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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Combined Bernstein Polynomial, Optimal Reciprocal Collision Avoidance, Differential Dynamic Programming for Trajectory Replanning and Collision Avoidance for UAM Vehicles

This paper presents an integration of Differential Dynamic Programming (DDP) with the Optimal Reciprocal Collision Avoidance (ORCA) algorithm as the basis for a new algorithm, titled Combined Bernstein Polynomial Optimal Reciprocal Collision Avoidance DDP (COBRA-DDP), for trajectory replanning and collision avoidance for Urban Air Mobility (UAM) vehicles. State-constrained variants of DDP provide the ability to plan trajectories while avoiding obstacles, but these methods require a large increase in computational time per iteration which hinders the overall speed of the algorithm. ORCA utilizes simplified dynamics to recognize potential collisions along a trajectory and provides an optimal velocity for the avoidance of multiple vehicles. These velocity commands, however, may not result in a dynamically feasible trajectory for DDP to plan around. As such, a Bernstein polynomial curve that considers the general dynamic constraints of the vehicle is generated to approximate a trajectory based on the velocity commands. COBRA-DDP optimizes this suggested trajectory via unconstrained DDP to provide a dynamically feasible trajectory that provides collision avoidance. This new trajectory can be applied to the vehicle or used to warm start the state constrained DDP algorithms to decrease computation time. Its benefits and effectiveness of the algorithm are demonstrated on a UAM Vertical Takeoff and Landing (VTOL) vehicle simulation with highly nonlinear dynamics.

Optimal Reciprocal Collision Avoidance↗
DOE OSTI2018

Application of polynomial chaos expansion in inverse transport problems with neutron multiplication measurements and multiple unknowns - 25623

The polynomial chaos expansion technique is used to build surrogate models of the dependences of gamma-ray fluxes and neutron multiplication to unknown physical parameters in radiological source/shield systems. These surrogate models are used with the Differential Evolution Adaptive Metropolis (DREAM), a method to solve and quantify uncertainty in inverse transport problems. Measured data in the inverse problems includes both passive gamma rays and neutron multiplication. The polynomial chaos expansion approach is shown to increase the speed of DREAM by factors of greater than 60 while not degrading the accuracy of the solution. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2015

Image Reconstruction from Under sampled Fourier Data Using the Polynomial Annihilation Transform

Fourier samples are collected in a variety of applications including magnetic resonance imaging and synthetic aperture radar. The data are typically under-sampled and noisy. In recent years, l 1 regularization has received considerable attention in designing image reconstruction algorithms from under-sampled and noisy Fourier data. The underlying image is assumed to have some sparsity features, that is, some measurable features of the image have sparse representation. The reconstruction algorithm is typically designed to solve a convex optimization problem, which consists of a fidelity term penalized by one or more l 1 regularization terms. The Split Bregman Algorithm provides a fast explicit solution for the case when TV is used for the l1l1 regularization terms. Due to its numerical efficiency, it has been widely adopted for a variety of applications. A well known drawback in using TV as an l 1 regularization term is that the reconstructed image will tend to default to a piecewise constant image. This issue has been addressed in several ways. Recently, the polynomial annihilation edge detection method was used to generate a higher order sparsifying transform, and was coined the “polynomial annihilation (PA) transform.” This paper adapts the Split Bregman Algorithm for the case when the PA transform is used as the l 1 regularization term. In so doing, we achieve a more accurate image reconstruction method from under-sampled and noisy Fourier data. Our new method compares favorably to the TV Split Bregman Algorithm, as well as to the popular TGV combined with shearlet approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Uncertainty propagation through an aeroelastic wind turbine model using polynomial surrogates

Polynomial surrogates are used to characterize the energy production and lifetime equivalent fatigue loads for different components of the DTU 10 MW reference wind turbine under realistic atmospheric conditions. The variability caused by different turbulent inflow fields are captured by creating independent surrogates for the mean and standard deviation of each output with respect to the inflow realizations. A global sensitivity analysis shows that the turbulent inflow realization has a bigger impact on the total distribution of equivalent fatigue loads than the shear coefficient or yaw miss-alignment. The methodology presented extends the deterministic power and thrust coefficient curves to uncertainty models and adds new variables like damage equivalent fatigue loads in different components of the turbine. These surrogate models can then be implemented inside other work-flows such as: estimation of the uncertainty in annual energy production due to wind resource variability and/or robust wind power plant layout optimization. It can be concluded that it is possible to capture the global behavior of a modern wind turbine and its uncertainty under realistic inflow conditions using polynomial response surfaces. In conclusion, the surrogates are a way to obtain power and load estimation under site specific characteristics without sharing the proprietary aeroelastic design.

17 WIND ENERGY↗
DOE OSTI2016

Efficient Temperature-Dependent Green’s Functions Methods for Realistic Systems: Compact Grids for Orthogonal Polynomial Transforms

The Matsubara Green’s function that is used to describe temperature-dependent behavior is expressed on a numerical grid. While such a grid usually has a couple of hundred points for low-energy model systems, for realistic systems with large basis sets the size of an accurate grid can be tens of thousands of points, constituting a severe computational and memory bottleneck. In this paper, we determine efficient imaginary time grids for the temperature-dependent Matsubara Green’s function formalism that can be used for calculations on realistic systems. Here we show that, because of the use of an orthogonal polynomial transform, we can restrict the imaginary time grid to a few hundred points and reach micro-Hartree accuracy in the electronic energy evaluation. Moreover, we show that only a limited number of orthogonal polynomial expansion coefficients are necessary to preserve accuracy when working with a dual representation of the Green’s function or self-energy and transforming between the imaginary time and frequency domain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Polynomial Scaling Localized Active Space Unitary Selective Coupled Cluster Singles and Doubles

We present a polynomial-scaling algorithm for the localized active space unitary selective coupled cluster singles and doubles (LAS-USCCSD) method. In this approach, cluster excitations are selected based on a threshold ϵ determined by the absolute gradients of the LAS-UCCSD energy with respect to cluster amplitudes. Using the generalized Wick’s theorem for multireference wave functions, we derive the gradient expression as a polynomial function of one-, two-, and three-body reduced density matrices and 1- and 2-electron integrals, valid for any multireference wave function. The resulting gradient implementation exhibits a memory scaling of 𝒪(N 6 ), with N spin orbitals in the combined active space of all fragments. The variational quantum eigensolver is used to optimize the selected cluster excitations on a quantum simulator. Furthermore, by plotting the energy error, defined as the difference between the LAS-USCCSD and corresponding CASCI energies, against the inverse cluster amplitude selection threshold (ϵ –1 ) for polyene chains containing 2 to 5 π-bond units, we establish a relationship between the energy error and the threshold. To further validate the accuracy of LAS-USCCSD, we computed the cis–trans isomerization energy of stilbene (a 20-qubit system) and the magnetic coupling constant of the tris-hydroxo-bridged chromium dimer [Cr 2 (OH) 3 (NH 3 ) 6 ] 3+ (evaluated as both 12- and 20-qubit systems) using the Qiskit-Qulacs simulator. Assessing such examples is important to determine the practical feasibility of quantum simulations for chemically realistic systems. Toward this goal, with the LAS-USCCSD algorithm we estimated the quantum resources required for simulating an active space of (30e,22o) in [Cr 2 (OH) 3 (NH 3 ) 6 ] 3+ , a size that remains beyond the reach of current quantum simulators for accurate treatment.

Algorithms↗
DOE OSTI2025

Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials

Abstract The remarkable complexity of a topologically ordered many-body quantum system is encoded in the characteristics of its anyons. Quintessential predictions emanating from this complexity employ the Fibonacci string net condensate (Fib SNC) and its anyons: sampling Fib-SNC would estimate chromatic polynomials while exchanging its anyons would implement universal quantum computation. However, physical realizations remained elusive. We introduce a scalable dynamical string net preparation (DSNP) that constructs Fib SNC and its anyons on reconfigurable graphs suitable for near-term superconducting processors. Coupling the DSNP approach with composite error-mitigation on deep circuits, we create, measure, and braids Fibonacci anyons; charge measurements show 94% accuracy, and exchanging the anyons yields the expected golden ratioϕwith 98% average accuracy. We then sample the Fib SNC to estimate chromatic polynomial atϕ + 2 for several graphs. Our results establish the proof of principle for using Fib-SNC and its anyons for fault-tolerant universal quantum computation and aim at a classically hard problem.

Science & Technology - Other Topics↗
DOE OSTI2026

Scalable quantum computational science: A perspective from block-encodings and polynomial transformations

Significant developments made in quantum hardware and error correction recently have been driving quantum computing toward practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications in computational sciences. In this perspective article, we propose several properties that scalable quantum computational science methods should possess. We further discuss how block-encodings and polynomial transformations can potentially serve as a unified framework with the desired properties. Recent advancements on these topics are presented, including the construction and assembly of block-encodings, and various generalizations of quantum signal processing (QSP) algorithms to perform polynomial transformations. The scalability of QSP methods on parallel and distributed quantum architectures is also highlighted. Promising applications in simulation and observable estimation in chemistry, physics, and optimization problems are presented. We hope this perspective serves as a gentle introduction to state-of-the-art quantum algorithms for the computational science community and inspires future development of scalable quantum computational science methodologies that bridge theory and practice.

Bayesian inference↗
DOE OSTI2018

Non-axisymmetric Aberration Patterns from Wide-field Telescopes Using Spin-weighted Zernike Polynomials

If the optical system of a telescope is perturbed from rotational symmetry, the Zernike wavefront aberration coefficients describing that system can be expressed as a function of position in the focal plane using spin-weighted Zernike polynomials. Methodologies are presented to derive these polynomials to arbitrary order. This methodology is applied to aberration patterns produced by a misaligned Ritchey Chretian telescope and to distortion patterns at the focal plane of the DESI optical corrector, where it is shown to provide a more efficient description of distortion than conventional expansions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Chiral-odd generalized parton distributions in the large-𝑁 𝑐 limit of QCD: Spin-flavor structure, polynomiality, and sum rules

We study the nonperturbative properties of the nucleon’s chiral-odd generalized parton distributions (transversity GPDs) in the large-𝑁 𝑐 limit of QCD. This includes the parametric ordering of the spin-flavor components, the polynomiality property of the moments, and the sum rules connecting the GPDs with the tensor form factors. A multipole expansion in the transverse momentum transfer is used to enumerate and interpret the structures in the nucleon matrix element of the chiral-odd partonic operator, including monopole, dipole and quadrupole terms. The 1/𝑁 𝑐 expansion of the GPDs is performed using the abstract mean-field picture of baryons in the large-𝑁 𝑐 limit and its symmetries. We derive a large-𝑁 𝑐 relation between the flavor-nonsinglet GPDs 𝐸$^{𝑢−𝑑}_𝑇$ and $\tilde{𝐻}^{𝑢−𝑑}_𝑇$ and test it with recent lattice QCD results. We show that the polynomiality property and sum rules of the GPDs are fulfilled with the restricted realization of translational and rotational invariance in the mean-field picture. The results provide a basis for the phenomenological analysis of chiral-odd GPDs and hard exclusive processes in the large-𝑁 𝑐 limit, and for calculations in specific dynamical models.

generalized parton distributions↗
DOE OSTI2023

Additive Polynomial Time Integrators, Part I: Framework and Fully Implicit-Explicit Collocation Methods

In this paper we generalize the polynomial time integration framework to additively partitioned initial value problems. The framework we present is general and enables the construction of many new families of additive integrators with arbitrary order-of-accuracy and varying degree of implicitness. In this first work, we focus on a new class of implicit-explicit polynomial block methods that are based on fully implicit Runge–Kutta methods with Radau nodes and that possess high stage order. Here, we show that the new fully implicit-explicit (FIMEX) integrators have improved stability compared to existing IMEX Runge–Kutta methods, while also being more computationally efficient due to recent developments in preconditioning techniques for solving the associated systems of nonlinear equations. For PDEs on periodic domains where the implicit component is trivial to invert, we will show how parallelization of the right-hand side evaluations can be exploited to obtain significant speedup compared to existing serial IMEX Runge–Kutta methods. For parallel (in space) finite element discretizations, the new methods can achieve orders of magnitude better accuracy than existing IMEX Runge–Kutta methods and/or achieve a given accuracy several times times faster in terms of computational runtime.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A Unified Approach to Unimodality of Gaussian Polynomials

In 2013, Pak and Panova proved the strict unimodality property of q-binomial coefficients (as polynomials in q) based on the combinatorics of Young tableaux and the semigroup property of Kronecker coefficients. They showed it to be true for all ℓ, m ≥ 8 and a few other cases. We propose a different approach to this problem based on computer algebra, where we establish a closed form for the coefficients of these polynomials and then use cylindrical algebraic decomposition to identify exactly the range of coefficients where strict unimodality holds. This strategy allows us to tackle generalizations of the problem, e.g., to show unimodality with larger gaps or unimodality of related sequences. In particular, we present proofs of two additional cases of a conjecture by Stanley and Zanello.

Koutschan, Christoph↗
DOE OSTI2017

Polynomial Chaos Characterization of Uncertainty in Multiscale Models and Behavior of Carbon Reinforced Composites

Design of non-crimp fabric (NCF) composites entails major challenges pertaining to (1) the complex fine-scale morphology of the constituents, (2) the manufacturing-produced inconsistency of this morphology spatially, and thus (3) the ability to build reliable, robust, and efficient computational surrogate models to account for this complex nature. Traditional approaches to construct computational surrogate models have been to average over the fluctuations of the material properties at different scale lengths. This fails to account for the fine-scale features and fluctuations in morphology, material properties of the constituents, as well as fine-scale phenomena such as damage and cracks. In addition, it fails to accurately predict the scatter in macroscopic properties, which is vital to the design process and behavior prediction. In this work, funded in part by the Department of Energy, we present an approach for addressing these challenges by relying on polynomial chaos representations of both input parameters and material properties at different scales. Moreover, we emphasize the efficiency and robustness of integrating the polynomial chaos expansion with multiscale tools to perform multiscale assimilation, characterization, propagation, and prediction, all of which are necessary to construct the data-driven surrogate models required to design under the uncertainty of composites. These data-driven constructions provide an accurate map from parameters (and their uncertainties) at all scales and the system-level behavior relevant for design. While this perspective is quite general and applicable to all multiscale systems, NCF composites present a particular hierarchy of scales that permits the efficient implementation of these concepts.

42 ENGINEERING↗
DOE OSTI2023

Use of Sobol’ Variance-Based Global Sensitivity Analysis and Multidimensional Legendre Polynomial Fitting for Reduced Order Modeling

Sandia National Laboratories (SNL) has developed a novel reduced order modeling approach. Prioritization of inputs is accomplished using Sobo' indices obtained through a more efficient variance-based global sensitivity analysis. To determine the Sobo' functions, simulated input values are aligned to collocation points to permit the use of Gauss-Lobatto integration, thereby reducing the number of simulation trials needed by more than an order of magnitude compared to standard Monte Carlo approaches. Furthermore, by leveraging the orthogonality of Legendre polynomials in conjunction with those same simulations at the collocation nodes, an efficient fitting method is developed to represent the Sobo' functions from which a reduced order model (ROM) is constructed. The developed method is both more efficient computationally, and the resulting ROM is more accurate. The efficacy of this technique is demonstrated on a nonlinear polynomial test function as well as the nonlinear Ishigami and Sobo' g functions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1967

Polynomial manipulator AP-168

Linear Systems Design Evaluation Program, AP-168 combines the many different analysis techniques used to evaluate and manipulate polynomials. The single program is a pseudo instruction abstraction. It allows the user to enter polynomials of the laplace operators and to manipulate them freely.

Tutt, G. E.↗
NASA NTRS1969

Root-cubing and general root-powering methods for finding the zeros of polynomials

Mathematical analysis technique generalizes a root squaring and root cubing method into a general root powering method. The introduction of partitioned polynomials into this general root powering method simplifies the coding of the polynomial transformations into input data suitable for processing by computer. The method includes analytic functions.

Bareiss, E. H.↗