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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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We provide the final report for this grant, detailing the publications, software produced, students trained who have joined the DOE workforce, and the impact our work has had on computational mathematics and related disciplines.
Differential dynamic programming algorithms of second and first order for optimal control, considering nonlinear unconstrained and constrained problems
This is a parallel variable population multi-objective optimizer with an adaptive unified differential evolution algorithm or a genetic algorithm. It can also be used for single objective optimization. Some features of this code include: 1) The population size varies from generation to generation to save the total # of objective function evaluations. 2) The population is uniformly distributed to a number of parallel processors for simultaneous objective function evaluation. 3) The objective function evaluation can be attained from an external simulation program with control variables in its input file and objectives calculated from its output files. 4) The optimizer includes an adaptive unified differential evolution algorithm and a real value genetic algorithm. The parameters in the unified differential evolution algorithm can be chosen to attain any mutation schemes in the published literature.
A digital computer algorithm is developed for on-line time differentiation of sampled analog voltage signals. The derivative is obtained by employing a least mean squares technique. The recursive algorithm results in a considerable reduction in computer time compared to a complete new solution of the normal equations each time a new data point is accepted. Implementation of the algorithm on a digital computer is discussed. Examples are simulated on a DEC PDP-8 computer.
We present substantially generalized and improved quantum algorithms over prior work for inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we show how the norm of the matrix exponential characterizes the run time of quantum algorithms for linear ODEs opening the door to an application to a wider class of linear and nonlinear ODEs. In [1], a quantum algorithm for a certain class of linear ODEs is given, where the matrix involved needs to be diagonalizable. The quantum algorithm for linear ODEs presented here extends to many classes of non-diagonalizable matrices including singular matrices. The algorithm here is also exponentially faster than the bounds derived in [1] for certain classes of diagonalizable matrices. Our linear ODE algorithm is then applied to nonlinear differential equations using Carleman linearization (an approach taken recently by us in [2]). The improvement over that result is two-fold. First, we obtain an exponentially better dependence on error. This kind of logarithmic dependence on error has also been achieved by [3], but only for homogeneous nonlinear equations. Second, the present algorithm can handle any sparse matrix (that models dissipation) if it has a negative log-norm (including non-diagonalizable matrices), whereas [2] and [3] additionally require normality.
An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.
Algorithm for reducing linear time-invariant differential systems to state form applied to systems described by transfer functions
Significant advances in atomically resolved imaging of crystals and surfaces have occurred in the last decade allowing unprecedented insight into local crystal structures and periodicity. Yet, the analysis of the long-range periodicity from the local imaging data, critical to correlation of functional properties and chemistry to the local crystallography, remains a challenge. Here, we introduce a Sliding Fast Fourier Transform (FFT) filter to analyze atomically resolved images of in-situ grown La5/8Ca3/8MnO3 films. We demonstrate the ability of sliding FFT algorithm to differentiate two sub-lattices, resulting from a mixed-terminated surface. Principal Component Analysis (PCA) and Independent Component Analysis (ICA) of the Sliding FFT dataset reveal the distinct changes in crystallography, step edges and boundaries between the multiple sub-lattices. The method is universal for images with any periodicity, and is especially amenable to atomically resolved probe and electron-microscopy data for rapid identification of the sub-lattices present.
ABSTRACT This paper presents a catalogue of optimized pointings for differential photometry of 23 779 quasars extracted from the Sloan Digital Sky Survey (SDSS) Catalogue and a Score for each indicating the quality of the Field of View (FoV) associated with that pointing. Observation of millimagnitude variability on a time-scale of minutes typically requires differential observations with reference to an ensemble of reference stars. For optimal performance, these reference stars should have similar colour and magnitude to the target quasar. In addition, the greatest quantity and quality of suitable reference stars may be found by using a telescope pointing which offsets the target object from the centre of the FoV. By comparing each quasar with the stars which appear close to it on the sky in the SDSS Catalogue, an optimum pointing can be calculated, and a figure of merit, referred to as the ‘Score’ is calculated for that pointing. Highly flexible software has been developed to enable this process to be automated and implemented in a distributed computing paradigm, which enables the creation of catalogues of pointings given a set of input targets. Applying this technique to a sample of 40 000 targets from the fourth SDSS quasar catalogue resulted in the production of pointings and Scores for 23 779 quasars based on their magnitudes in the SDSS r-band. This catalogue is a useful resource for observers planning differential photometry studies and surveys of quasars to select those which have many suitable celestial neighbours for differential photometry.
Online tuning of particle accelerators is necessary in order to achieve optimal machine performance. However, it is also a major challenge due to the large parameter space which must be searched and the fact that many of the desir- able objectives compete with one another, and so will not reach their optimal values simultaneously. In order to mitigate these issues, we have explored using dimension-reduction techniques to reduce the size of the parameter space which must be searched and multi-objective genetic algorithms to obtain the sets of tuning parameters which provide pareto-optimal values for the objectives. These methods have enabled us to obtain improved values of the vertical emittance at the Cornell Electron Storage Ring (CESR), and to do so with greater control of orbit errors. Algorithmic tuning is a multidisciplinary endeavour, requiring expertise in beam dynamics, diagnostics, control systems and computer science, and thus a key practical problem is to formulate a common language in which experts with different specialties can communicate. We developed a solution to this problem in the form of a generic accelerator software interface that allows for rapid prototyping of optimization and control algorithms. Our interface is built on the Experimental Physics and Industrial Control Systems (EPICS) and makes possible testing control code in simulation before deployment on real accelerators, as well as deployment of third-party optimization code.
Abstract not provided.
GPT-crafted control software and graphical user interface for Keithley 2400 Source Measure Units and global optimization algorithm. It contains Numba-compatible self-adaptive differential evolution algorithm for optimization tasks. This software is comprised of two repositories: https://github.com/NREL/Keithley_GPT https://github.com/NREL/DE
Differential dynamic programming methods for solving bang bang control problems
We propose a dynamically bi-orthogonal method (DyBO) to solve time dependent stochastic partial differential equations (SPDEs). The objective of our method is to exploit some intrinsic sparse structure in the stochastic solution by constructing the sparsest representation of the stochastic solution via a bi-orthogonal basis. It is well-known that the Karhunen–Loeve expansion (KLE) minimizes the total mean squared error and gives the sparsest representation of stochastic solutions. However, the computation of the KL expansion could be quite expensive since we need to form a covariance matrix and solve a large-scale eigenvalue problem. The main contribution of this paper is that we derive an equivalent system that governs the evolution of the spatial and stochastic basis in the KL expansion. Unlike other reduced model methods, our method constructs the reduced basis on-the-fly without the need to form the covariance matrix or to compute its eigendecomposition. In the first part of our paper, we introduce the derivation of the dynamically bi-orthogonal formulation for SPDEs, discuss several theoretical issues, such as the dynamic bi-orthogonality preservation and some preliminary error analysis of the DyBO method. We also give some numerical implementation details of the DyBO methods, including the representation of stochastic basis and techniques to deal with eigenvalue crossing. In the second part of our paper [11], we will present an adaptive strategy to dynamically remove or add modes, perform a detailed complexity analysis, and discuss various generalizations of this approach. An extensive range of numerical experiments will be provided in both parts to demonstrate the effectiveness of the DyBO method.
This paper categorizes the qualitative behavior of the Command and Control Segment (CCS) differential correction algorithm as applied to attitude estimation using simultaneous spin axis sun angle and Earth cord length measurements. The categories of interest are the domains of convergence, divergence, and their boundaries. Three series of plots are discussed that show the dependence of the estimation algorithm on the vehicle radius, the sun/Earth angle, and the spacecraft attitude. Common qualitative dynamics to all three series are tabulated and discussed. Out-of-limits conditions for the estimation algorithm are identified and discussed.
Understanding parallel algorithms is crucial for accelerating scientific simulations on complex, distributed memory, high-performance computers. Modern algorithm classification approaches learn semantics directly from source code to differentiate between algorithms, however, accessing source code is not always possible. We can learn about parallel algorithms from observing their performance, as programs running the same algorithms and using the same hardware should exhibit similar performance characteristics. We present an approach to learn algorithm classes from parallel performance data directly in order to classify algorithms without access to the source code. We extend previous work to enable classifying parallel sorting algorithms using automatic instrumentation instead of requiring manual region annotations in the source code. In this work, we design and demonstrate a study for classification of parallel sorting algorithms using parallel performance data collected from automatic instrumentation, and evaluate the performance of our new methodology on classification. We leverage Caliper to collect the performance data, Thicket for our exploratory data analysis (EDA), and PyTorch and Scikit-learn to evaluate the effectiveness of random forests, support vector machines (SVMs), decision trees, neural networks, and logistic regressions on parallel performance data. Additionally, we study noise in parallel performance data, whether the removal of noise and pre-processing of the data is necessary to accurately classify parallel sorting algorithms, and determine the effectiveness of features created from performance data. In conclusion, we demonstrate classification accuracy for these five different models of up to 97.7% across four different parallel algorithm classes.
The Computer Aided Process Planning (CAPP) module was developed to facilitate and accelerate the process planning workflow for Automated Fiber Placement (AFP). CAPP assists process planners in identifying optimal starting point locations and layup strategies for each ply of a laminate. Ply optimization operates on measurement and scoring of geometry-based defects such as gaps, overlaps, angle deviation, and steering. This paper expands on the established framework for analyzing defect stack-up through thickness of a laminate. Four different combinatorial optimization algorithms are implemented and evaluated: (1) genetic algorithm, (2) differential evolution, (3) particle swarm, and (4) greedy search. The algorithms identify the optimal combination of ply-level layup strategies, by scoring potential laminates on defect stacking, using two different objective functions. A final optimization approach is also presented which trades some performance for a large gain in efficiency. These approaches are compared to a randomized combination using a complex tool surface in a virtual case study. The result is a streamlined methodology for comparing different laminate-level manufacturing strategies and minimizing the through thickness defect stack up.
Tests of a new method for the simultaneous estimation of spacecraft attitude and sensor biases, based on a quaternion estimation algorithm minimizing Wahba's loss function are presented. The new method is compared with a conventional batch least-squares differential correction algorithm. The estimates are based on data from strapdown gyros and star trackers, simulated with varying levels of Gaussian noise for both inertially-fixed and Earth-pointing reference attitudes. Both algorithms solve for the spacecraft attitude and the gyro drift rate biases. They converge to the same estimates at the same rate for inertially-fixed attitude, but the new algorithm converges more slowly than the differential correction for Earth-pointing attitude. The slower convergence of the new method for non-zero attitude rates is believed to be due to the use of an inadequate approximation for a partial derivative matrix. The new method requires about twice the computational effort of the differential correction. Improving the approximation for the partial derivative matrix in the new method is expected to improve its convergence at the cost of increased computational effort.