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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Construction of approximate invariants for non-integrable Hamiltonian systems

We present a method to construct high-order polynomial approximate invariants (AI) for non integrable Hamiltonian dynamical systems, and apply it to a modern ring-based particle accelerator. Taking advantage of a special property of one-turn transformation maps in the form of a square matrix, AIs can be constructed order-by-order iteratively. Evaluating AI with simulation data, we observe that AI’s fluctuation is actually a measure of chaos. Through minimizing the fluctuations, the stable region of long-term motions, i.e., the dynamic aperture of the accelerator, could be enlarged.

43 PARTICLE ACCELERATORS↗
NASA NTRS1979

On the efficient computation of Fraunhofer and Fresnel region fields radiated by reflector and planar-aperture antennas

Computation of fields radiated by parabolic reflectors and planar apertures is a problem of prime importance, and conventional approaches to performing these computations are often very time-consuming. The paper demonstrates the usefulness of a series expansion technique for efficient computation of radiated fields in both the Fraunhofer and Fresnel regions. The series approach is based on the use of the Jacobi polynomials. The application of the series method to determining the far-field pattern of the antenna from the near-field measurements for an arbitrary aperture antenna is also discussed.

Mittra, R.↗
NASA NTRS1988

Domain decomposition preconditioners for the spectral collocation method

Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles. It is shown that convergence is achieved with a rate which does not depend on the polynomial degree of the spectral solution. The iterative methods here presented can be effectively implemented on multiprocessor systems due to their high degree of parallelism.

Quarteroni, Alfio↗
NASA NTRS1994

Splines and control theory

In this work, the relationship between splines and the control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical exponential spline. We have also discovered some new spline functions such as trigonometric splines and the combination of polynomial, exponential and trigonometric splines. The method proposed in this paper is easy to implement. Some numerical experiments are performed to investigate properties of different spline approximations.

Zhang, Zhimin↗
NASA NTRS2005

Computation of Symmetric Discrete Cosine Transform Using Bakhvalov's Algorithm

A number of algorithms for recursive computation of the discrete cosine transform (DCT) have been developed recently. This paper presents a new method for computing the discrete cosine transform and its inverse using Bakhvalov's algorithm, a method developed for evaluation of a polynomial at a point. In this paper, we will focus on both the application of the algorithm to the computation of the DCT-I and its complexity. In addition, Bakhvalov s algorithm is compared with Clenshaw s algorithm for the computation of the DCT.

Aburdene, Maurice F.↗
DOE OSTI2026

Spectra-to-exposure conversion using polynomial response models for gamma-ray field characterization

Accurate measurement of exposure rate from gamma-ray spectral data remains a critical challenge during radiological emergency response operations. Conventional methods rely on pre-defined static conversion factors derived from fixed geometries and isotopic compositions, which often fail to capture real-world environmental variability. This study presents a generalized approach as a "next-step" for converting gamma-ray spectral data into exposure rate using polynomial response models. The method introduces a flexible weighting scheme based on the in-situ detector response to distributed sources, enabling a pathway towards improved correspondence between measured spectra and "ground-truth" exposure rates. Experimental data from sodium iodide NaI(Tl) detectors were used to validate the approach as, at least equivalent to the current count-to-exposure method employed in emergency response CONOPS. Results show that the polynomial weighting model is sufficiently equal to the count-to-exposure method and may help improve accuracy given its adaptability to real-world conditions.

61 RADIATION PROTECTION AND DOSIMETRY↗
NASA NTRS1992

High-order wide-band frequency domain identification using composite curve fitting

A method is presented for curve fitting nonparametric frequency domain data so as to identify a parametric model composed of two models in parallel, where each model has dynamics in a specified portion of the frequency band. This decomposition overcomes the problem of numerical sensitivity since lower order polynomials can be used compared to existing methods which estimate the model as a single entity. Consequently, composite curve fitting is useful for frequency domain identification of high-order systems and/or systems whose dynamics are spread over a large bandwidth. The approach can be extended to identify an arbitrary number of parallel subsystems in specified frequency regimes.

Bayard, D. S.↗
NASA NTRS2021

PolyFit: A C++ code for Polynomial Curve Fit with Calculation of Error Bars

In radiobiology, many dose-response results are modeled using the so-called linear-quadratic (LQ)model, which means that results are modeled as a function of dose Das 𝑅(𝐷)=𝛽0+𝛽1𝐷+𝛽2𝐷2. The coefficients 𝛽0, 𝛽1and 𝛽2are obtained from fitting a series of data points (𝑥𝑖, 𝑦𝑖), which is usually done using a least-square method. The LQ and more generally the polynomial fit capability is implemented in many software that analyzes data. However, there are some instances where the fitting needs to be done programmatically. Furthermore, depending on the software used, some features may not be implemented. In this mini-review, I discuss the basis of polynomial fitting, including the calculation of errors on the coefficients and results, use of weighting and fixing the intercept value (the coefficient 𝛽0). A simple C++ code to perform the polynomial curve fitting is also provided. This code should be useful not only in radiobiology but in other fields of science as well.

Ianik Plante↗
NASA NTRS2021

PolyFit: A C++ code for Polynomial Curve Fit with Calculation of Error Bars

In radiobiology, many dose-response results are modeled using the so-called linear-quadratic(LQ)model, which means that results are modeled as a function of dose Das 𝑅(𝐷)=𝛽0+𝛽1𝐷+𝛽2𝐷2. The coefficients 𝛽0, 𝛽1and 𝛽2are obtained from fitting a series of data points (𝑥𝑖,𝑦𝑖), which is usually done using a least-square method. The LQ and more generally the polynomial fit capability is implemented in many software that analyzes data. However, it is often convenient to do the fitting programmatically, especially when a large number of datasets should be analyzed. Furthermore, depending on the software used, some features may not be implemented. In this mini-review, I discuss the basis of polynomial fitting, including the calculation of errors on the coefficients and results, use of weighting and fixing the intercept value (the coefficient 𝛽0). A simple C++ code to perform the polynomial curve fitting is also provided. This code should be useful not only in radiobiology but in other fields of science as well.

Ianik Plante↗
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↗
NASA NTRS1987

Inverse of polynomial matrices in the irreducible form

An algorithm is developed for finding the inverse of polynomial matrices in the irreducible form. The computational method involves the use of the left (right) matrix division method and the determination of linearly dependent vectors of the remainders. The obtained transfer function matrix has no nontrivial common factor between the elements of the numerator polynomial matrix and the denominator polynomial.

Chang, Fan R.↗
NASA NTRS1976

Use of variational methods in the determination of wind-driven ocean circulation

Simple polynomial approximations and a variational approach were used to predict wind-induced circulation in rectangular ocean basins. Stommel's and Munk's models were solved in a unified fashion by means of the proposed method. Very good agreement with exact solutions available in the literature was shown to exist. The method was then applied to more complex situations where an exact solution seems out of the question.

Gelos, R.↗
DOE OSTI2025

Boosting efficiency and reducing graph reliance: Basis adaptation integration in Bayesian multi-fidelity networks

The computational cost of high-fidelity numerical models makes outer-loop analysis, which requires repeated interrogation of the model such as uncertainty quantification, computationally demanding. Multi-fidelity methods, which construct a surrogate model using data from an ensemble of models of varying cost and accuracy, can substantially reduce the cost of outer-loop analysis. However, these methods can be difficult to apply when the model ensemble does not admit a clear hierarchy a priori and the correlations between models are low. Consequently, in this paper, we present a multi-fidelity method that leverages dimension reduction to enhance the correlation between models, thereby reducing the amount of data needed to train a surrogate from an unordered ensemble of models. Our method utilizes basis adaptation to build low-dimensional polynomial chaos expansions of each model and employs Multi-fidelity Networks to encode the relationships among models. We show that the resulting method exhibit two notable advantages over its counterpart: (1) enhanced accuracy (both reduced bias and variance); and (2) reduced dependency on the graph structure encoding relationships among models. We demonstrate the approach on an analytical test problem and a challenging finite element model for a spent nuclear fuel. Our method produces a surrogate model that is significantly more accurate than either a single-fidelity surrogate or a multi-fidelity surrogate constructed without basis adaptation.

42 ENGINEERING↗
NASA NTRS1992

Upper bounds for convergence rates of vector extrapolation methods on linear systems with initial iterations

The application of the minimal polynomial extrapolation (MPE) and the reduced rank extrapolation (RRE) to a vector sequence obtained by the linear iterative technique x(sub j) + 1 = Ax(sub j) = b,j = 1,2,..., is considered. Both methods produce a two dimensional array of approximations s(sub n,k) to the solution of the system (I - A)x = b. Here, s(sub n,k) is obtained from the vectors x(sub j), n is less than or equal to j is less than or equal to n + k + 1. It was observed in an earlier publication by the first author that the sequence s(sub n,k), k = 1,2,..., for n greater than 0, but fixed, possesses better convergence properties than the sequence s(sub 0,k), k = 1,2,.... A detailed theoretical explanation for this phenomenon is provided in the present work. This explanation is heavily based on approximations by incomplete polynomials. It is demonstrated by numerical examples when the matrix A is sparse that cycling with s(sub n,k) for n greater than 0, but fixed, produces better convergence rates and costs less computationally than cycling with s(sub 0,k). It is also illustrated numerically with a convection-diffusion problem that the former may produce excellent results where the latter may fail completely. As has been shown in an earlier publication, the results produced by s(sub 0,k) are identical to the corresponding results obtained by applying the Arnoldi method or generalized minimal residual scheme (GMRES) to the system (I - A)x = b.

Sidi, Avram↗
DOE OSTI2025

Ansatz-Free Hamiltonian Learning with Heisenberg-Limited Scaling

Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that interactions are local, but this assumption may not hold for arbitrary Hamiltonians. Previous methods all require high-order inverse polynomial dependency with precision, unable to surpass the standard quantum limit and reach the gold-standard Heisenberg-limited scaling. Whether Heisenberg-limited Hamiltonian learning is possible without prior assumptions about the interaction structures, a challenge we term ansatz-free Hamiltonian learning , remains an open question. In this work, we present a quantum algorithm to learn arbitrary sparse Hamiltonians without any structure constraints using only black-box queries of the system’s real-time evolution and minimal digital controls to attain Heisenberg-limited scaling in estimation error. Our method is also resilient to state-preparation-and-measurement errors, enhancing its practical feasibility. We numerically demonstrate our ansatz-free protocol for learning physical Hamiltonians and validating analog quantum simulations, benchmarking our performance against the state-of-the-art Heisenberg-limited learning approach. Moreover, we establish a fundamental trade-off between total evolution time and quantum control on learning arbitrary interactions, revealing the intrinsic interplay between controllability and total evolution-time complexity for any learning algorithm. These results pave the way for further exploration into Heisenberg-limited Hamiltonian learning in complex quantum systems under minimal assumptions, potentially enabling new benchmarking and verification protocols.

machine learning↗
NASA NTRS1987

Approximate polynomial preconditioning applied to biharmonic equations on vector supercomputers

Applying a finite difference approximation to a biharmonic equation results in a very ill-conditioned system of equations. This paper examines the conjugate gradient method used in conjunction with the generalized and approximate polynomial preconditionings for solving such linear systems. An approximate polynomial preconditioning is introduced, and is shown to be more efficient than the generalized polynomial preconditionings. This new technique provides a simple but effective preconditioning polynomial, which is based on another coefficient matrix rather than the original matrix operator as commonly used.

Wong, Yau Shu↗