Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “POLYNOMIAL”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

SU-E-T-638: Evaluation and Comparison of Landauer Microstar (OSLD) Readers

Purpose: To evaluate and compare characteristic performance of a new Landauer nanodot Reader with the previous model. Methods: In order to calibrate and test the reader, a set of nanodots were irradiated using a Varian Truebeam Linac. Solid water slabs and bolus were used in the process of irradiation. Calibration sets of nanodots were irradiated for radiation dose ranges: 0 to 10 and 20 to 1000 cGy, using 6MV photons. Additionally, three sets of nanodots were each irradiated using 6MV, 10MV and 15MV beams. For each beam energy, and selected dose in the range of 3 to 1000 cGy, a pair of nanodots was irradiated and three readings were obtained with both readers. Results: The analysis shows that for 3 photon beam energies and selected ranges of dose, the calculated absorbed dose agrees well with the expected value. The results illustrate that the new Microstar II reader is a highly consistent system and that the repeated readings provide results with a reasonably small standard deviation. For all practical purposes, the response of system is linear for all radiation beam energies. Conclusion: The Microstar II nanodot reader is consistent, accurate, and reliable. The new hardware design and corresponding software contain several advantages over the previous model. The automatic repeat reading mechanism, that helps improve reproducibility and reduce processing time, and the smaller unit size that renders ease of transport, are two of such features. Present study shows that for high dose ranges a polynomial calibration equation provides more consistent results. A 3rd order polynomial calibration curve was used to analyze the readings of dosimeters exposed to high dose range radiation. It was observed that the results show less error compared to those calculated by using linear calibration curves, as provided by Landauer system software for all dose ranges.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

WE-E-18A-04: Precision In-Vivo Dosimetry Using Optically Stimulated Luminescence Dosimeters and a Pulsed-Stimulating Dose Reader

Purpose: A new readout technology based on pulsed optically stimulating luminescence is introduced (microSTARii, Landauer, Inc, Glenwood, IL60425). This investigation searches for approaches that maximizes the dosimetry accuracy in clinical applications. Methods: The sensitivity of each optically stimulated luminescence dosimeter (OSLD) was initially characterized by exposing it to a given radiation beam. After readout, the luminescence signal stored in the OSLD was erased by exposing its sensing area to a 21W white LED light for 24 hours. A set of OSLDs with consistent sensitivities was selected to calibrate the dose reader. Higher order nonlinear curves were also derived from the calibration readings. OSLDs with cumulative doses below 15 Gy were reused. Before an in-vivo dosimetry, the OSLD luminescence signal was erased with the white LED light. Results: For a set of 68 manufacturer-screened OSLDs, the measured sensitivities vary in a range of 17.3%. A sub-set of the OSLDs with sensitivities within ±1% was selected for the reader calibration. Three OSLDs in a group were exposed to a given radiation. Nine groups were exposed to radiation doses ranging from 0 to 13 Gy. Additional verifications demonstrated that the reader uncertainty is about 3%. With an external calibration function derived by fitting the OSLD readings to a 3rd-order polynomial, the dosimetry uncertainty dropped to 0.5%. The dose-luminescence response curves of individual OSLDs were characterized. All curves converge within 1% after the sensitivity correction. With all uncertainties considered, the systematic uncertainty is about 2%. Additional tests emulating in-vivo dosimetry by exposing the OSLDs under different radiation sources confirmed the claim. Conclusion: The sensitivity of individual OSLD should be characterized initially. A 3rd-order polynomial function is a more accurate representation of the dose-luminescence response curve. The dosimetry uncertainty specified by the manufacturer is 4%. Following the proposed approach, it can be controlled to 2%.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

SU-E-T-678: Response Calibration Using Electron Depth-Dose Data for MRI-Based 3D Polymer Gel Dosimetry

Purpose: To evaluate a calibration method using the depth-dose data of an electron beam for MRI-based polymer gel dosimetry. Methods: MAGAT was manufactured in-house to fill two 400mL-cylindrical phantoms and nine 22mL-glass vials. Phantom-A was irradiated along the cylinder axis with a 9MeV electron beam of 6 cm x 6 cm field size (FS). Phantom-B was irradiated with a 6MV photon beam of 3 cm x 3 cm FS by a 360-degree arc technique. Eight vials were irradiated in a water-bath to various doses with a 20 cm x 20 cm FS 6MV photon beam. All irradiated phantoms and one un-irradiated vial were scanned with a 3T MRI scanner to obtain the spin-spin relaxation rate (R2) distributions. By comparing the measured R2-to-depth data with the known depth-dose data for Phantom-A, R2-to-dose calibration data were obtained (e-beam method). Another calibration data were obtained from the 9 vials data (9-vial method). We tested two regression equations, i.e., third-order polynomial and tangent functions, and two dose normalization methods, i.e., one-point and two-point methods. Then, these two calibration methods were used to obtain the 3D dose distribution of Phantom-B and evaluated by comparing the measured data with the dose distribution from a treatment planning system. The comparison was made with gamma passing rate (2%/2mm criteria). Results: We did not observe a clear advantage of the e-beam method over the 9-vial method for the 3D dose comparison with the test case. Nevertheless, we found that the e-beam method required a smaller dose scaling for the dose comparison. Furthermore, the tangent function showed better data fitting than the polynomial function with smaller uncertainty of the estimated coefficients. Conclusions: Considering the overall superior performance, we recommend the e-beam method with the tangent function as the regression equation and one-point dose normalization for the MRI-based polymer gel dosimetry.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

Technical Note: SPEKTR 3.0—A computational tool for x-ray spectrum modeling and analysis

Purpose: A computational toolkit (SPEKTR 3.0) has been developed to calculate x-ray spectra based on the tungsten anode spectral model using interpolating cubic splines (TASMICS) algorithm, updating previous work based on the tungsten anode spectral model using interpolating polynomials (TASMIP) spectral model. The toolkit includes a MATLAB (The Mathworks, Natick, MA) function library and improved user interface (UI) along with an optimization algorithm to match calculated beam quality with measurements. Methods: The SPEKTR code generates x-ray spectra (photons/mm{sup 2}/mAs at 100 cm from the source) using TASMICS as default (with TASMIP as an option) in 1 keV energy bins over beam energies 20–150 kV, extensible to 640 kV using the TASMICS spectra. An optimization tool was implemented to compute the added filtration (Al and W) that provides a best match between calculated and measured x-ray tube output (mGy/mAs or mR/mAs) for individual x-ray tubes that may differ from that assumed in TASMICS or TASMIP and to account for factors such as anode angle. Results: The median percent difference in photon counts for a TASMICS and TASMIP spectrum was 4.15% for tube potentials in the range 30–140 kV with the largest percentage difference arising in the low and high energy bins due to measurement errors in the empirically based TASMIP model and inaccurate polynomial fitting. The optimization tool reported a close agreement between measured and calculated spectra with a Pearson coefficient of 0.98. Conclusions: The computational toolkit, SPEKTR, has been updated to version 3.0, validated against measurements and existing models, and made available as open source code. Video tutorials for the SPEKTR function library, UI, and optimization tool are available.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-G-IeP2-12: The Effect of Iterative Reconstruction and CT Tube Voltage On Hounsfield Unit Values of Iodinated Contrast

Purpose: To investigate the effects of changing iterative reconstruction strength and tube voltage on Hounsfield Unit (HU) values of varying concentrations of Iodinated contrast medium in a phantom. Method: Iodinated contrast (Omnipaque 300, GE Healthcare, Princeton NJ) was diluted with distilled water to concentrations of 0.6, 0.9, 1.8, 3.6, 7.2, and 10.8 mg/mL of Iodine. The solutions were scanned in a patient equivalent water phantom on two MDCT scanners: VCT 64 slice (GE Medical Systems, Waukesha, WI) and an Aquilion One 320 slice scanner (Toshiba America Medical Systems, Tustin CA). The phantom was scanned at 80, 100, 120, 140 kV using 400, 255, 180, and 130 mAs, respectively, for the VCT scanner, and 80, 100, 120, and 135 kV using 400, 250, 200, and 150 mAs, respectively, on the Aquilion One. Images were reconstructed at 2.5 mm (VCT) and 0.5 mm (Aquilion One). The VCT images were reconstructed using Advanced Statistical Iterative Reconstruction (ASIR) at 6 different strengths: 0%, 20%, 40%, 60%, 80%, and 100%. Aquilion One images were reconstructed using Adaptive Iterative Dose Reduction (AIDR) at 4 strengths: no AIDR, Weak AIDR, Standard AIDR, and Strong AIDR. Regions of interest (ROIs) were drawn on the images to measure the HU values and standard deviations of the diluted contrast. Second order polynomials were used to fit the HU values as a function of Iodine concentration. Results: For both scanners, there was no significant effect of changing the iterative reconstruction strength. The polynomial fits yielded goodness-of-fit (R2) values averaging 0.997. Conclusion: Changing the strength of the iterative reconstruction has no significant effect on the HU values of Iodinated contrast in a tissue-equivalent phantom. Fit values of HU vs Iodine concentration are useful in quantitative imaging protocols such as the determination of cardiac output from time-density curves in the main pulmonary artery.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2013

Generating moment matching scenarios using optimization techniques

An optimization based method is proposed to generate moment matching scenarios for numerical integration and its use in stochastic programming. The main advantage of the method is its flexibility: it can generate scenarios matching any prescribed set of moments of the underlying distribution rather than matching all moments up to a certain order, and the distribution can be defined over an arbitrary set. This allows for a reduction in the number of scenarios and allows the scenarios to be better tailored to the problem at hand. The method is based on a semi-infinite linear programming formulation of the problem that is shown to be solvable with polynomial iteration complexity. A practical column generation method is implemented. The column generation subproblems are polynomial optimization problems; however, they need not be solved to optimality. It is found that the columns in the column generation approach can be efficiently generated by random sampling. The number of scenarios generated matches a lower bound of Tchakaloff's. The rate of convergence of the approximation error is established for continuous integrands, and an improved bound is given for smooth integrands. Extensive numerical experiments are presented in which variants of the proposed method are compared to Monte Carlo and quasi-Monte Carlo methods on both numerical integration problems and stochastic optimization problems. The benefits of being able to match any prescribed set of moments, rather than all moments up to a certain order, is also demonstrated using optimization problems with 100-dimensional random vectors. Here, empirical results show that the proposed approach outperforms Monte Carlo and quasi-Monte Carlo based approaches on the tested problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Manycore Parallel Computing for a Hybridizable Discontinuous Galerkin Nested Multigrid Method

In this work, we present a parallel computing strategy for a hybridizable discontinuous Galerkin (HDG) nested geometric multigrid (GMG) solver. Parallel GMG solvers require a combination of coarse-grain and fine-grain parallelism to improve time-to-solution performance. In this work we focus on fine-grain parallelism. We use Intel's second generation Xeon Phi (Knights Landing) manycore processor. The GMG method achieves ideal convergence rates of 0.2 or less, for high polynomial orders. A matrix free (assembly free) technique is exploited to save considerable memory usage and increase arithmetic intensity. HDG enables static condensation, and due to the discontinuous nature of the discretization, we developed a matrix vector multiply routine that does not require any costly synchronizations or barriers. Our algorithm is able to attain 80% of peak bandwidth performance for higher order polynomials. This is possible due to the data locality inherent in the HDG method. Very high performance is realized for high order schemes, due to good arithmetic intensity, which declines as the order is reduced.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification

Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this paper, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating direction method, which is used to enhance sparsity of the Hermite polynomial expansion of stochastic state variables. The sparsity improvement increases both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the initial guess from SIR is more suitable for the cases when the available data is very limited (Algorithm 4). We also propose another algorithm (Algorithm 5) that performs dimension reduction first with sliced inverse regression, then constructs a Hermite polynomial expansion of the reduced model. This method allows us to approximate the statistics accurately with even less available data. Both methods are non-intrusive and require no a priori information of the sparsity of the system. We demonstrate the effectiveness of these two methods (Algorithms 4 and 5) using problems with up to 500 random dimensions.

Yang, Xiu↗
DOE OSTI2024

Robust Iterative Method for Symmetric Quantum Signal Processing in All Parameter Regimes

Here, this paper addresses the problem of solving nonlinear systems in the context of symmetric quantum signal processing (QSP), a powerful technique for implementing matrix functions on quantum computers. Symmetric QSP focuses on representing target polynomials as products of matrices in SU(2) that possess symmetry properties. We present a novel Newton’s method tailored for efficiently solving the nonlinear system involved in determining the phase factors within the symmetric QSP framework. Our method demonstrates rapid and robust convergence in all parameter regimes, including the challenging scenario with ill-conditioned Jacobian matrices, using standard double precision arithmetic operations. For instance, solving symmetric QSP for a highly oscillatory target function α cos(1000x) (polynomial degree ≈ 1433) takes 6 iterations to converge to machine precision when α = 0.9, and the number of iterations only increases to 18 iterations when α = 1 – 10 -9 with a highly ill-conditioned Jacobian matrix. Leveraging the matrix product state structure of symmetric QSP, the computation of the Jacobian matrix incurs a computational cost comparable to a single function evaluation. Moreover, we introduce a reformulation of symmetric QSP using real-number arithmetics, further enhancing the method’s efficiency. Extensive numerical tests validate the effectiveness and robustness of our approach, which has been implemented in the QSPPACK software package.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Learning Nonlinear Reduced Models from Data with Operator Inference

This review discusses Operator Inference, a nonintrusive reduced modeling approach that incorporates physical governing equations by defining a structured polynomial form for the reduced model, and then learns the corresponding reduced operators from simulated training data. The polynomial model form of Operator Inference is sufficiently expressive to cover a wide range of nonlinear dynamics found in fluid mechanics and other fields of science and engineering, while still providing efficient reduced model computations. The learning steps of Operator Inference are rooted in classical projection-based model reduction; thus, some of the rich theory of model reduction can be applied to models learned with Operator Inference. This connection to projection-based model reduction theory offers a pathway toward deriving error estimates and gaining insights to improve predictions. Furthermore, through formulations of Operator Inference that preserve Hamiltonian and other structures, important physical properties such as energy conservation can be guaranteed in the predictions of the reduced model beyond the training horizon. This review illustrates key computational steps of Operator Inference through a large-scale combustion example.

Mechanics↗
DOE OSTI2013

Sandia Higher Order Elements (SHOE) v 0.5 alpha

SHOE is research code for characterizing and visualizing higher-order finite elements; it contains a framework for defining classes of interpolation techniques and element shapes; methods for interpolating triangular, quadrilateral, tetrahedral, and hexahedral cells using Lagrange and Legendre polynomial bases of arbitrary order; methods to decompose each element into domains of constant gradient flow (using a polynomial solver to identify critical points); and an isocontouring technique that uses this decomposition to guarantee topological correctness. Please note that this is an alpha release of research software and that some time has passed since it was actively developed; build- and run-time issues likely exist.

Thompson, David↗
DOE OSTI2019

Compadre Toolkit

The Compadre Toolkit solves a minimization problem, that once solved allows a user to reconstruct a function from sample data collected from a cloud of data sites. The solution to this minimization can also be used to assemble a linear system that can be solved numerically using some other software. The minimization problem the toolkit solves is to find the optimal finite polynomial in a user specified finite dimensional space with regards to minimizing an objective function which measures a linear sampling functional applied to the polynomial, compared to the same sampling functional applied to the source function, weighted by a positive kernel that has compact support.

SciDAC↗
DOE OSTI2026

NN-OpInf

SAND2026-18878O The NN-OpInf tool is a PyTorch-based approach to operator inference that uses composable, structure-preserving neural networks to represent nonlinear operators. Operator inference is a machine learning method for inferring low-dimensional systems from data and polynomial models for system dynamics. However, many systems do not conform to polynomial structures, which NN-OpInf addresses by parameterizing operators with neural networks. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
DOE OSTI2019

Fast approximate STEM image simulations from a machine learning model

Abstract Accurate quantum mechanical scanning transmission electron microscopy image simulation methods such as the multislice method require computation times that are too large to use in applications in high-resolution materials imaging that require very large numbers of simulated images. However, higher-speed simulation methods based on linear imaging models, such as the convolution method, are often not accurate enough for use in these applications. We present a method that generates an image from the convolution of an object function and the probe intensity, and then uses a multivariate polynomial fit to a dataset of corresponding multislice and convolution images to correct it. We develop and validate this method using simulated images of Pt and Pt–Mo nanoparticles and find that for these systems, once the polynomial is fit, the method runs about six orders of magnitude faster than parallelized CPU implementations of the multislice method while achieving a 1 − R 2 error of 0.010–0.015 and root-mean-square error/standard deviation of dataset being predicted of about 0.1 when compared to full multislice simulations.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. As a result, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem.

Lei, Jinlong↗
DOE OSTI2015

Final Report on Subcontract B605152. Multigrid Methods for Systems of PDEs

The project team has continued with work on developing aggressive coarsening techniques for AMG methods. Of particular interest is the idea to use aggressive coarsening with polynomial smoothing. Using local Fourier analysis the optimal values for the parameters involved in defining the polynomial smoothers are determined automatically in a way to achieve fast convergence of cycles with aggressive coarsening. Numerical tests have the sharpness of the theoretical results. The methods are highly parallelizable and efficient multigrid algorithms on structured and semistructured grids in two and three spatial dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Sythesis of MCMC and Belief Propagation

Markov Chain Monte Carlo (MCMC) and Belief Propagation (BP) are the most popular algorithms for computational inference in Graphical Models (GM). In principle, MCMC is an exact probabilistic method which, however, often suffers from exponentially slow mixing. In contrast, BP is a deterministic method, which is typically fast, empirically very successful, however in general lacking control of accuracy over loopy graphs. In this paper, we introduce MCMC algorithms correcting the approximation error of BP, i.e., we provide a way to compensate for BP errors via a consecutive BP-aware MCMC. Our framework is based on the Loop Calculus (LC) approach which allows to express the BP error as a sum of weighted generalized loops. Although the full series is computationally intractable, it is known that a truncated series, summing up all 2-regular loops, is computable in polynomial-time for planar pair-wise binary GMs and it also provides a highly accurate approximation empirically. Motivated by this, we first propose a polynomial-time approximation MCMC scheme for the truncated series of general (non-planar) pair-wise binary models. Our main idea here is to use the Worm algorithm, known to provide fast mixing in other (related) problems, and then design an appropriate rejection scheme to sample 2-regular loops. Furthermore, we also design an efficient rejection-free MCMC scheme for approximating the full series. The main novelty underlying our design is in utilizing the concept of cycle basis, which provides an efficient decomposition of the generalized loops. In essence, the proposed MCMC schemes run on transformed GM built upon the non-trivial BP solution, and our experiments show that this synthesis of BP and MCMC outperforms both direct MCMC and bare BP schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Greenhouse Gas Source Attribution: Measurements Modeling and Uncertainty Quantification

In this project we have developed atmospheric measurement capabilities and a suite of atmospheric modeling and analysis tools that are well suited for verifying emissions of green- house gases (GHGs) on an urban-through-regional scale. We have for the first time applied the Community Multiscale Air Quality (CMAQ) model to simulate atmospheric CO 2 . This will allow for the examination of regional-scale transport and distribution of CO 2 along with air pollutants traditionally studied using CMAQ at relatively high spatial and temporal resolution with the goal of leveraging emissions verification efforts for both air quality and climate. We have developed a bias-enhanced Bayesian inference approach that can remedy the well-known problem of transport model errors in atmospheric CO 2 inversions. We have tested the approach using data and model outputs from the TransCom3 global CO 2 inversion comparison project. We have also performed two prototyping studies on inversion approaches in the generalized convection-diffusion context. One of these studies employed Polynomial Chaos Expansion to accelerate the evaluation of a regional transport model and enable efficient Markov Chain Monte Carlo sampling of the posterior for Bayesian inference. The other approach uses de- terministic inversion of a convection-diffusion-reaction system in the presence of uncertainty. These approaches should, in principle, be applicable to realistic atmospheric problems with moderate adaptation. We outline a regional greenhouse gas source inference system that integrates (1) two ap- proaches of atmospheric dispersion simulation and (2) a class of Bayesian inference and un- certainty quantification algorithms. We use two different and complementary approaches to simulate atmospheric dispersion. Specifically, we use a Eulerian chemical transport model CMAQ and a Lagrangian Particle Dispersion Model - FLEXPART-WRF. These two models share the same WRF assimilated meteorology fields, making it possible to perform a hybrid simulation, in which the Eulerian model (CMAQ) can be used to compute the initial condi- tion needed by the Lagrangian model, while the source-receptor relationships for a large state vector can be efficiently computed using the Lagrangian model in its backward mode. In ad- dition, CMAQ has a complete treatment of atmospheric chemistry of a suite of traditional air pollutants, many of which could help attribute GHGs from different sources. The inference of emissions sources using atmospheric observations is cast as a Bayesian model calibration problem, which is solved using a variety of Bayesian techniques, such as the bias-enhanced Bayesian inference algorithm, which accounts for the intrinsic model deficiency, Polynomial Chaos Expansion to accelerate model evaluation and Markov Chain Monte Carlo sampling, and Karhunen-Lo %60 eve (KL) Expansion to reduce the dimensionality of the state space. We have established an atmospheric measurement site in Livermore, CA and are collect- ing continuous measurements of CO 2 , CH 4 and other species that are typically co-emitted with these GHGs. Measurements of co-emitted species can assist in attributing the GHGs to different emissions sectors. Automatic calibrations using traceable standards are performed routinely for the gas-phase measurements. We are also collecting standard meteorological data at the Livermore site as well as planetary boundary height measurements using a ceilometer. The location of the measurement site is well suited to sample air transported between the San Francisco Bay area and the California Central Valley.

54 ENVIRONMENTAL SCIENCES↗