment was performed to assess situation awareness (SA) and workload of pilots while monitoring simulated autoland operations in Instrument Meteorological Conditions with three advanced display concepts: two enhanced electronic flight information system (EFIS)-type display concepts and one totally synthetic, integrated pictorial display concept. Each concept incorporated sensor-derived wireframe runway and iconic depictions of sensor-detected traffic in different locations on the display media. Various scenarios, involving conflicting traffic situation assessments, main display failures, and navigation/autopilot system errors, were used to assess the pilots' SA and workload during autoland approaches with the display concepts. From the results, for each scenario, the integrated pictorial display concept provided the pilots with statistically equivalent or substantially improved SA over the other display concepts. In addition to increased SA, subjective rankings indicated that the pictorial concept offered reductions in overall pilot workload (in both mean ranking and spread) over the two enhanced EFIS-type display concepts. Out of the display concepts flown, the pilots ranked the pictorial concept as the display that was easiest to use to maintain situational awareness, to monitor an autoland approach, to interpret information from the runway and obstacle detecting sensor systems, and to make the decision to go around.

Kramer, Lynda J.↗
DOE OSTI2026

CORE-BFS: Communication-Optimized REctangular-partitioned BFS Achieving 160.845 TeraTEPS on Frontier Supercomputer

Distributed Breadth-First Search (BFS) is fundamental to many large-scale graph applications, but its performance on parallel systems is often limited by high communication overhead. This paper presents CORE-BFS, an extremely scalable GPU-based BFS implementation that introduces a unique rectangular 2D partitioning-based design for Frontier supercomputer. To further improve performance, we propose four key optimizations: (1) Rectangular 2D-partition specific data formats that use two compressed row and one compressed column status array bitmaps combined with a Double Compressed Sparse Row (DCSR) format per partition, reducing memory footprint and inter-rank traffic; (2) Adaptive frontier & communication strategy that unifies top-down and bottom-up traversal on the rectangular layout, uses lazy synchronization in top-down levels, and switches variants based on frontier size to minimize communication overhead; (3) Frontier-split degree-aware update that maps frontier vertices to thread-centric, wavefront-centric, and block-centric kernels based on their degree to improve GPU utilization and memory coalescing; (4) Row-reduction pipeline that overlaps bottom-up adjacency list processing with row-wise bitmap reduction to hide inter-rank latency. Together, these techniques increase parallelism while reducing memory and communication overhead. On the Graph500 benchmark, CORE - BFS scales up to 9,248 Frontier nodes with scale-42 graphs and reaches 160.845 TTEPS, delivering a 5.42 × speedup over our previous Frontier implementation.

Yang, Haoshen [Rutgers University]↗