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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Grover-QAOA for 3-SAT: quadratic speedup, fair-sampling, and parameter clustering

Abstract The SAT problem is a prototypical NP-complete problem of fundamental importance in computational complexity theory with many applications in science and engineering; as such, it has long served as an essential benchmark for classical and quantum algorithms. This study shows numerical evidence for a quadratic speedup of the Grover Quantum Approximate Optimization Algorithm (G-QAOA) over random sampling for finding all solutions to 3-SAT (All-SAT) and Max-SAT problems. G-QAOA is less resource-intensive and more adaptable for these problems than Grover’s algorithm, and it surpasses conventional QAOA in its ability to sample all solutions. We show these benefits by classical simulations of many-round G-QAOA on thousands of random 3-SAT instances. We also observe G-QAOA advantages on the IonQ Aria quantum computer for small instances, finding that current hardware suffices to determine and sample all solutions. Interestingly, a single-angle-pair constraint that uses the same pair of angles at each G-QAOA round greatly reduces the classical computational overhead of optimizing the G-QAOA angles while preserving its quadratic speedup. We also find parameter clustering of the angles. The single-angle-pair protocol and parameter clustering significantly reduce obstacles to classical optimization of the G-QAOA angles.

Zhang, Zewen (ORCID:000000032258613X)↗
NASA NTRS1980

Improved local linearization algorithm for solving the quaternion equations

The objective of this paper is to develop a new and more accurate local linearization algorithm for numerically solving sets of linear time-varying differential equations. Of special interest is the application of this algorithm to the quaternion rate equations. The results are compared, both analytically and experimentally, with previous results using local linearization methods. The new algorithm requires approximately one-third more calculations per step than the previously developed local linearization algorithm; however, this disadvantage could be reduced by using parallel implementation. For some cases the new algorithm yields significant improvement in accuracy, even with an enlarged sampling interval. The reverse is true in other cases. The errors depend on the values of angular velocity, angular acceleration, and integration step size. One important result is that for the worst case the new algorithm can guarantee eigenvalues nearer the region of stability than can the previously developed algorithm.

Yen, K.↗
NASA NTRS2022

Optimal Estimation Framework for Ocean Color Atmospheric Correction and Pixel-level Uncertainty Quantification

Ocean color remote sensing requires compensation for atmospheric scattering and absorption (aerosol, Rayleigh, and trace gases), referred to as atmospheric correction (AC). AC allows inference of parameters such as spectrally resolved remote sensing reflectance ( R rs )(λ) ; sr 1 ) at the ocean surface from the top-of-atmosphere reflectance. Often, the uncertainty of this process is not fully explored. Bayesian inference techniques provide a simultaneous AC and uncertainty assessment via a full posterior distribution of the relevant variables, given the prior distribution of those variables and the radiative transfer (RT) likelihood function. Given uncertainties in the algorithm inputs, the Bayesian framework enables better constraints on the AC process by using the complete spectral information compared to traditional approaches that use only a subset of bands for AC. This paper investigates a Bayesian inference research method (Optimal Estimation, OE) for ocean color AC by simultaneously retrieving atmospheric and ocean properties using all visible and near-infrared spectral bands. The OE algorithm analytically approximates the posterior distribution of parameters based on normality assumptions and provides a potentially viable operational algorithm with a reduced computational expense. We developed a Neural Network (NN) RT forward model look-up-table-based emulator to increase algorithm efficiency further and thus speed up the likelihood computations. We then applied the OE algorithm to synthetic data and observations from the MODerate resolution Imaging Spectroradiometer (MODIS) on NASA’s Aqua spacecraft. We compared the R rs )(λ) retrieval and its uncertainty estimates from the OE method with in-situ validation data from the SeaWiFS Bio-optical Archive and Storage System (SeaBASS) and Aerosol Robotic Network Ocean Color (AERONET-OC) datasets. The OE algorithm improved R rs )(λ) estimates relative to the NASA standard operational algorithm by improving all statistical metrics at 443, 555, and 667 nm. Unphysical negative R rs )(λ) , which often appear in complex water conditions, was reduced by a factor of 3. The OE-derived pixel-level R rs )(λ) uncertainty estimates were also assessed relative to in-situ data and were shown to have skill.

Atmospheric correction↗
NASA NTRSDate not supplied

Optimization Algorithms as Quantum Performance Benchmarks

Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing (QA) have the potential to demonstrate significant run-time performance benefits over current state-of-the-art solutions. Using existing methods for characterizing classical optimization algorithms, we analyze solution quality obtained by solving Max-Cut problems using a quantum annealing device and gate-model quantum simulators and devices. This is used to guide the development of an advanced benchmarking framework for quantum computers designed to evaluate the trade-off between run-time execution performance and the solution quality for iterative hybrid quantum-classical applications. The framework generates performance profiles through effective visualizations that show performance progression as a function of time for various problem sizes and illustrates algorithm limitations uncovered by the benchmarking approach. The framework is an enhancement to the existing open-source QED-C Application-Oriented Benchmark suite and can connect to the open-source analysis libraries. The suite can be executed on various quantum simulators and quantum hardware systems.

benchmarking↗
NASA NTRS1983

Monotone implicit algorithms for the small-disturbance and full potential equations applied to transonic flows

Numerical calculations of transonic flows by potential equations typically use algorithms that change the method of calculation for regions of subsonic and supersonic flow. In this paper, implicit approximate-factorization algorithms are modified to use the monotonic switch in the type of finite-differencing that was developed by Godunov for the Euler equations. Calculations of flows over airfoils by these algorithms are compared with calculations by other methods that are in common usage. For the small-disturbance potential equation, comparisons are made with the Murman-Cole method and the monotone method of Engquist and Osher for both steady and unsteady flows. For the full potential equation, comparisons are made with the methods of Jameson and of Holst and Ballhaus for steady flows. The comparisons show that the monotone methods are more stable. For steady flows, solutions are obtained for cases where the Murman-Cole switch requires a time step over ten times smaller in order for the calculations to remain stable. These improvements are achieved with no increase in computer storage and only minor modifications in current codes.

Goorjian, P. M.↗
NASA NTRS1992

Performance and state-space analyses of systems using Petri nets

The goal of any modeling methodology is to develop a mathematical description of a system that is accurate in its representation and also permits analysis of structural and/or performance properties. Inherently, trade-offs exist between the level detail in the model and the ease with which analysis can be performed. Petri nets (PN's), a highly graphical modeling methodology for Discrete Event Dynamic Systems, permit representation of shared resources, finite capacities, conflict, synchronization, concurrency, and timing between state changes. By restricting the state transition time delays to the family of exponential density functions, Markov chain analysis of performance problems is possible. One major drawback of PN's is the tendency for the state-space to grow rapidly (exponential complexity) compared to increases in the PN constructs. It is the state space, or the Markov chain obtained from it, that is needed in the solution of many problems. The theory of state-space size estimation for PN's is introduced. The problem of state-space size estimation is defined, its complexities are examined, and estimation algorithms are developed. Both top-down and bottom-up approaches are pursued, and the advantages and disadvantages of each are described. Additionally, the author's research in non-exponential transition modeling for PN's is discussed. An algorithm for approximating non-exponential transitions is developed. Since only basic PN constructs are used in the approximation, theory already developed for PN's remains applicable. Comparison to results from entropy theory show the transition performance is close to the theoretic optimum. Inclusion of non-exponential transition approximations improves performance results at the expense of increased state-space size. The state-space size estimation theory provides insight and algorithms for evaluating this trade-off.

Watson, James Francis, III↗
NASA NTRS2003

Luminous Binary Supersoft X-Ray Sources

We have made remarkable progress in the study of luminous supersoft X-ray sources during the past year. We have begun to discover a population of ultraluminous SSSs (e.g., in NGC 300 [Kong & Di Stefano 20031 as well as in Ml0l [Di Stefano & Kong 2003]), which may be accreting intermediate-mass (50-100 solar mass) black holes. This work follows from an algorithm we have developed (Di Stefano & Kong 2003) to identify SSSs in external galaxies, selecting them from among each galaxy s total population of X-ray sources. We have applied the algorithm to approximately one dozen galaxies and will make it public after it has been published in its entirety. Through our own application of the algorithm, we have discovered SSSs in every galaxy, mapping their spatial distribution, to obtain important clues to their fundamental natures. We have discovered that there is a large population of X-ray sources which are slightly hotter (100-250 eV) than standard SSSs. Some of these may be accreting BHs with masses between roughly 50 anf 100 solar masses. To explore this possibility, we are working on theoretical models for the formation and evolution of such systems (Di Stefano 2003).

Oliversen, Ronald J.↗
NASA NTRS1974

An algorithm for a general class of routing problems derived from Huygens' principle

If a set of N points or nodes with a nonnegative cost associated with each ordered pair is known, it is desired to find a path from one given node to another given node which minimizes the cost sum. An algorithm is presented which yields a global minimum solution after at most N - 1 iterations or on a typical large third-generation computer, after 1 hour of computation time for a 10,000-node problem. The rapid-access data storage capacity demanded by the algorithm is approximately 3N words for costs read in from slow-access storage or 2N words for calculable costs. The time-storage requirements of the algorithm known to the authors. When the problem is viewed as a discretized optimal control problem, after N-1 iterations, an optimal control or node transition is established for each of the N nodes or states; thus, the algorithm can be applied to situations were there may be errors in the control that necessitate a closed loop control that necessitate a closed loop control philosophy.

Avis, L. M.↗
NASA NTRS1990

The simultaneous integration of many trajectories using nilpotent normal forms

Taylor's formula shows how to approximate a certain class of functions by polynomials. The approximations are arbitrarily good in some neighborhood whenever the function is analytic and they are easy to compute. The main goal is to give an efficient algorithm to approximate a neighborhood of the configuration space of a dynamical system by a nilpotent, explicitly integrable dynamical system. The major areas covered include: an approximating map; the generalized Baker-Campbell-Hausdorff formula; the Picard-Taylor method; the main theorem; simultaneous integration of trajectories; and examples.

Grayson, Matthew A.↗
NASA NTRS1994

A splitting algorithm for Vlasov simulation with filamentation filtration

A Fourier-Fourier transformed version of the splitting algorithm for simulating solutions of the Vlasov-Poisson system of equations is introduced. It is shown that with the inclusion of filamentation filtration in this transformed algorithm it is both faster and more stable than the standard splitting algorithm. It is further shown that in a scalar computer environment this new algorithm is approximately equal in speed and far less noisy than its particle-in-cell counterpart. It is conjectured that in a multiprocessor environment the filtered splitting algorithm would be faster while producing more precise results.

Klimas, A. J.↗
DOE OSTI2024

A Novel Noise-Aware Classical Optimizer for Variational Quantum Algorithms

A key component of variational quantum algorithms (VQAs) is the choice of classical optimizer employed to update the parameterization of an ansatz. It is well recognized that quantum algorithms will, for the foreseeable future, necessarily be run on noisy devices with limited fidelities. Thus, the evaluation of an objective function (e.g., the guiding function in the quantum approximate optimization algorithm (QAOA) or the expectation of the electronic Hamiltonian in variational quantum eigensolver (VQE)) required by a classical optimizer is subject not only to stochastic error from estimating an expected value but also to error resulting from intermittent hardware noise. Model-based derivative-free optimization methods have emerged as popular choices of a classical optimizer in the noisy VQA setting, based on empirical studies. However, these optimization methods were not explicitly designed with the consideration of noise. In this work we adapt recent developments from the “noise-aware numerical optimization” literature to these commonly used derivative-free model-based methods. We introduce the key defining characteristics of these novel noise-aware derivative-free model-based methods that separate them from standard model-based methods. In conclusion, we study an implementation of such noise-aware derivative-free model-based methods and compare its performance on demonstrative VQA simulations to classical solvers packaged in scikit-quant.

classical optimizers↗
NASA NTRS2004

Vegetation Effects on Soil Moisture Estimation

Several successful algorithms have been developed to estimate soil moisture of bare surfaces. We previously reported a new algorithm using the tilted Bragg approximation. However, these algorithms are only applicable to bare surfaces. When vegetation is present, soil moisture is typically underestimated by bare surface algorithms. In order to derive soil moisture under vegetation, we have to understand the complex scattering process due to vegetation. Our main interest is to retrieve the global soil moisture information using Hydros L-band polarimetric radar data. The Hydros mission will provide the first global view of land soil moisture using L-band radar and radiometer. The unique characteristics of the Hydros data are the availability of the low resolution soil moisture information from radiometer data and the continuous time series radar data collected at the same incidence angle. In this paper, we will examine a potential inversion algorithm to retrieve soil moisture under vegetation canopies using Hydros L-band polarimetric radar data.

soil moisture↗
NASA NTRS1985

A fast efficient implicit scheme for the gasdynamic equations using a matrix reduction technique

An efficient implicit finite-difference algorithm for the gasdynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved without loss of the stability characteristics generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows and used to show that the method offers computational advantages over the conventional Beam and Warming scheme. Existing Beam and Warming codes can be retrofit with minimal effort. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations.

Barth, T. J.↗
NASA NTRS2004

Review of TRMM/GPM Rainfall Algorithm Validation

A review is presented concerning current progress on evaluation and validation of standard Tropical Rainfall Measuring Mission (TRMM) precipitation retrieval algorithms and the prospects for implementing an improved validation research program for the next generation Global Precipitation Measurement (GPM) Mission. All standard TRMM algorithms are physical in design, and are thus based on fundamental principles of microwave radiative transfer and its interaction with semi-detailed cloud microphysical constituents. They are evaluated for consistency and degree of equivalence with one another, as well as intercompared to radar-retrieved rainfall at TRMM's four main ground validation sites. Similarities and differences are interpreted in the context of the radiative and microphysical assumptions underpinning the algorithms. Results indicate that the current accuracies of the TRMM Version 6 algorithms are approximately 15% at zonal-averaged / monthly scales with precisions of approximately 25% for full resolution / instantaneous rain rate estimates (i.e., level 2 retrievals). Strengths and weaknesses of the TRMM validation approach are summarized. Because the dew of convergence of level 2 TRMM algorithms is being used as a guide for setting validation requirements for the GPM mission, it is important that the GPM algorithm validation program be improved to ensure concomitant improvement in the standard GPM retrieval algorithms. An overview of the GPM Mission's validation plan is provided including a description of a new type of physical validation model using an analytic 3-dimensional radiative transfer model.

Smith, Eric A.↗
DOE OSTI2024

Variational Quantum Algorithms for Semidefinite Programming

A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum algorithms for approximately solving SDPs. For one class of SDPs, we provide a rigorous analysis of their convergence to approximate locally optimal solutions, under the assumption that they are weakly constrained (i.e., N$\gg$M, where N is the dimension of the input matrices and M is the number of constraints). We also provide algorithms for a more general class of SDPs that requires fewer assumptions. Finally, we numerically simulate our quantum algorithms for applications such as MaxCut, and the results of these simulations provide evidence that convergence still occurs in noisy settings.

97 MATHEMATICS AND COMPUTING↗