Search NASA⌕ Search

SEARCH · Search NASA

Results for “gradient methods”

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 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Novel pore size-controlled, susceptibility matched, 3D-printed MRI phantoms

We report the design concept and fabrication of MRI phantoms, containing blocks of aligned microcapillaires that can be stacked into larger arrays to construct diameter distribution phantoms or fractured, to create a “powder-averaged” emulsion of randomly oriented blocks for vetting or calibrating advanced MRI methods, that is, diffusion tensor imaging, AxCaliber MRI, MAP-MRI, and multiple pulsed field gradient or double diffusion-encoded microstructure imaging methods. The goal was to create a susceptibility-matched microscopically anisotropic but macroscopically isotropic phantom with a ground truth diameter that could be used to vet advanced diffusion methods for diameter determination in fibrous tissues. Two-photon polymerization, a novel three-dimensional printing method is used to fabricate blocks of capillaries. Double diffusion encoding methods were employed and analyzed to estimate the expected MRI diameter. Susceptibility-matched microcapillary blocks or modules that can be assembled into large-scale MRI phantoms have been fabricated and measured using advanced diffusion methods, resulting in microscopic anisotropy and random orientation. This phantom can vet and calibrate various advanced MRI methods and multiple pulsed field gradient or diffusion-encoded microstructure imaging methods. We demonstrated that two double diffusion encoding methods underestimated the ground truth diameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1999

A Priori Subgrid Analysis of Temporal Mixing Layers with Evaporating Droplets

Subgrid analysis of a transitional temporal mixing layer with evaporating droplets has been performed using three sets of results from a Direct Numerical Simulation (DNS) database, with Reynolds numbers (based on initial vorticity thickness) as large as 600 and with droplet mass loadings as large as 0.5. In the DNS, the gas phase is computed using a Eulerian formulation, with Lagrangian droplet tracking. The Large Eddy Simulation (LES) equations corresponding to the DNS are first derived, and key assumptions in deriving them are first confirmed by computing the terms using the DNS database. Since LES of this flow requires the computation of unfiltered gas-phase variables at droplet locations from filtered gas-phase variables at the grid points, it is proposed to model these by assuming the gas-phase variables to be the sum of the filtered variables and a correction based on the filtered standard deviation; this correction is then computed from the Subgrid Scale (SGS) standard deviation. This model predicts the unfiltered variables at droplet locations considerably better than simply interpolating the filtered variables. Three methods are investigated for modeling the SGS standard deviation: the Smagorinsky approach, the Gradient model and the Scale-Similarity formulation. When the proportionality constant inherent in the SGS models is properly calculated, the Gradient and Scale-Similarity methods give results in excellent agreement with the DNS.

Okongo, Nora↗
NASA NTRS1993

Corrections to fringe distortion due to flow density gradients in optical interferometry

An analytical method is formulated to account for distortions of optical interferograms used for studies of flow over airfoils experiencing dynamic stall. It is shown that such distortions are generated primarily due to optical path deflections in the test flow, caused by large density gradients. Such in-flow optical path deflections are neglected in conventional optical techniques for flow studies. The present method employs a ray analysis to determine these in-flow optical path deflections, and accurately predicts the interferogram distortions.

Cho, Y. C.↗
DOE OSTI2018

Exploiting graphical processing units to enable quantum chemistry calculation of large solvated molecules with conductor-like polarizable continuum models

The conductor–like polarizable continuum model (C–PCM) with switching/Gaussian smooth discretization is a widely used implicit solvation model in quantum chemistry. We have previously implemented C–PCM solvation for Hartree–Fock (HF) and density functional theory (DFT) on graphical processing units (GPUs), enabling the quantum mechanical treatment of large solvated biomolecules. Here, we first propose a GPU–based algorithm for the PCM conjugate gradient linear solver that greatly improves the performance for very large molecules. The overhead for PCM–related evaluations now consumes less than 15% of the total runtime for DFT calculations on large molecules. Second, we demonstrate that our algorithms tailored for ground state C–PCM are transferable to excited state properties. Using a single GPU, our method evaluates the analytic gradient of the linear response PCM time–dependent density functional theory energy up to 80× faster than a conventional central processing unit (CPU)–based implementation. In addition, our C–PCM algorithms are transferable to other methods that require electrostatic potential (ESP) evaluations. For example, we achieve speed–ups of up to 130× for restricted ESP–based atomic charge evaluations, when compared to CPU–based codes. As a result, we also summarize and compare the different PCM cavity discretization schemes used in some popular quantum chemistry packages as a reference for both users and developers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2015

Adaptive State Predictor Based Human Operator Modeling on Longitudinal and Lateral Control

Control-theoretic modeling of the human operator dynamic behavior in manual control tasks has a long and rich history. In the last two decades, there has been a renewed interest in modeling the human operator. There has also been significant work on techniques used to identify the pilot model of a given structure. The purpose of this research is to attempt to go beyond pilot identification based on collected experimental data and to develop a predictor of pilot behavior. An experiment was conducted to categorize these interactions of the pilot with an adaptive controller compensating during control surface failures. A general linear in-parameter model structure is used to represent a pilot. Three different estimation methods are explored. A gradient descent estimator (GDE), a least squares estimator with exponential forgetting (LSEEF), and a least squares estimator with bounded gain forgetting (LSEBGF) used the experiment data to predict pilot stick input. Previous results have found that the GDE and LSEEF methods are fairly accurate in predicting longitudinal stick input from commanded pitch. This paper discusses the accuracy of each of the three methods - GDE, LSEEF, and LSEBGF - to predict both pilot longitudinal and lateral stick input from the flight director's commanded pitch and bank attitudes.

Trujillo, Anna C.↗
DOE OSTI2013

Fabricating functionally graded films with designed gradient profiles using pulsed laser deposition

A novel picosecond-laser pulsed laser deposition method has been developed for fabricating functionally graded films with pre-designed gradient profiles. Theoretically, the developed method is capable of precisely fabricating films with any thicknesses and any gradient profiles by controlling the laser beam powers for the two different targets based on the film composition profiles. As an implementation example, we have successfully constructed functionally graded diamond-like carbon films with six different gradient profiles: linear, quadratic, cubic, square root, cubic root, and sinusoidal. Energy dispersive X-ray spectroscopy is employed for investigating the chemical composition along the thickness of the film, and the deposition profile and thickness errors are found to be less than 3% and 1.04%, respectively. To the best of the authors' knowledge, this is the first method for fabricating films with designed gradient profiles and has huge potential in many areas of coatings and films, including multifunctional optical films. We believe that this method is not only limited to the example considered in this study, but also can be applied to all material combinations as long as they can be deposited using the pulsed laser deposition technique.

36 MATERIALS SCIENCE↗
DOE OSTI2017

A high-order staggered meshless method for elliptic problems

Here, we present a new meshless method for scalar diffusion equations, which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of nearby neighbor connectivity of the discretization points. This graph defines a local primal-dual grid complex with a virtual dual grid, in the sense that specification of the dual metric attributes is implicit in the method's construction. Our method combines a topological gradient operator on the local primal grid with a generalized moving least squares approximation of the divergence on the local dual grid. We show that the resulting approximation of the div-grad operator maintains polynomial reproduction to arbitrary orders and yields a meshless method, which attains $O(h^{m})$ convergence in both $L^2$- and $H^1$-norms, similar to mixed finite element methods. We demonstrate this convergence on curvilinear domains using manufactured solutions in two and three dimensions. Application of the new method to problems with discontinuous coefficients reveals solutions that are qualitatively similar to those of compatible mesh-based discretizations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

An FFT-based approach for Bloch wave analysis: application to polycrystals

A method based on the Fast Fourier Transform is proposed to obtain the dispersion relation of acoustic waves in heterogeneous periodic media with arbitrary microstructures. The microstructure is explicitly considered using a voxelized Representative Volume Element (RVE). The dispersion diagram is obtained solving an eigenvalue problem for Bloch waves in Fourier space. To this aim, two linear operators representing stiffness and mass are defined through the use of differential operators in Fourier space. The smallest eigenvalues are obtained using the implicitly restarted Lanczos and the subspace iteration methods, and the required inverse of the stiffness operator is done using the conjugate gradient with a preconditioner. The method is used to study the propagation of acoustic waves in elastic polycrystals, showing the strong effect of crystal anistropy and polycrystaline texture on the propagation. It is shown that the method combines the simplicity of classical Fourier series analysis with the versatility of Finite Elements to account for complex geometries proving an efficient and general approach which allows the use of large RVEs in 3D.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Theoretical prediction of the band offsets at the ZnO/anatase TiO{sub 2} and GaN/ZnO heterojunctions using the self-consistent ab initio DFT/GGA-1/2 method

The band offsets of the ZnO/anatase TiO{sub 2} and GaN/ZnO heterojunctions are calculated using the density functional theory/generalized gradient approximation (DFT/GGA)-1/2 method, which takes into account the self-energy corrections and can give an approximate description to the quasiparticle characteristics of the electronic structure of semiconductors. We present the results of the ionization potential (IP)-based and interfacial offset-based band alignments. In the interfacial offset-based band alignment, to get the natural band offset, we use the surface calculations to estimate the change of reference level due to the interfacial strain. Based on the interface models and GGA-1/2 calculations, we find that the valence band maximum and conduction band minimum of ZnO, respectively, lie 0.64 eV and 0.57 eV above those of anatase TiO{sub 2}, while lie 0.84 eV and 1.09 eV below those of GaN, which agree well with the experimental data. However, a large discrepancy exists between the IP-based band offset and the calculated natural band offset, the mechanism of which is discussed. Our results clarify band alignment of the ZnO/anatase TiO{sub 2} heterojunction and show good agreement with the GW calculations for the GaN/ZnO heterojunction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Modified niche optima and breadths explain the historical contingency of bacterial community responses to eutrophication in coastal sediments

Abstract Previous studies have shown that the response of bacterial communities to disturbances depends on their environmental history. Historically fluctuating habitats host communities that respond better to disturbance than communities of historically stable habitats. However, the exact ecological mechanism that drives this dependency remains unknown. Here, we experimentally demonstrate that modifications of niche optima and niche breadths of the community members are driving this dependency of bacterial responses to past environmental conditions. First, we develop a novel, simple method to calculate the niche optima and breadths of bacterial taxa regarding single environmental gradients. Then, we test this method on sediment bacterial communities of three habitats, one historically stable and less loaded and two historically more variable and more loaded habitats in terms of historical chlorophyll‐α water concentration, that we subject to hypoxia via organic matter addition ex situ . We find that communities containing bacterial taxa differently adapted to hypoxia show different structural and functional responses, depending on the sediment's environmental history. Specifically, in the historically less fluctuating and loaded sediments where we find more taxa poorly adapted to hypoxic conditions, communities change a lot over time and organic matter is not degraded efficiently. The opposite is true for the historically more fluctuating and loaded sediments where we find more taxa well adapted to hypoxia. Based on the community responses observed here, we also propose an alternative calculation of community resistance that takes into account how rapidly the communities respond to disturbances and not just the initial and final states of the community.

Fodelianakis, S.↗
DOE OSTI2023

Density functional based methods for light harvesting molecules

The goal of the proposal was to computationally study the photoinduced charge transfer excited states of organic molecules. The systems of interest are the large organic supramolecules that have potential for photovoltaic applications. The simulation of the charge transfer excited states in large supramolecular assemblies require quantum mechanical methods that can be applied to systems with hundreds of atoms. Through this project we have implemented a perturbative delta-self-consistent field method that can easily describe the charge transfer excited states with regular density functionals without range separation. The cost of the calculations of an excited state is similar to that of the ground state. The method also allows for calculation of the energy gradients of the excited state. The developed method was applied to study a number of different supramolecular systems containing hundreds of atoms with excellent agreement with experiment. The absorption characteristics and the influence of density functional approximations were also examined. These led to several studies on the variety of organic electron donor and acceptor molecules. Apart from these developments through this project we also improved the code capabilities by implementing new meta-GGA functionals. This was a major step since the code is purely density functional and earlier the functional capabilities were limited only to generalized gradient approximations. A total of 23 peer-reviewed publications in top chemical physics journals resulted from this grant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

An FFT-based micromechanical model for gradient enhanced brittle fracture

Damage models incorporated within FFT-based micromechanical methods have received much attention recently because of the need to better understand and predict brittle and ductile fracture. An important aspect of a damage model is non-local regularization, which removes the mesh dependence of the predictions that otherwise become physically unacceptable upon grid refinement. In this work, the Helmholtz-type equation for non-local gradient regularization of a damage model on a distorted grid is solved using an FFT-based approach. Further, the resulting system of equations is solved using the Jacobi iterative method. The model is applied to simulate brittle fracture of an intermetallic. The influence of the time and space discretization, the length-scale parameter, and intermetallic crystallographic orientation on crack evolution is studied.

36 MATERIALS SCIENCE↗
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↗
NASA NTRS2010

Modeling and Characterization of Near-Crack-Tip Plasticity from Micro- to Nano-Scales

Methodologies for understanding the plastic deformation mechanisms related to crack propagation at the nano-, meso- and micro-length scales are being developed. These efforts include the development and application of several computational methods including atomistic simulation, discrete dislocation plasticity, strain gradient plasticity and crystal plasticity; and experimental methods including electron backscattered diffraction and video image correlation. Additionally, methodologies for multi-scale modeling and characterization that can be used to bridge the relevant length scales from nanometers to millimeters are being developed. The paper focuses on the discussion of newly developed methodologies in these areas and their application to understanding damage processes in aluminum and its alloys.

Glaessgen, Edward H.↗
NASA NTRS2011

Modeling and Characterization of Near-Crack-Tip Plasticity from Micro- to Nano-Scales

Methodologies for understanding the plastic deformation mechanisms related 10 crack propagation at the nano, meso- and micro-length scales are being developed. These efforts include the development and application of several computational methods including atomistic simulation, discrete dislocation plasticity, strain gradient plasticity and crystal plasticity; and experimental methods including electron backscattered diffraction and video image correlation. Additionally, methodologies for multi-scale modeling and characterization that can be used to bridge the relevant length scales from nanometers to millimeters are being developed. The paper focuses on the discussion of newly developed methodologies in these areas and their application to understanding damage processes in aluminum and its alloys.

Glaessgen, Edward H.↗
DOE OSTI2017

Gradient-based Optimization for Regression in the Functional Tensor-Train Format

We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of gradient-based optimization procedures, including stochastic gradient descent and quasi-Newton methods, for learning the parameters of a functional tensor-train (FT) that yields improved accuracy over standard alternating least squares methods. The functional tensor-train uses the tensor-train (TT) representation of low-rank arrays as an ansatz for a class of low-multilinear-rank functions. The FT is represented by a set of matrix-valued functions that contain a set of univariate functions, and the regression task is to learn the parameters of these univariate functions. Our second contribution demonstrates that using nonlinearly parameterized univariate functions, e.g., symmetric kernels with moving centers, within each core can outperform the standard approach of using a linear expansion of basis functions. Our final contributions are new rank adaptation and group-sparsity regularization procedures to minimize overfitting. We use several benchmark problems to demonstrate at least an order of magnitude lower accuracy with gradient-based optimization methods than ALS in the low-sample number regime. We also demonstrate an order of magnitude reduction in accuracy on a test problem resulting from nonlinear parameterizations over linear parameterizations. Finally we compare regression performance with 22 other nonparametric and parametric regression methods on 10 real-world data sets. We achieve top-five accuracy for seven of the data sets and best accuracy for two of the data sets. These rankings are the best amongst parametric models and competetive with the best non-parametric methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

Function-space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs

Two existing function-space quasi-Newton algorithms, the Davidon algorithm and the projected gradient algorithm, are modified so that they may handle directly control-variable inequality constraints. A third quasi-Newton-type algorithm, developed by Broyden, is extended to optimal control problems. The Broyden algorithm is further modified so that it may handle directly control-variable inequality constraints. From a computational viewpoint, dyadic operator implementation of quasi-Newton methods is shown to be superior to the integral kernel representation. The quasi-Newton methods, along with the steepest descent method and two conjugate gradient algorithms, are simulated on three relatively simple (yet representative) bounded control problems, two of which possess singular subarcs. Overall, the Broyden algorithm was found to be superior. The most notable result of the simulations was the clear superiority of the Broyden and Davidon algorithms in producing a sharp singular control subarc.

Edge, E. R.↗
DOE OSTI2025

Efficient proximal subproblem solvers for a nonsmooth trust-region method

In [R. J. Baraldi and D. P. Kouri, Mathematical Programming, (2022), pp. 1-40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex and nonsmooth convex function. The principle expense of this method is in computing a trial iterate that satisfies the so-called fraction of Cauchy decrease condition—a bound that ensures the trial iterate produces sufficient decrease of the subproblem model. In this paper, we expound on various proximal trust-region subproblem solvers that generalize traditional trust-region methods for smooth unconstrained and convex-constrained problems. We introduce a simplified spectral proximal gradient solver, a truncated nonlinear conjugate gradient solver, and a dogleg method. Finally, we compare algorithm performance on examples from data science and PDE-constrained optimization.

97 MATHEMATICS AND COMPUTING↗