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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Gradient-Informed Design Optimization of Select Nuclear Systems

In this work, we present a gradient-informed design optimization of nuclear reactor core components based on neutronics objectives with both continuous and discrete materials. The main argument in favor of using gradient-informed design optimization is that it scales well with increasing dimensionality of the design space. First, a challenge problem with 121 free parameters is solved with a gradient-informed method and then with a genetic algorithm. Then, a challenge problem to optimize the flux profile of a simplified assembly with eight axial zones is solved. Both challenge problems are solved using directly calculated derivatives from Tools for Sensitivity and Uncertainty Analysis Methodology Implementation (TSUNAMI) in the SCALE package. Furthermore, we demonstrate how a discrete optimization problem—selection of materials for 121 voxels—can be lifted into a continuous problem with mixed materials. In the continuous space, adjoint-based gradients are well-defined, and gradient descent is applicable. Then, a forcing function is introduced that with the selection of an appropriately sized hyperparameter can be used to guide the optimized continuous solution back into a discrete solution. This paper presents an account of the challenges that were faced when applying a gradient-informed optimization algorithm using a Monte Carlo calculation to estimate the gradient information and compares a gradient descent optimization method to a genetic algorithm optimization of the same geometry. Overall, this work demonstrates the potential use of adjoint-based gradient calculations in design optimization of nuclear systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Efficient ptychographic phase retrieval via a matrix-free Levenberg-Marquardt algorithm

The phase retrieval problem, where one aims to recover a complex-valued image from far-field intensity measurements, is a classic problem encountered in a range of imaging applications. Modern phase retrieval approaches usually rely on gradient descent methods in a nonlinear minimization framework. Calculating closed-form gradients for use in these methods is tedious work, and formulating second order derivatives is even more laborious. Additionally, second order techniques often require the storage and inversion of large matrices of partial derivatives, with memory requirements that can be prohibitive for data-rich imaging modalities. We use a reverse-mode automatic differentiation (AD) framework to implement an efficient matrix-free version of the Levenberg-Marquardt (LM) algorithm, a longstanding method that finds popular use in nonlinear least-square minimization problems but which has seen little use in phase retrieval. Furthermore, we extend the basic LM algorithm so that it can be applied for more general constrained optimization problems (including phase retrieval problems) beyond just the least-square applications. Since we use AD, we only need to specify the physics-based forward model for a specific imaging application; the first and second-order derivative terms are calculated automatically through matrix-vector products, without explicitly forming the large Jacobian or Gauss-Newton matrices typically required for the LM method. We demonstrate that this algorithm can be used to solve both the unconstrained ptychographic object retrieval problem and the constrained “blind” ptychographic object and probe retrieval problems, under the popular Gaussian noise model as well as the Poisson noise model. We compare this algorithm to state-of-the-art first order ptychographic reconstruction methods to demonstrate empirically that this method outperforms best-in-class first-order methods: it provides excellent convergence guarantees with (in many cases) a superlinear rate of convergence, all with a computational cost comparable to, or lower than, the tested first-order algorithms.

36 MATERIALS SCIENCE↗
NASA NTRS2017

A Smoothed Eclipse Model for Solar Electric Propulsion Trajectory Optimization

Solar electric propulsion (SEP) is the dominant design option for employing low-thrust propulsion on a space mission. Spacecraft solar arrays power the SEP system but are subject to blackout periods during solar eclipse conditions. Discontinuity in power available to the spacecraft must be accounted for in trajectory optimization, but gradient-based methods require a differentiable power model. This work presents a power model that smooths the eclipse transition from total eclipse to total sunlight with a logistic function. Example trajectories are computed with differential dynamic programming, a second-order gradient-based method.

trajectory design↗
NASA NTRS2017

A Smoothed Eclipse Model for Solar Electric Propulsion Trajectory Optimization

Solar electric propulsion (SEP) is the dominant design option for employing low-thrust propulsion on a space mission. Spacecraft solar arrays power the SEP system but are subject to blackout periods during solar eclipse conditions. Discontinuity in power available to the spacecraft must be accounted for in trajectory optimization, but gradient-based methods require a differentiable power model. This work presents a power model that smooths the eclipse transition from total eclipse to total sunlight with a logistic function. Example trajectories are computed with differential dynamic programming, a second-order gradient-based method.

optimization↗
NASA NTRS1973

A study of numerical methods of solution of the equations of motion of a controlled satellite under the influence of gravity gradient torque

Numerical methods of integration of the equations of motion of a controlled satellite under the influence of gravity-gradient torque are considered. The results of computer experimentation using a number of Runge-Kutta, multi-step, and extrapolation methods for the numerical integration of this differential system are presented, and particularly efficient methods are noted. A large bibliography of numerical methods for initial value problems for ordinary differential equations is presented, and a compilation of Runge-Kutta and multistep formulas is given. Less common numerical integration techniques from the literature are noted for further consideration.

Thompson, J. F.↗
DOE OSTI2025

Analytical gradient-based optimization of CALPHAD model parameters

The calibration of CALPHAD (CALculation of PHAse Diagrams) models involves the solution of a very challenging high-dimensional multiobjective optimization problem. Traditional approaches to parameter fitting predominantly rely on gradient-free methods, which while robust, are computationally inefficient and often scale poorly with model complexity. In this work, we introduce and demonstrate a generalizable framework for analytic gradient-based optimization of the parameters of the CALPHAD model enabled by the recently formalized Jansson derivative technique. This method allows for efficient evaluation of gradients of thermodynamic properties at equilibrium with respect to model parameters, even in the presence of arbitrarily complex internal degrees of freedom. Leveraging these semi-analytic gradients, we employ the conjugate gradient (CG) method to optimize thermodynamic model parameters for four binary alloy systems: Cu-Mg, Fe-Ni, Cr-Ni, and Cr-Fe. Across all systems, CG achieves comparable or superior optimality relative to Bayesian ensemble Markov Chain Monte Carlo (MCMC) with improvements in computational efficiency ranging from one to three orders of magnitude. Furthermore, our results establish a new paradigm for CALPHAD assessments in which high fidelity data-rich model calibration becomes tractable using deterministic gradient-informed algorithms.

CALPHAD↗
NASA NTRS1998

A Novel Ultrasonic Method for Characterizing Microstructural Gradients in Tubular Structures

Ultrasonic velocity and time-of-flight (TOF) imaging that uses back surface reflections to gage volumetric material quality is highly suited for quantitative characterization of microstructural gradients including those due to pore fraction, density, fiber fraction, and chemical composition variations. However, a weakness of conventional pulse echo ultrasonic velocity and TOF imaging is that the image shows the effects of thickness as well as microstructural variations, unless the part is uniformly thick. This limits this imaging method's usefulness in practical applications. Prior studies have described a pulse echo TOF based ultrasonic imaging method that requires using a single transducer in combination with a reflector plate placed behind samples which, eliminates the effect of thickness variation in the image. In those studies, this method was successful at isolating ultrasonic variations due to material in plate like samples of silicon nitride, metal matrix composite, and polymer matrix composite. In this study, the method is engineered for inspection of more complex shaped structures- those having (hollow) tubular or curved geometry. The experimental inspection technique and results are described as applied to a polymer matrix composite "proof of concept" tube that contains machined patches of various depths and an as manufactured monolithic silicon nitride ceramic tube that might be used in "real world" applications.

Roth, Don J.↗
NASA NTRS2010

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC-NN, CC-SA, and CC-FA schemes on all grids and for NC schemes on triangular grids; the discretization errors of the CC-NA scheme without clipping do not converge on irregular grids. Accurate gradient reconstruction can be achieved by introducing a local approximate mapping; without approximate mapping, only the NC scheme with weighted LSQ method provides accurate gradients. Defect correction iterations for the CC-NA scheme without clipping diverge; for the NC scheme with weighted LSQ method, the iterations either diverge or converge very slowly. The best option in curved geometries is the CC-SA scheme that offers low complexity, second-order discretization errors, and fast convergence.

Diskin, Boris↗
DOE OSTI2023

SwitchX : Gmin-Gmax Switching for Energy-efficient and Robust Implementation of Binarized Neural Networks on ReRAM Xbars

Memristive crossbars can efficiently implement Binarized Neural Networks (BNNs) wherein the weights are stored in high-resistance states (HRS) and low-resistance states (LRS) of the synapses. We propose SwitchX mapping of BNN weights onto ReRAM crossbars such that the impact of crossbar non-idealities, that lead to degradation in computational accuracy, are minimized. Essentially, SwitchX maps the binary weights in such a manner that a crossbar instance comprises of more HRS than LRS synapses. We find BNNs mapped onto crossbars with SwitchX to exhibit better robustness against adversarial attacks than the standard crossbar mapped BNNs, the baseline. Finally, we combine SwitchX with state-aware training (that further increases the feasibility of HRS states during weight mapping) to boost the robustness of a BNN on hardware. We find that this approach yields stronger defense against adversarial attacks than adversarial training, a state-of the-art software defense. We perform experiments on a VGG16 BNN with benchmark datasets (CIFAR-10, CIFAR-100 and TinyImagenet) and use Fast Gradient Sign Method (ϵ = 0.05 to 0.3) and Projected Gradient Descent (ϵ = $\frac{2}{255}$ to $\frac{32}{255}$, α = $\frac{2}{255}$) adversarial attacks. We show that SwitchX combined with state-aware training can yield upto ~35% improvements in clean accuracy and ~6–16% in adversarial accuracies against conventional BNNs. Furthermore, an important by-product of SwitchX mapping is increased crossbar power savings, owing to an increased proportion of HRS synapses, which is furthered with state-aware training. We obtain upto ~21–22% savings in crossbar power consumption for state-aware trained BNN mapped via SwitchX on 16 × 16 and 32 × 32 crossbars using the CIFAR-10 and CIFAR-100 datasets.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

The development of two-dimensional object identification techniques

This report marks the end of the first year of an anticipated three year effort to study methods for numerically identifying objects according to shape in two dimensions. The method is based upon comparing the unit gradient of an observed object and the unit gradient of a standard object over a specified range of points. The manner in which the gradients are compared forms the basis of a shape recognition scheme, which is then applied to simple closed plane figures. The gradient based method is calibrated by using various distorted objects in comparison with a set of standard reference objects. The use of pattern recognition techniques for computer identification of two-dimensional figures will be investigated during the second and third years of this project.

Lebby, Gary↗
NASA NTRS1994

Neural networks applications to control and computations

Several interrelated problems in the area of neural network computations are described. First an interpolation problem is considered, then a control problem is reduced to a problem of interpolation by a neural network via Lyapunov function approach, and finally a new, faster method of learning as compared with the gradient descent method, was introduced.

Luxemburg, Leon A.↗
NASA NTRS2014

Application of Sequential Quadratic Programming to Minimize Smart Active Flap Rotor Hub Loads

In an analytical study, SMART active flap rotor hub loads have been minimized using nonlinear programming constrained optimization methodology. The recently developed NLPQLP system (Schittkowski, 2010) that employs Sequential Quadratic Programming (SQP) as its core algorithm was embedded into a driver code (NLP10x10) specifically designed to minimize active flap rotor hub loads (Leyland, 2014). Three types of practical constraints on the flap deflections have been considered. To validate the current application, two other optimization methods have been used: i) the standard, linear unconstrained method, and ii) the nonlinear Generalized Reduced Gradient (GRG) method with constraints. The new software code NLP10x10 has been systematically checked out. It has been verified that NLP10x10 is functioning as desired. The following are briefly covered in this paper: relevant optimization theory; implementation of the capability of minimizing a metric of all, or a subset, of the hub loads as well as the capability of using all, or a subset, of the flap harmonics; and finally, solutions for the SMART rotor. The eventual goal is to implement NLP10x10 in a real-time wind tunnel environment.

HUB LOADS↗
NASA NTRS2018

Real-Time Adaptive Drag Minimization Wind Tunnel Investigation of a Flexible Wing with Variable Camber Continuous Trailing Edge Flap System

This paper reports the results of a recently completed real-time adaptive drag minimization wind tunnel investigation of a highly flexible wing wind tunnel model equipped with the Variable Camber Continuous Trailing Flap (VCCTEF) technology at the University of Washington Aeronautical Laboratory (UWAL). The wind tunnel investigation is funded by NASA SBIR Phase II contract with Scientific Systems Company, Inc. (SSCI) and University of Washington (UW) as a subcontractor. The wind tunnel model is a sub-scale Common Research Model (CRM) wing constructed of foam core and fiberglass skin and is aeroelastically scaled to achieve a wing tip deflection of 10% of the wing semi-span which represents a typical wing tip deflection for a modern transport such as Boeing 787. The jig-shape twist of the CRM wing is optimized using a CART3D aero-structural model to achieve the minimum induced drag for the design cruise lift coefficient of 0.5. The wing is equipped with two chord wise cambered segments for each of the six span wise flap sections for a total of 12 individual flap segments that comprise the VCCTEF system. Each of the 12 flap segments is actively controlled by an electric servo-actuator. The real-time adaptive drag optimization strategy includes an on-board aerodynamic model identification, a model excitation, and a real-time drag optimization. The on-board aerodynamic model is constructed parametrically as a function of the angle of attack and flap positions to model the lift and drag coefficients of the wing. The lift coefficient models include a linear model and a second-order model. The drag coefficient models include a quadratic model and a higher-order up to 6th-order model to accurately model the drag coefficient at high angles of attack. The onboard aerodynamic model identification includes a recursive least-squares (RLS) algorithm and a batch least-squares (BLS) algorithm designed to estimate the model parameters. The model excitation method is designed to sample the input set that comprises the angle of attack and the flap positions. Three model excitation methods are developed: random excitation method, sweep method, and iterative angle-of-attack seeking method. The real-time drag optimization includes a generic algorithm developed by SSCI and several optimization methods developed by NASA which include a second-order gradient Newton-Raphson optimization method, an iterative gradient optimization method, a pseudo-inverse optimization method, an analytical optimization method, and an iterative refinement optimization method. The first wind tunnel test entry took place in September 2017. This test revealed major hardware issues and required further redesign of the flap servo mechanisms. The second test entry took place in April 2018. However, the test was not successful due to the issues with the onboard aerodynamic model identification RLS algorithm which incorrectly identified model parameters. This test also provides an experimental comparison study between the VCCTEF and a variable camber discrete trailing edge flap (VCDTEF) without the elastomer transition mechanisms. The experimental result confirms the benefit of the VCCTEF which produces lower drag by 5% than the VCDTEF. The third and final test entry took place in June 2018 after the issues with the RLS algorithm have been identified and corrected. Additional improvements were implemented. These include the BLS algorithm, the iterative angle-of-attack seeking method, the iterative gradient optimization method, and the pseudo-inverse optimization method. The test objectives were successfully demonstrated as the real-time drag optimization identifies several optimal solutions at off-design lift coefficients. The iterative gradient optimization method is found to achieve up to 4.7% drag reduction for the off-design lift coefficient of 0.7. The pseudo-inverse optimization method which does not require the drag coefficient model is found to be quite effective in reducing drag. Up to 9.4% drag reduction for the off-design lift coefficient of 0.7 is achieved with the pseudo-inverse optimization method. The wind tunnel investigation demonstrates the potential of real-time drag optimization technology. Several new capabilities are developed that could enable future adaptive wing technologies for flexible wings equipped with drag control devices such as the VCCTEF.

Drag Optimization↗
NASA NTRS2008

Accuracy of Gradient Reconstruction on Grids with High Aspect Ratio

Gradient approximation methods commonly used in unstructured-grid finite-volume schemes intended for solutions of high Reynolds number flow equations are studied comprehensively. The accuracy of gradients within cells and within faces is evaluated systematically for both node-centered and cell-centered formulations. Computational and analytical evaluations are made on a series of high-aspect-ratio grids with different primal elements, including quadrilateral, triangular, and mixed element grids, with and without random perturbations to the mesh. Both rectangular and cylindrical geometries are considered; the latter serves to study the effects of geometric curvature. The study shows that the accuracy of gradient reconstruction on high-aspect-ratio grids is determined by a combination of the grid and the solution. The contributors to the error are identified and approaches to reduce errors are given, including the addition of higher-order terms in the direction of larger mesh spacing. A parameter GAMMA characterizing accuracy on curved high-aspect-ratio grids is discussed and an approximate-mapped-least-square method using a commonly-available distance function is presented; the method provides accurate gradient reconstruction on general grids. The study is intended to be a reference guide accompanying the construction of accurate and efficient methods for high Reynolds number applications

Thomas, James↗
DOE OSTI2020

Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

Here we propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing a scalable parameter in each layer (layer-wise) and for every neuron (neuron-wise) separately, and then optimizing it using a variant of stochastic gradient descent algorithm. In order to further increase the training speed, an activation slope-based slope recovery term is added in the loss function, which further accelerates convergence, thereby reducing the training cost. On the theoretical side, we prove that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposed method is not achievable by base methods with any (adaptive) learning rates. We further show that the adaptive activation methods accelerate the convergence by implicitly multiplying conditioning matrices to the gradient of the base method without any explicit computation of the conditioning matrix and the matrix–vector product. The different adaptive activation functions are shown to induce different implicit conditioning matrices. Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Electronic structure and thermoelectric properties of CoAsSb with post-DFT approaches

Here, we study the electronic structure and thermoelectric properties of recently synthesized CoAsSb. The calculated bandgap becomes more accurate for increasingly-complex electronic structure methods: generalized gradient approximation, hybrid functionals, selfconsistent linearized quasiparticle GW method (LQSGW), and LQSGW with simplified vertex corrections. By equating the bandgaps of each method from a rigid shift of the bands, we evaluate the contributions made to thermoelectric properties beyond the bandgap. In doing so, we evaluate the efficacy of a commonpractice: a rigid shift applied to less-costly electronic structure methods in order to gain some accuracy of the more-costly methods. We find that while the shift made the Seebeck coefficients much closer to one another than from the original electronic structures, there remain differences in the Goldsmid-Sharp (thermoelectric) bandgap between the methods and from the intended electronic bandgap. Additionally, some lasting differences in temperature dependence remain between the methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Validating methods for modeling composition gradients in planar shock experiments

An interface is Rayleigh–Taylor (RT) unstable when acceleration pushes a less dense material into a more dense one, and the growth of the instability is governed partly by the Atwood number gradient. Double-shell inertial confinement fusion capsules have a foam spacer layer pushing on an inner capsule composed of a beryllium tamper and high-Z inner shell, and so have RT unstable interfaces that require benchmarking. To this end, the results of a planar shock experiment with beryllium/tungsten targets are presented. One target had the normal bilayer construction of beryllium and tungsten in two distinct layers; the second target had the beryllium grading into tungsten with a quasi-exponential profile, motivated by the potential for reduced RT growth with the gradient profile. Simulations mimic the shock profiles for both targets and match the shock velocity to within 5%. These results validate the ability of our simulations to model double-shell capsules with bilayer or graded layer Be/W inner shells, which are needed to design future experiments at the National Ignition Facility.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗