Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “approximation algorithm”

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 1,207 records · Page 67
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Cloud and Aerosol Retrieval for the 2001 GLAS Satellite Lidar Mission

The Geoscience Laser Altimeter System (GLAS) is scheduled for launch in July of 2001 aboard the Ice, Cloud and Land Elevation Satellite (ICESAT). In addition to being a precision altimeter for mapping the height of the Earth's icesheets, GLAS will be an atmospheric lidar, sensitive enough to detect gaseous, aerosol, and cloud backscatter signals, at horizontal and vertical resolutions of 175 and 75m, respectively. GLAS will be the first lidar to produce temporally continuous atmospheric backscatter profiles with nearly global coverage (94-degree orbital inclination). With a projected operational lifetime of five years, GLAS will collect approximately six billion lidar return profiles. The large volume of data dictates that operational analysis algorithms, which need to keep pace with the data yield of the instrument, must be efficient. So, we need to evaluate the ability of operational algorithms to detect atmospheric constituents that affect global climate. We have to quantify, in a statistical manner, the accuracy and precision of GLAS cloud and aerosol observations. Our poster presentation will show the results of modeling studies that are designed to reveal the effectiveness and sensitivity of GLAS in detecting various atmospheric cloud and aerosol features. The studies consist of analyzing simulated lidar returns. Simulation cases are constructed either from idealized renditions of atmospheric cloud and aerosol layers or from data obtained by the NASA ER-2 Cloud Lidar System (CLS). The fabricated renditions permit quantitative evaluations of operational algorithms to retrieve cloud and aerosol parameters. The use of observational data permits the evaluations of performance for actual atmospheric conditions. The intended outcome of the presentation is that climatology community will be able to use the results of these studies to evaluate and quantify the impact of GLAS data upon atmospheric modeling efforts.

Hart, William D.↗
NASA NTRS2007

Probabilistic Reasoning for Robustness in Automated Planning

A general-purpose computer program for planning the actions of a spacecraft or other complex system has been augmented by incorporating a subprogram that reasons about uncertainties in such continuous variables as times taken to perform tasks and amounts of resources to be consumed. This subprogram computes parametric probability distributions for time and resource variables on the basis of user-supplied models of actions and resources that they consume. The current system accepts bounded Gaussian distributions over action duration and resource use. The distributions are then combined during planning to determine the net probability distribution of each resource at any time point. In addition to a full combinatoric approach, several approximations for arriving at these combined distributions are available, including maximum-likelihood and pessimistic algorithms. Each such probability distribution can then be integrated to obtain a probability that execution of the plan under consideration would violate any constraints on the resource. The key idea is to use these probabilities of conflict to score potential plans and drive a search toward planning low-risk actions. An output plan provides a balance between the user s specified averseness to risk and other measures of optimality.

Schaffer, Steven↗
NASA NTRSDate not supplied

Generation of Continental Scale Percent Tree Cover Product Using Deep-learning and Multi-scale Remote Sensing Data

Spatially explicit percent tree cover (TC) estimation is critical for mapping forest aboveground biomass and its dynamics. While various TC products have been developed, there has not been a generalized framework that can be applied to diverse terrestrial ecosystems due to underlain extreme complexities. Deep learning algorithms can learn a spatial pattern and radiometric characteristics of tree canopy as a robust approximation of physical or empirical models, and thus have emerged as promising and efficient tools for large-scale TC mapping. In this study, we synergistically use very high-resolution aerial imageries (National Agriculture Imagery Program, NAIP) and medium resolution Landsat data to map continental-scale TC (CONUS and Mexico) through a hierarchical deep learning approach (Convolutional Neural Network), i.e., NAIP TC generated from a NAIP model is utilized to train a Landsat model. The produced TC product (hereafter, NEX-TC) is able to capture the spatial pattern of TC distribution and its changes driven by natural disturbance and human land management. We further explore and analyze the reliability and potential uncertainty of the NEX-TC by comparing it to lidar- (lidar-TC), National Land Cover Database (NLCD-TC), and MODIS Vegetation Continuous Field (MODIS-TC). This evaluation practice reveals that TC products based on passive optical sensors tend to underestimate TC across all land cover types while Landsat-based TCs (i.e., NEX-TC & NLCD-TC) perform better than the coarser MODIS TC estimate. Our results show that the NEX-TC is generally comparable to NLCD-TC but it particularly outperforms NLCD-TC and MODIS-TC over the dense forests where lidar-TC indicates >80% TC. These results indicate that our hierarchical deep learning approach and TC product will be effective and useful for characterizing large-scale tree cover and possibly associated carbon dynamics.

Landsat↗
DOE OSTI2020

A Modular Optimal Power Flow Method for Integrating New Technologies in Distribution Grids

This work proposes a modular concept to build optimal power flow (OPF) models for distribution networks containing various emerging technologies under diverse ownership structures, to efficiently deal with evolving technology capabilities and information sharing or privacy constraints. This concept will support any typical OPF application (e.g., optimal dispatch of a given asset without violating grid constraints) by coordinating between grid module and technology module without the need to recreate various modeling elements as technology capability changes due to innovation. Moreover, the modularity of the proposed concept enables achieving system level objectives without sharing detailed information on module level objectives and constraints among modules. To achieve this, the proposed work develops a gradient-descent algorithm which builds upon the literature on the state-of-the-art power flow approximation. The proposed concept is demonstrated with two case studies of i) controllable loads and ii) battery energy storage system (BESS) on an actual large-scale distribution grid.

Hanif, Sarmad↗
DOE OSTI2022

A comprehensive guide to the physics and usage of PYTHIA 8.3

This manual describes the PYTHIA 8.3 event generator, the most recent version of an evolving physics tool used to answer fundamental questions in particle physics. The program is most often used to generate high-energy-physics collision "events", i.e. sets of particles produced in association with the collision of two incoming high-energy particles, but has several uses beyond that. The guiding philosophy is to produce and reproduce properties of experimentally obtained collisions as accurately as possible. The program includes a wide ranges of reactions within and beyond the Standard Model, and extending to heavy ion physics. Emphasis is put on phenomena where strong interactions play a major role. The manual contains both pedagogical and practical components. All included physics models are described in enough detail to allow the user to obtain a cursory overview of used assumptions and approximations, enabling an informed evaluation of the program output. A number of the most central algorithms are described in enough detail that the main results of the program can be reproduced independently, allowing further development of existing models or the addition of new ones. Finally, a chapter dedicated fully to the user is included towards the end, providing pedagogical examples of standard use cases, and a detailed description of a number of external interfaces. The program code, the online manual, and the latest version of this print manual can be found on the PYTHIA web page: https://www.pythia.org/

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1992

A multiresolution wavelet representation in two or more dimensions

In the multiresolution approximation, a signal is examined on a hierarchy of resolution scales by projection onto sets of smoothing functions. Wavelets are used to carry the detail information connecting adjacent sets in the resolution hierarchy. An algorithm has been implemented to perform a multiresolution decomposition in n greater than or equal to 2 dimensions based on wavelets generated from products of 1-D wavelets and smoothing functions. The functions are chosen so that an n-D wavelet may be associated with a single resolution scale and orientation. The algorithm enables complete reconstruction of a high resolution signal from decomposition coefficients. The signal may be oversampled to accommodate non-orthogonal wavelet systems, or to provide approximate translational invariance in the decomposition arrays.

Bromley, B. C.↗
NASA NTRS2004

Hexagonal Pixels and Indexing Scheme for Binary Images

A scheme for resampling binaryimage data from a rectangular grid to a regular hexagonal grid and an associated tree-structured pixel-indexing scheme keyed to the level of resolution have been devised. This scheme could be utilized in conjunction with appropriate image-data-processing algorithms to enable automated retrieval and/or recognition of images. For some purposes, this scheme is superior to a prior scheme that relies on rectangular pixels: one example of such a purpose is recognition of fingerprints, which can be approximated more closely by use of line segments along hexagonal axes than by line segments along rectangular axes. This scheme could also be combined with algorithms for query-image-based retrieval of images via the Internet. A binary image on a rectangular grid is generated by raster scanning or by sampling on a stationary grid of rectangular pixels. In either case, each pixel (each cell in the rectangular grid) is denoted as either bright or dark, depending on whether the light level in the pixel is above or below a prescribed threshold. The binary data on such an image are stored in a matrix form that lends itself readily to searches of line segments aligned with either or both of the perpendicular coordinate axes. The first step in resampling onto a regular hexagonal grid is to make the resolution of the hexagonal grid fine enough to capture all the binaryimage detail from the rectangular grid. In practice, this amounts to choosing a hexagonal-cell width equal to or less than a third of the rectangular- cell width. Once the data have been resampled onto the hexagonal grid, the image can readily be checked for line segments aligned with the hexagonal coordinate axes, which typically lie at angles of 30deg, 90deg, and 150deg with respect to say, the horizontal rectangular coordinate axis. Optionally, one can then rotate the rectangular image by 90deg, then again sample onto the hexagonal grid and check for line segments at angles of 0deg, 60deg, and 120deg to the original horizontal coordinate axis. The net result is that one has checked for line segments at angular intervals of 30deg. For even finer angular resolution, one could, for example, then rotate the rectangular-grid image +/-45deg before sampling to perform checking for line segments at angular intervals of 15deg.

Johnson, Gordon G.↗
DOE OSTI2022

Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle

Recent work shows that quantum signal processing (QSP) and its multi-qubit lifted version, quantum singular value transformation (QSVT), unify and improve the presentation of most quantum algorithms. QSP/QSVT characterize the ability, by alternating ansätze, to obliviously transform the singular values of subsystems of unitary matrices by polynomial functions; these algorithms are numerically stable and analytically well-understood. That said, QSP/QSVT require consistent access to a single oracle, saying nothing about computing joint properties of two or more oracles; these can be far cheaper to determine given an ability to pit oracles against one another coherently. This work introduces a corresponding theory of QSP over multiple variables: M-QSP. Surprisingly, despite the non-existence of the fundamental theorem of algebra for multivariable polynomials, there exist necessary and sufficient conditions under which a desired stable multivariable polynomial transformation is possible. Moreover, the classical subroutines used by QSP protocols survive in the multivariable setting for non-obvious reasons, and remain numerically stable and efficient. Up to a well-defined conjecture, we give proof that the family of achievable multivariable transforms is as loosely constrained as could be expected. The unique ability of M-QSP to obliviously approximate joint functions of multiple variables coherently leads to novel speedups incommensurate with those of other quantum algorithms, and provides a bridge from quantum algorithms to algebraic geometry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1998

A Globally Convergent Augmented Lagrangian Pattern Search Algorithm for Optimization with General Constraints and Simple Bounds

We give a pattern search adaptation of an augmented Lagrangian method due to Conn, Gould, and Toint. The algorithm proceeds by successive bound constrained minimization of an augmented Lagrangian. In the pattern search adaptation we solve this subproblem approximately using a bound constrained pattern search method. The stopping criterion proposed by Conn, Gould, and Toint for the solution of this subproblem requires explicit knowledge of derivatives. Such information is presumed absent in pattern search methods; however, we show how we can replace this with a stopping criterion based on the pattern size in a way that preserves the convergence properties of the original algorithm. In this way we proceed by successive, inexact, bound constrained minimization without knowing exactly how inexact the minimization is. So far as we know, this is the first provably convergent direct search method for general nonlinear programming.

Lewis, Robert Michael↗
DOE OSTI2022

Dynamic mode decomposition with core sketch

With the increase in collected data volumes, either from experimental measurements or high fidelity simulations, there is an ever-growing need to develop computationally efficient tools to process, analyze, and interpret these datasets. Modal analysis techniques have gained great interest due to their ability to identify patterns in the data and extract valuable information about the system being considered. Dynamic mode decomposition (DMD) relies on elements of the Koopman approximation theory to compute a set of modes, each associated with a fixed oscillation frequency and a decay/growth rate. Extracting these details from large datasets can be computationally expensive due to the need to implement singular value decomposition of the input data matrix. Sketching algorithms have become popular in numerical linear algebra where statistical theoretic approaches are utilized to reduce the cost of major operations. A sketch of a matrix is another matrix, which is significantly smaller, but still sufficiently approximates the original system. We put forth an efficient DMD framework, SketchyDMD, based on a core sketching algorithm that captures information about the range and corange (their mutual relationship) of input data. The proposed sketching-based framework can accelerate various portions of the DMD routines, compared to classical methods that operate directly on the raw input data. We conduct numerical experiments using the spherical shallow water equations as a prototypical model in the context of geophysical flows. In conclusion, we show that the proposed SketchyDMD is superior to existing randomized DMD methods that are based on capturing only the range of the input data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Machine Learning Calabi–Yau Metrics

We apply machine learning to the problem of finding numerical Calabi–Yau metrics. Building on Donaldson's algorithm for calculating balanced metrics on Kähler manifolds, we combine conventional curve fitting and machine-learning techniques to numerically approximate Ricci-flat metrics. We show that machine learning is able to predict the Calabi–Yau metric and quantities associated with it, such as its determinant, having seen only a small sample of training data. Using this in conjunction with a straightforward curve fitting routine, we demonstrate that it is possible to find highly accurate numerical metrics much more quickly than by using Donaldson's algorithm alone, with our new machine-learning algorithm decreasing the time required by between one and two orders of magnitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A robust fourth-order finite-difference discretization for the strongly anisotropic transport equation in magnetized plasmas

We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following Du Toit et al. (2018), the scheme transforms mixed-derivative diffusion fluxes (which are responsible for the lack of a discrete maximum principle) into nonlinear advective fluxes, amenable to nonlinear-solver-friendly monotonicity-preserving limiters. The scheme enables accurate multi-dimensional heat transport simulations with up to seven orders of magnitude of heat-transport-coefficient anisotropies with low cross-field numerical error pollution and excellent algorithmic performance, with the number of linear iterations scaling very weakly with grid resolution and grid anisotropy, and scaling with the square-root of the implicit timestep. We propose a multigrid preconditioning strategy based on a lower-order approximation that renders the scheme efficient and scalable under grid refinement. Several numerical tests are presented that display the expected spatial convergence rates and strong algorithmic performance, including fully nonlinear magnetohydrodynamics simulations of kink instabilities in a Bennett pinch in 2D helical geometry and of ITER in 3D toroidal geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Reducing measurement costs by recycling the Hessian in adaptive variational quantum algorithms

Abstract Adaptive protocols enable the construction of more efficient state preparation circuits in variational quantum algorithms (VQAs) by utilizing data obtained from the quantum processor during the execution of the algorithm. This idea originated with Adaptive Derivative-Assembled Problem-Tailored variational quantum eigensolver (ADAPT-VQE), an algorithm that iteratively grows the state preparation circuit operator by operator, with each new operator accompanied by a new variational parameter, and where all parameters acquired thus far are optimized in each iteration. In ADAPT-VQE and other adaptive VQAs that followed it, it has been shown that initializing parameters to their optimal values from the previous iteration speeds up convergence and avoids shallow local traps in the parameter landscape. However, no other data from the optimization performed at one iteration is carried over to the next. In this work, we propose an improved quasi-Newton optimization protocol specifically tailored to adaptive VQAs. The distinctive feature in our proposal is that approximate second derivatives of the cost function are recycled across iterations in addition to optimal parameter values. We implement a quasi-Newton optimizer where an approximation to the inverse Hessian matrix is continuously built and grown across the iterations of an adaptive VQA. The resulting algorithm has the flavor of a continuous optimization where the dimension of the search space is augmented when the gradient norm falls below a given threshold. We show that this inter-optimization exchange of second-order information leads the approximate Hessian in the state of the optimizer to be consistently closer to the exact Hessian. As a result, our method achieves a superlinear convergence rate even in situations where the typical implementation of a quasi-Newton optimizer converges only linearly. Our protocol decreases the measurement costs in implementing adaptive VQAs on quantum hardware as well as the runtime of their classical simulation.

Ramôa, Mafalda (ORCID:0000000302187801)↗
NASA NTRS1980

Development and test results of a flight management algorithm for fuel conservative descents in a time-based metered traffic environment

A simple flight management descent algorithm designed to improve the accuracy of delivering an airplane in a fuel-conservative manner to a metering fix at a time designated by air traffic control was developed and flight tested. This algorithm provides a three dimensional path with terminal area time constraints (four dimensional) for an airplane to make an idle thrust, clean configured (landing gear up, flaps zero, and speed brakes retracted) descent to arrive at the metering fix at a predetermined time, altitude, and airspeed. The descent path was calculated for a constant Mach/airspeed schedule from linear approximations of airplane performance with considerations given for gross weight, wind, and nonstandard pressure and temperature effects. The flight management descent algorithm is described. The results of the flight tests flown with the Terminal Configured Vehicle airplane are presented.

Knox, C. E.↗
NASA NTRS1981

Test results of flight guidance for fuel conservative descents in a time-based metered air traffic environment

The NASA developed, implemented, and flight tested a flight management algorithm designed to improve the accuracy of delivering an airplane in a fuel-conservative manner to a metering fix at a time designated by air traffic control. This algorithm provides a 3D path with time control (4D) for the TCV B-737 airplane to make an idle-thrust, clean configured (landing gear up, flaps zero, and speed brakes retracted) descent to arrive at the metering fix at a predetermined time, altitude, and airspeed. The descent path is calculated for a constant Mach/airspeed schedule from linear approximations of airplane performance with considerations given for gross weight, wind, and nonstandard pressure and temperature effects. The flight management descent algorithms are described and flight test results are presented.

Knox, C. E.↗
NASA NTRS2006

An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems

Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.

Monte Carlo↗
NASA NTRS1989

Methods for local gravity field approximation

The most widely known modern method for estimating gravity field values from observed data is least-squares collocation. Its advantages are that it can make estimates at arbitrary locations based on irregularly spaced observations, and that it makes use of statistical information about errors in the input data while providing corresponding information about the quality of the output estimates. Disadvantages of collocation include the necessity of inverting square matrices of dimension equal to the number of data values and the need to assume covariance models for the gravity field and the data errors. Fourier methods are an important alternative to collocation; having the advantage of greater computational efficiency, but requiring data estimates to be on a regular grid and not using or providing statistical accuracy information. The GEOFAST algorithm is an implementation of collocation that achieves high computational efficiency by transforming the estimation equations into the frequency domain where an accurate approximation may be made to reduce the workload. The forward and inverse Fast Fourier Transforms (FFTs) are utilized. The accuracy and computational efficiency of the GEOFAST algorithm is demonstrated using two sets of synthetic gravity data: marine gravity for an ocean trench region including wavelengths longer than 200 km; and local land gravity containing wavelengths as short as 5 km. These results are discussed along with issues such as the advantages of first removing reference field models before carrying out the estimation algorithm.

Sailor, R. V.↗