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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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22 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Iterated Gauss-Seidel GMRES

The GMRES algorithm of Saad and Schultz [SIAM J. Sci. Stat. Comput., 7 (1986), pp. 856-869] is an iterative method for approximately solving linear systems Ax = b, with initial guess x0 and residual r0 = b Ax0. The algorithm employs the Arnoldi process to generate the Krylov basis vectors (the columns of Vk ). It is well known that this process can be viewed as a QR factorization of the matrix Bk = [r0, AVk] at each iteration. Despite an O (..epsilon..)..kappa.. (Bk ) loss of orthogonality, for unit roundoff ..epsilon..and condition number ..kappa.. , the modified Gram-Schmidt formulation was shown to be backward stable in the seminal paper by Paige et al. [SIAM J. Matrix Anal.Appl., 28 (2006), pp. 264-284]. We present an iterated Gauss-Seidel formulation of the GMRES algorithm (IGS-GMRES) based on the ideas of Ruhe [Linear Algebra Appl., 52 (1983), pp. 591-601] and Swirydowicz et al. [Numer. Linear Algebra Appl., 28 (2020), pp. 1-20]. IGS-GMRES maintains orthogonality to the level O (..epsilon..)..kappa.. (Bk ) or O (..epsilon..), depending on the choice of one or two iterations; for two Gauss-Seidel iterations, the computed Krylov basis vectors remain orthogonal to working accuracy and the smallest singular value of Vk remains close to one. The resulting GMRES method is thus backward stable. We show that IGS-GMRES can be implemented with only a single synchronization point per iteration, making it relevant to large-scale parallel computing environments. We also demonstrate that, unlike MGS-GMRES, in IGS-GMRES the relative Arnoldi residual corresponding to the computed approximate solution no longer stagnates above machine precision even for highly nonnormal systems.

Arnoldi-QR↗
DOE OSTI2021

What Can and Cannot Be Expected from Tokamak Fusion

This article is a response to the analysis of nuclear fusion by V. V. Orlov and L. I. Ponomarev in their article “Nuclear problems of thermonuclear power generation” [Atomnaya Energiya, 124, No. 2, 105–110 (2018); Atomic Energy, 124, No. 2, 129–138 (2018)], pointing to the decades-long lack-of-progress in thermonuclear energy research. Here, the authors of the article attribute the lack-of-progress to fundamental problems in the nuclear aspects of thermonuclear fusion. Here, the reason for the current stagnation – essentially, the degeneration of thermonuclear fusion that commenced in the 1950s–1970s with rapid development – is presented. The scientific investigations have been and remain within the scope of the Tamm–Sakharov concept of toroidal plasma confinement, which provided the first impetus to progress but soon showed its insufficiency. An additional element is considered – the suppression of plasma cooling by using moving liquid lithium to pump out plasma. For tokamaks this opens up new prospects for obtaining burning plasma suitable for use in hybrid (fission-fusion) reactors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Mixing in ICF implosions on the National Ignition Facility caused by the fill-tube

The micrometer-scale tube that fills capsules with thermonuclear fuel in inertial confinement fusion experiments at the National Ignition Facility is also one of the implosion's main degradation sources. It seeds a perturbation that injects the ablator material into the center, radiating away some of the hot-spot energy. This paper discusses how the perturbation arises in experiments using high-density carbon ablators and how the ablator mix interacts once it enters the hot-spot. Both modeling and experiments show an in-flight areal-density perturbation and localized x-ray emission at stagnation from the fill-tube. Simulations suggest that the fill-tube is degrading an otherwise 1D implosion by ~2×, but when other degradation sources are present, the yield reduction is closer to 20%. Characteristics of the fill-tube assembly, such as the through-hole size and the glue mass, alter the dynamics and magnitude of the degradation. Overall, these aspects point the way toward improvements in the design, some of which (smaller diameter fill-tube) have already shown improvements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Plateau Phenomenon in Gradient Descent Training of RELU Networks: Explanation, Quantification, and Avoidance

The ability of neural networks to provide ‘best in class’ approximation across a wide range of applications is well-documented. Nevertheless, the powerful expressivity of neural networks comes to naught if one is unable to effectively train (choose) the parameters defining the network. In general, neural networks are trained by gradient descent type optimization methods,a stochastic variant thereof. In practice, such methods result in the loss function decreases rapidly at the beginning of training but then, after a relatively small number of steps, significantly slow down. The loss may even appear to stagnate over the period of a large number of epochs, only to then suddenly start to decrease fast again for no apparent reason. This so-called plateau phenomenon manifests itself in many learning tasks. The present work aims to identify and quantify the root causes of plateau phenomenon.analysis is carried out in the setting of univariate ReLU networks. No assumptions are made on the number of neurons relative to the number of training data, and our results hold for both the lazy and adaptive regimes. Here, the main findings are: plateaux correspond to periods during which activation patterns remain constant, where activation pattern refers to the number of data points that activate a given neuron; quantification of convergence of the gradient flow dynamics; and, characterization stationary points in terms solutions of local least squares regression lines over subsets of the training data. Based on these conclusions, we propose a new iterative training method, the Active Neuron Least Squares (ANLS), characterised by the explicit adjustment of the activation pattern at each step, which is designed to enable a quick exit from a plateau. Illustrative numerical examples are included throughout.

97 MATHEMATICS AND COMPUTING↗