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Results for “algorithmic differentiation”

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 127 records · Page 7

Material Science Image Analysis using Quant-CT in ImageJ

We introduce a computational analysis workflow to access properties of solid objects using nondestructive imaging techniques that rely on X-ray imaging. The goal is to process and quantify structures from material science sample cross sections. The algorithms can differentiate the porous media (high density material) from the void (background, low density media) using a Boolean classifier, so that we can extract features, such as volume, surface area, granularity spectrum, porosity, among others. Our workflow, Quant-CT, leverages several algorithms from ImageJ, such as statistical region merging and 3D object counter. It also includes schemes for bilateral filtering that use a 3D kernel, for parallel processing of sub-stacks, and for handling over-segmentation using histogram similarities. The Quant-CT supports fast user interaction, providing the ability for the user to train the algorithm via subsamples to feed its core algorithms with automated parameterization. Quant-CT plugin is currently available for testing by personnel at the Advanced Light Source and Earth Sciences Divisions and Energy Frontier Research Center (EFRC), LBNL, as part of their research on porous materials. The goal is to understand the processes in fluid-rock systems for the geologic sequestration of CO2, and to develop technology for the safe storage of CO2 in deep subsurface rock formations. We describe our implementation, and demonstrate our plugin on porous material images. This paper targets end-users, with relevant information for developers to extend its current capabilities.

97 MATHEMATICS AND COMPUTING↗

Differentially Private K -Means Clustering Applied to Meter Data Analysis and Synthesis

The proliferation of smart meters has resulted in a large amount of data being generated. It is increasingly apparent that methods are required for allowing a variety of stakeholders to leverage the data in a manner that preserves the privacy of the consumers. The sector is scrambling to define policies, such as the so called ‘15/15 rule’, to respond to the need. However, the current policies fail to adequately guarantee privacy. Here, in this paper, we address the problem of allowing third parties to apply K-means clustering, obtaining customer labels and centroids for a set of load time series by applying the framework of differential privacy. We leverage the method to design an algorithm that generates differentially private synthetic load data consistent with the labeled data. We test our algorithm’s utility by answering summary statistics such as average daily load profiles for a 2-dimensional synthetic dataset and a real-world power load dataset.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Machine Learning Pattern Recognition Algorithm With Applications to Coherent Laser Combination

Herein we analyze a new kind of machine learning algorithm designed to feedback stabilize coherently combined lasers. This algorithm learns differential, rather than absolute, values of action in phase space, in order to facilitate learning on initially unstable systems. Experiments have shown that this approach can control small-scale spatial beam combination with high stability. In this paper we analyze the algorithm's performance and limitations in depth, showing that it can continuously learn during operation in order to track changes. Using simulation, we extend the application to temporal combination, and show that it scales to more complex instances by combining 81 beams.

97 MATHEMATICS AND COMPUTING↗

Rexsss Performance Analysis: Domain Decomposition Algorithm Implementations for Resilient Numerical Partial Differential Equation Solvers

The future of extreme-scale computing is expected to magnify the influence of soft faults as a source of inaccuracy or failure in solutions obtained from distributed parallel computations. The development of resilient computational tools represents an essential recourse for understanding the best methods for absorbing the impacts of soft faults without sacrificing solution accuracy. The Rexsss (Resilient Extreme Scale Scientific Simulations) project pursues the development of fault resilient algorithms for solving partial differential equations (PDEs) on distributed systems. Performance analyses of current algorithm implementations assist in the identification of runtime inefficiencies.

97 MATHEMATICS AND COMPUTING↗

Differential sampling for fast frequency acquisition via adaptive extended least squares algorithm

This paper presents a differential signal model along with appropriate sampling techinques for least squares estimation of the frequency and frequency derivatives and possibly the phase and amplitude of a sinusoid received in the presence of noise. The proposed algorithm is recursive in mesurements and thus the computational requirement increases only linearly with the number of measurements. The dimension of the state vector in the proposed algorithm does not depend upon the number of measurements and is quite small, typically around four. This is an advantage when compared to previous algorithms wherein the dimension of the state vector increases monotonically with the product of the frequency uncertainty and the observation period. Such a computational simplification may possibly result in some loss of optimality. However, by applying the sampling techniques of the paper such a possible loss in optimality can made small.

Kumar, Rajendra↗

Evaluation of the Index and Singular Points of Linear Differential-Algebraic Equations of Higher Order

We study linear systems of ordinary differential equations of higher order with an identically singular matrix at the higher derivative of the required vector-valued function in the domain of definition. We give definitions of the index and singular points for these systems, formulate the conditions of solvability, and deduce a formula for the general solution. The algorithms for finding the index and singular points are presented.

97 MATHEMATICS AND COMPUTING↗

Reconstructing magnetic deflections from sets of proton images using differential evolution

Proton imaging is a powerful technique for imaging electromagnetic fields within an experimental volume, in which spatial variations in proton fluence are a result of deflections to proton trajectories due to interaction with the fields. When deflections are large, proton trajectories can overlap, and this nonlinearity creates regions of greatly increased proton fluence on the image, known as caustics. The formation of caustics has been a persistent barrier to reconstructing the underlying fields from proton images. We have developed a new method for reconstructing the path-integrated magnetic fields, which begins to address the problem posed by caustics. Our method uses multiple proton images of the same object, each image at a different energy, to fill in the information gaps and provide some uniqueness when reconstructing caustic features. We use a differential evolution algorithm to iteratively estimate the underlying deflection function, which accurately reproduces the observed proton fluence at multiple proton energies simultaneously. We test this reconstruction method using synthetic proton images generated for three different, cylindrically symmetric field geometries at various field amplitudes and levels of proton statistics and present reconstruction results from a set of experimental images. Here, the method we propose requires no assumption of deflection linearity and can reliably solve for fields underlying linear, nonlinear, and caustic proton image features for the selected geometries and is shown to be fairly robust to noise in the input proton intensity.

47 OTHER INSTRUMENTATION↗

Comparison and testing of extended Kalman filters for attitude estimation of the Earth Radiation Budget Satellite

This paper presents the testing and comparison of two extended Kalman filters (EKFs) developed for the Earth Radiation Budget Satellite (ERBS). One EKF updates the attitude quaternion using a four-component additive error quaternion. This technique is compared to that of a second EKF, which uses a multiplicative error quaternion. Brief developments of the algorithms are included. The convergence properties, singularity problems, and normalization techniques of the two filters are addressed. Both filters are tested with simulated ERBS sensor data in addition to real ERBS sensor data. The results of the two filters are also compared to those from the ERBS operational ground support software, which uses a batch differential correction algorithm to estimate attitude and gyro biases.

Bar-Itzhack, Itzhack Y.↗

Testing Surrogate-Based Optimization with the Fortified Branin-Hoo Extended to Four Dimensions

Some popular functions used to test global optimization algorithms have multiple local optima, all with the same value, making them all global optima. It is easy to make them more challenging by fortifying them via adding a localized bump at the location of one of the optima. In previous work the authors illustrated this for the Branin-Hoo function and the popular differential evolution algorithm, showing that the fortified Branin-Hoo required an order of magnitude more function evaluations. This paper examines the effect of fortifying the Branin-Hoo function on surrogate- based optimization, which usually proceeds by adaptive sampling. Two algorithms are considered. The EGO algorithm, which is based on a Gaussian process (GP) and an algorithm based on radial basis functions (RBF). EGO is found to be more frugal in terms of the number of required function evaluations required to identify the correct basin, but it is expensive to run on a desktop, limiting the number of times the runs could be repeated to establish sound statistics on the number of required function evaluations. The RBF algorithm was cheaper to run, providing more sound statistics on performance. A four-dimensional version of the Branin-Hoo function was introduced in order to assess the effect of dimensionality. Furthermore, it was found that the difference between the ordinary function and the fortified one was much more pronounced for the four-dimensional function compared to the two dimensional one.

97 MATHEMATICS AND COMPUTING↗

Station Keeping of Small Outboard-Powered Boats

Three station keeping controllers have been developed which work to minimize displacement of a small outboard-powered vessel from a desired location. Each of these three controllers has a common initial layer that uses fixed-gain feedback control to calculate the desired heading of the vessel. A second control layer uses a common fixed-gain feedback controller to calculate the net forward thrust, one of two algorithms for controlling engine angle (Fixed-Gain Proportional-integral-derivative (PID) or PID with Adaptively Augmented Gains), and one of two algorithms for differential throttle control (Fixed-Gain PID and PID with Adaptive Differential Throttle gains), which work together to eliminate heading error. The three selected controllers are evaluated using a numerical simulation of a 33-foot center console vessel with twin outboards that is subject to wave, wind, and current disturbances. Each controller is tested for its ability to maintain position in the presence of three sets of environmental disturbances. These algorithms were tested with current velocity of 1.5 m/s, significant wave height of 0.5 m, and wind speeds of 2, 5, and 10 m/s. These values were chosen to model conditions a small vessel may experience in the Gulf Stream off of Fort Lauderdale. The Fixed-gain PID controller progressively got worse as wind speeds increased, while the controllers using adaptive methodologies showed consistent performance over all weather conditions and decreased heading error by as much as 20%. Thus, enhanced robustness to environmental changes has been gained by using an adaptive algorithm.

Fisher, A. D.↗

Circular polarization analyzer with polarization tunable focusing of surface plasmon polaritons

A practical circular polarization analyzer (CPA) that can selectively focus surface plasmon polaritons (SPPs) at two separate locations, according to the helicity of the circularly polarized light, is designed and experimentally verified in the terahertz frequency range. The CPA consists of fishbone-slit units and is designed using the simulated annealing algorithm. By differentially detecting the intensities of the two SPPs focuses, the helicity of the incident circularly polarized light can be obtained and the CPA is less vulnerable to the noise of incident light. The proposed device may also have wide potential applications in chiral SPPs photonics and the analysis of chiral molecules in biology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

THE ADJOINT METHOD APPLIED TO TIME-DISTANCE HELIOSEISMOLOGY

For a given misfit function, a specified optimality measure of a model, its gradient describes the manner in which one may alter properties of the system to march toward a stationary point. The adjoint method, arising from partial-differential-equation-constrained optimization, describes a means of extracting derivatives of a misfit function with respect to model parameters through finite computation. It relies on the accurate calculation of wavefields that are driven by two types of sources, namely, the average wave-excitation spectrum, resulting in the forward wavefield, and differences between predictions and observations, resulting in an adjoint wavefield. All sensitivity kernels relevant to a given measurement emerge directly from the evaluation of an interaction integral involving these wavefields. The technique facilitates computation of sensitivity kernels (Frechet derivatives) relative to three-dimensional heterogeneous background models, thereby paving the way for nonlinear iterative inversions. An algorithm to perform such inversions using as many observations as desired is discussed.

79 ASTRONOMY AND ASTROPHYSICS↗

Rate determination from vector observations

Vector observations are a common class of attitude data provided by a wide variety of attitude sensors. Attitude determination from vector observations is a well-understood process and numerous algorithms such as the TRIAD algorithm exist. These algorithms require measurement of the line of site (LOS) vector to reference objects and knowledge of the LOS directions in some predetermined reference frame. Once attitude is determined, it is a simple matter to synthesize vehicle rate using some form of lead-lag filter, and then, use it for vehicle stabilization. Many situations arise, however, in which rate knowledge is required but knowledge of the nominal LOS directions are not available. This paper presents two methods for determining spacecraft angular rates from vector observations without a priori knowledge of the vector directions. The first approach uses an extended Kalman filter with a spacecraft dynamic model and a kinematic model representing the motion of the observed LOS vectors. The second approach uses a 'differential' TRIAD algorithm to compute the incremental direction cosine matrix, from which vehicle rate is then derived.

Weiss, Jerold L.↗

OPTIMIZATION OF FAST FISSION GAS RELEASE MODEL PARAMETERS USING MACHINE LEARNING ACCELERATED EVOLUTIONARY ALGORITHMS

Fission gas release models used in FRAPCON and FAST are based on equations that describe the physical transport phenomena that control release from the fuel pellet to the rod void volume of fission gas produced during irradiation. Although these models are physically based, many of the parameters that control the release such as the impact of burnup on diffusion and bubble formation and saturation are critical to the accurate prediction of fission gas release, but cannot be measured in any quantitative way. To overcome this problem, these parameters have been empirically derived to provide a best fit to the available data that includes rod puncture data and electron probe microanalysis (EMPA) and X-ray fluorescence (XRF) data of radial location of residual gas within the pellet. In general, a heuristic approach for deriving these parameters via practical implementation of expert analyses on just a few dependent variables has been shown to perform quite well in most situations. In this paper, we present an approach for applying machine learning to expedite model development. This approach is based on developing a deep artificial neural network which describes FRAPCON’s fission gas release models, and optimizes parameters by a differential evaluation algorithm. This approach allows us to quickly and accurately tune physical models based on expert judgment, and works as a human-in-the-loop approach, to assist the modeler in identifying and addressing regions of high uncertainty in a multi-parameter space. Results of the updated fission gas release model will be shown for all the FAST assessment data.

Johns, Jesse M.↗

HFBTHO-AD: Differentiation of a nuclear energy density functional code

The HFBTHO code implements a nuclear energy density functional solver to model the structure of atomic nuclei. HFBTHO has previously been used to calibrate energy functionals and perform sensitivity analysis by using derivative-free methods. To enable derivative-based optimization and uncertainty quantification approaches, we must compute the derivatives of HFBTHO outputs with respect to the parameters of the energy functional, which are a subset of all input parameters of the code. Here, we use the algorithmic/automatic differentiation (AD) tool Tapenade to differentiate HFBTHO. We compare the derivatives obtained using AD against finite-difference approximation and examine the performance of the derivative computation.

Algorithmic differentiation↗

Q-POP-Thermo: A general-purpose thermodynamics solver for ferroelectric materials

We report that Q-POP-Thermo is a program designed to compute thermodynamic monodomain equilibrium states and their properties for ferroelectric single crystals and thin films based on the Landau-Ginzburg-Devonshire (LGD) Theory. Utilizing symbolic manipulation with the SymPy Library, the governing equations along with appropriate boundary conditions are solved for speedy minimization of the free energy of a crystal. Utilizing the popular Differential Evolution algorithm, with appropriate hybridization, multiple phase diagrams, such as the pressure-temperature phase diagram for bulk single crystals and the common strain-temperature phase diagram for monodomain thin-film systems can be readily generated. Furthermore, a variety of material properties of stable ferroelectric phases, including dielectric, piezoelectric, and electrocaloric properties, can simultaneously be calculated. Validation studies are presented for both thin-film and single crystal systems to test the effectiveness and capability of the open-source program.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Privacy-Preserving Knowledge Transfer with Bootstrap Aggregation of Teacher Ensembles

There is a need to transfer knowledge among institutions and organizations to save effort in annotation and labeling or in enhancing task performance. However, knowledge transfer is difficult because of restrictions that are in place to ensure data security and privacy. Institutions are not allowed to exchange data or perform any activity that may expose personal information. With the leverage of a differential privacy algorithm in a high-performance computing environment, we propose a new training protocol, Bootstrap Aggregation of Teacher Ensembles (BATE), which is applicable to various types of machine learning models. The BATE algorithm is based on and provides enhancements to the PATE algorithm, maintaining competitive task performance scores on complex datasets with underrepresented class labels.We conducted a proof-of-the-concept study of the information extraction from cancer pathology report data from four cancer registries and performed comparisons between four scenarios: no collaboration, no privacy-preserving collaboration, the PATE algorithm, and the proposed BATE algorithm. The results showed that the BATE algorithm maintained competitive macro-averaged F1 scores, demonstrating that the suggested algorithm is an effective yet privacy-preserving method for machine learning and deep learning solutions.

Yoon, Hong-Jun↗

Performance investigation of a high-field active magnetic regenerator

Regenerative magnetic cycles are of interest for small-scale, high-efficiency cryogen liquefiers; however, commercially relevant performance has yet to be demonstrated. To develop improved engineering prototypes, an efficient modeling tool is required to screen the multi-parameter design space. In this work, we describe an Active Magnetic Regenerative Refrigerator (AMRR) prototype using a high-field superconducting magnet that produces a 100 K temperature span. Using the experimental data, a semi-analytic AMR element model is validated and enhanced system performance is simulated using liquid propane as a heat transfer fluid. In addition, the regenerator composition and fluid flow are simultaneously optimized using a differential evolution algorithm. Simulation results indicate that a natural gas liquefier with a 160 K span and a second-law efficiency exceeding 20% is achievable.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗