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Results for “mathematical regularization”

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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

An elliptic regularity theorem for fractional partial differential operators

We present and prove a version of the elliptic regularity theorem for partial differential equations involving fractional Riemann–Liouville derivatives. In this case, regularity is defined in terms of Sobolev spaces H{sup s}(X): if the forcing of a linear elliptic fractional PDE is in one Sobolev space, then the solution is in the Sobolev space of increased order corresponding to the order of the derivatives. We also mention a few applications and potential extensions of this result.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Decomposing Loosely Coupled Mixed-Integer Programs for Optimal Microgrid Design

Microgrids are frequently employed in remote regions, in part because access to a larger electric grid is impossible, difficult, or compromises reliability and independence. Although small microgrids often employ spot generation, in which a diesel generator is attached directly to a load, microgrids that combine these individual loads and augment generators with photovoltaic cells and batteries as a distributed energy system are emerging as a safer, less costly alternative. In this work, we present a model that seeks the minimum-cost microgrid design and ideal dispatched power to support a small remote site for one year with hourly fidelity under a detailed battery model; this mixed-integer nonlinear program (MINLP) is intractable with commercial solvers but loosely coupled with respect to time. A mixed-integer linear program (MIP) approximates the model, and a partitioning scheme linearizes the bilinear terms. We introduce a novel policy for loosely coupled MIPs in which the system reverts to equivalent conditions at regular time intervals; this separates the problem into subproblems that we solve in parallel. We obtain solutions within 5% of optimality in at most six minutes across 14 MIP instances from the literature and solutions within 5% of optimality to the MINLP instances within 20 minutes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Assessment of Grizzly Capabilities for Reactor Pressure Vessels and Reinforced Concrete Structures

Over the last several years, capabilities to simulate the progression and effects of degradation in critical structures in light water reactor (LWR) nuclear power plants have been under development in the Grizzly code. Age-related material degradation is important for a number of systems in LWRs, but the main focus for Grizzly development has been on reactor pressure vessels (RPVs) and concrete structures because of their central role and the difficulty of replacement of these structures if they are found to be degraded to an unacceptable degree. The capabilities for analyzing both RPVs and concrete structures in Grizzly have reached a point where the feature sets are sufficiently complete to perform credible analyses of those types of structures. Because of this, the emphasis has shifted from foundational development to assessing the accuracy of these modeling capabilities on representative problems of interest and on improving the physical basis of those models to improve their ability to predict the actual response of those structural systems. This report documents a first set of test cases that have been developed to assess the Grizzly code on real-world problems for these two types of structures. For RPVs, these test cases consist of a set of benchmark problems where Grizzly is compared to another code. For concrete structures, a set of models of experimental specimens designed to characterize the multidimensional swelling response of reinforced concrete members due to alkali-silica reaction (ASR) has been developed and compared with experimental results. Both the RPV and concrete test cases developed here are much more computationally intensive than the small regression tests that are used in the testing that Grizzly undergoes every time a proposed set of changes is made to ensure that those changes do not adversely affect previously established behavior. A system for regularly running these large problems to monitor the behavior of the code as it is developed has been instituted. While these test cases generally indicate good comparison with the benchmark results, they also indicate areas where further development is warranted.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Extended Lagrangian Born–Oppenheimer molecular dynamics using a Krylov subspace approximation

It is shown how the electronic equations of motion in extended Lagrangian Born–Oppenheimer molecular dynamics simulations can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born–Oppenheimer molecular dynamics. We note the low-rank approximation of the Jacobian is directly related to Broyden’s class of quasi-Newton algorithms and Jacobian-free Newton–Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Learning Canonical Embeddings for Unsupervised Shape Correspondence With Locally Linear Transformations

We present a new approach to unsupervised shape correspondence learning between pairs of point clouds. We make the first attempt to adapt the classical locally linear embedding algorithm (LLE)-originally designed for nonlinear dimensionality reduction-for shape correspondence. The key idea is to find dense correspondences between shapes by first obtaining high-dimensional neighborhood-preserving embeddings of low-dimensional point clouds and subsequently aligning the source and target embeddings using locally linear transformations. We demonstrate that learning the embedding using a new LLE-inspired point cloud reconstruction objective results in accurate shape correspondences. More specifically, the approach comprises an end-to-end learnable framework of extracting high-dimensional neighborhood-preserving embeddings, estimating locally linear transformations in the embedding space, and reconstructing shapes via divergence measure-based alignment of probability density functions built over reconstructed and target shapes. Our approach enforces embeddings of shapes in correspondence to lie in the same universal/canonical embedding space, which eventually helps regularize the learning process and leads to a simple nearest neighbors approach between shape embeddings for finding reliable correspondences. Comprehensive experiments show that the new method makes noticeable improvements over state-of-the-art approaches on standard shape correspondence benchmark datasets covering both human and nonhuman shapes.

deformation↗
NASA NTRS2012

Advances in Spectral-Spatial Classification of Hyperspectral Images

Recent advances in spectral-spatial classification of hyperspectral images are presented in this paper. Several techniques are investigated for combining both spatial and spectral information. Spatial information is extracted at the object (set of pixels) level rather than at the conventional pixel level. Mathematical morphology is first used to derive the morphological profile of the image, which includes characteristics about the size, orientation, and contrast of the spatial structures present in the image. Then, the morphological neighborhood is defined and used to derive additional features for classification. Classification is performed with support vector machines (SVMs) using the available spectral information and the extracted spatial information. Spatial postprocessing is next investigated to build more homogeneous and spatially consistent thematic maps. To that end, three presegmentation techniques are applied to define regions that are used to regularize the preliminary pixel-wise thematic map. Finally, a multiple-classifier (MC) system is defined to produce relevant markers that are exploited to segment the hyperspectral image with the minimum spanning forest algorithm. Experimental results conducted on three real hyperspectral images with different spatial and spectral resolutions and corresponding to various contexts are presented. They highlight the importance of spectral–spatial strategies for the accurate classification of hyperspectral images and validate the proposed methods.

hyperspectral image↗
DOE OSTI2024

A variational phase-field framework for thermal softening and dynamic ductile fracture

A variational phase field model for dynamic ductile fracture is presented. Here, the model is designed for elasto-viscoplastic materials subjected to rapid deformations in which the effects of heat generation and material softening are dominant. The variational framework allows for the consistent inclusion of plastic dissipation in the heat equation as well as thermal softening. It employs a coalescence function to degrade fracture energy during regimes of high plastic flow. A variationally consistent form of the Johnson–Cook model is developed for use with the framework. Results from various benchmark problems in dynamic ductile fracture are presented to demonstrate capabilities. In particular, the ability of the model to regularize shear band formation and subsequent damage evolution in two- and three-dimensional problems is demonstrated. Importantly, these phenomena are naturally captured through the underlying physics without the need for phenomenological criteria such as stability thresholds for the onset of shear band formation.

42 ENGINEERING↗
NASA NTRS2012

Advances in Spectral-Spatial Classification of Hyperspectral Images

Recent advances in spectral-spatial classification of hyperspectral images are presented in this paper. Several techniques are investigated for combining both spatial and spectral information. Spatial information is extracted at the object (set of pixels) level rather than at the conventional pixel level. Mathematical morphology is first used to derive the morphological profile of the image, which includes characteristics about the size, orientation and contrast of the spatial structures present in the image. Then the morphological neighborhood is defined and used to derive additional features for classification. Classification is performed with support vector machines using the available spectral information and the extracted spatial information. Spatial post-processing is next investigated to build more homogeneous and spatially consistent thematic maps. To that end, three presegmentation techniques are applied to define regions that are used to regularize the preliminary pixel-wise thematic map. Finally, a multiple classifier system is defined to produce relevant markers that are exploited to segment the hyperspectral image with the minimum spanning forest algorithm. Experimental results conducted on three real hyperspectral images with different spatial and spectral resolutions and corresponding to various contexts are presented. They highlight the importance of spectral-spatial strategies for the accurate classification of hyperspectral images and validate the proposed methods.

Fauvel, Mathieu↗
DOE OSTI2021

An approach to characterizing spatial aspects of image system blur

Quantitative X-ray radiographic imaging systems that utilize a charged couple device (CCD) camera connected to a thick, monolithic scintillator can exhibit blur that varies spatially across the field of view, especially for thick scintillators used in pulse-power radiography of dynamically compressed objects. Here, a three-point approach to estimating and accounting for this effect is demonstrated by (a) using a local estimation technique to measure the effect of blurring a calibration object at key locations across the field of view, (b) combining each of the local estimates into a spatially varying blurring function via partitions of unity interpolation, and (c) resolving the effects of that blur on the image by solving an ill-posed inverse problem using a spatially varying regularization term. The technique is demonstrated on synthetic examples and actual radiographs collected at the Naval Research Laboratory’s (NRL)Mercury pulsed power facility.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Particle Method for the Multispecies Landau Equation

Abstract The multispecies Landau collision operator describes the two-particle, small scattering angle or grazing collisions in a plasma made up of different species of particles such as electrons and ions. Recently, a structure preserving deterministic particle method (Carrillo et al. in J. Comput. Phys. 7:100066, 2020) has been developed for the single species spatially homogeneous Landau equation. This method relies on a regularization of the Landau collision operator so that an approximate solution, which is a linear combination of Dirac delta distributions, is well-defined. Based on a weak form of the regularized Landau equation, the time dependent locations of the Dirac delta functions satisfy a system of ordinary differential equations. In this work, we extend this particle method to the multispecies case, and examine its conservation of mass, momentum, and energy, and decay of entropy properties. We show that the equilibrium distribution of the regularized multispecies Landau equation is a Maxwellian distribution, and state a critical condition on the regularization parameters that guarantees a species independent equilibrium temperature. A convergence study comparing an exact multispecies Bobylev-Krook-Wu (BKW) solution to the particle solution shows approximately 2nd order accuracy. Important physical properties such as conservation, decay of entropy, and equilibrium distribution of the particle method are demonstrated with several numerical examples.

Mathematics↗
DOE OSTI2023

Double Diffusion Maps and their Latent Harmonics for scientific computations in latent space

In this work, we introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion Maps on those latent coordinates allows the approximation of the reduced dynamical models. This second round enables mapping the latent space coordinates back to the full ambient space (what is called lifting); it also enables the approximation of full state functions of interest in terms of the reduced coordinates. In our work, we develop and test three different reduced numerical simulation methodologies, either through pre-tabulation in the latent space and integration on the fly or by going back and forth between the ambient space and the latent space. The data-driven latent space simulation results, based on the three different approaches, are validated through (a) the latent space observation of the full simulation through the Nyström Extension formula, or through (b) lifting the reduced trajectory back to the full ambient space, via Latent Harmonics. Latent space modeling often involves additional regularization to favor certain properties of the space over others, and the mapping back to the ambient space is then constructed mostly independently from these properties; here, we use the same data-driven approach to construct the latent space and then map back to the ambient space.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

Parallel architectures for computing cyclic convolutions

In the paper two parallel architectural structures are developed to compute one-dimensional cyclic convolutions. The first structure is based on the Chinese remainder theorem and Kung's pipelined array. The second structure is a direct mapping from the mathematical definition of a cyclic convolution to a computational architecture. To compute a d-point cyclic convolution the first structure needs d/2 inner product cells, while the second structure and Kung's linear array require d cells. However, to compute a cyclic convolution, the second structure requires less time than both the first structure and Kung's linear array. Another application of the second structure is to multiply a Toeplitz matrix by a vector. A table is listed to compare these two structures and Kung's linear array. Both structures are simple and regular and are therefore suitable for VLSI implementation.

Yeh, C.-S.↗
NASA NTRS1997

Error Analysis System for Spacecraft Navigation Using the Global Positioning System (GPS)

The Flight Dynamics Division (FDD) at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC) is currently developing improved space-navigation filtering algorithms to use the Global Positioning System (GPS) for autonomous real-time onboard orbit determination. In connection with a GPS technology demonstration on the Small Satellite Technology Initiative (SSTI)/Lewis spacecraft, FDD analysts and programmers have teamed with the GSFC Guidance, Navigation, and Control Branch to develop the GPS Enhanced Orbit Determination Experiment (GEODE) system. The GEODE system consists of a Kalman filter operating as a navigation tool for estimating the position, velocity, and additional states required to accurately navigate the orbiting Lewis spacecraft by using astrodynamic modeling and GPS measurements from the receiver. A parallel effort at the FDD is the development of a GPS Error Analysis System (GEAS) that will be used to analyze and improve navigation filtering algorithms during development phases and during in-flight calibration. For GEAS, the Kalman filter theory is extended to estimate the errors in position, velocity, and other error states of interest. The estimation of errors in physical variables at regular intervals will allow the time, cause, and effect of navigation system weaknesses to be identified. In addition, by modeling a sufficient set of navigation system errors, a system failure that causes an observed error anomaly can be traced and accounted for. The GEAS software is formulated using Object Oriented Design (OOD) techniques implemented in the C++ programming language on a Sun SPARC workstation. The Phase 1 of this effort is the development of a basic system to be used to evaluate navigation algorithms implemented in the GEODE system. This paper presents the GEAS mathematical methodology, systems and operations concepts, and software design and implementation. Results from the use of the basic system to evaluate navigation algorithms implemented on GEODE are also discussed. In addition, recommendations for generalization of GEAS functions and for new techniques to optimize the accuracy and control of the GPS autonomous onboard navigation are presented.

Truong, S. H.↗
DOE OSTI2019

On Dimensional Regularization in the Yang–Mills Theory

We suggest an asymptotic approach to renormalization in the case of dimensional regularization. As an example, the quantum Yang–Mills theory in the four-dimensional space-time is considered. A formula for the renormalized effective action is derived by using the asymptotic behavior of the bare coupling constant. Then we discuss the dimensional transmutation, the process of renormalization, and the properties of the coupling constant.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Avoiding Communication in Primal and Dual Block Coordinate Descent Methods

Primal and dual block coordinate descent methods are iterative methods for solving regularized and unregularized optimization problems. Distributed-memory parallel implementations of these methods have become popular in analyzing large machine learning datasets. However, existing implementations communicate at every iteration, which, on modern data center and supercomputing architectures, often dominates the cost of floating-point computation. Recent results on communication-avoiding Krylov subspace methods suggest that large speedups are possible by re-organizing iterative algorithms to avoid communication. We show how applying similar algorithmic transformations can lead to primal and dual block coordinate descent methods that only communicate every $s$ iterations---where $s$ is a tuning parameter---instead of every iteration for the regularized least-squares problem. We show that the communication-avoiding variants reduce the number of synchronizations by a factor of $s$ on distributed-memory parallel machines without altering the convergence rate and attain strong scaling speedups of up to $6.1\times$ over the “standard algorithm" on a Cray XC30 supercomputer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Stochastic gradient descent algorithm for stochastic optimization in solving analytic continuation problems

We propose a stochastic gradient descent based optimization algorithm to solve the analytic continuation problem in which we extract real frequency spectra from imaginary time Quantum Monte Carlo data. The procedure of analytic continuation is an ill-posed inverse problem which is usually solved by regularized optimization methods, such like the Maximum Entropy method, or stochastic optimization methods. The main contribution of this work is to improve the performance of stochastic optimization approaches by introducing a supervised stochastic gradient descent algorithm to solve a flipped inverse system which processes the random solutions obtained by a type of Fast and Efficient Stochastic Optimization Method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Cybersecurity of DER Systems: Cybersecurity Training for State Commissions

NARUC regularly hosts multi-day cybersecurity training events for commissioners and their staff to gain knowledge of IT/OT technologies, understand the spectrum of state and federal approaches to cybersecurity, and explore cybersecurity cost recovery challenges and innovative solutions to address them. About 300 commissioners and staffers typically register for these virtual events.

cybersecurity cost recovery↗