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Results for “projected gradient method”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A Subspace-Inclusive Sampling Method for the Computational Design of Compositionally Graded Alloys

Abstract Compositionally graded alloys, a subclass of functionally graded materials (FGMs), utilize localized variations in composition with a single metal part to achieve higher performance than traditional single material parts. In previous work [Kirk, T., Galvan, E., Malak, R., and Arroyave, R., 2018, “Computational Design of Gradient Paths in Additively Manufactured Functionally Graded Materials,” J. Mech. Des., 140, p. 111410. 10.1115/1.4040816], the authors presented a computational design methodology that avoids common issues which limit a gradient alloy’s feasibility, such as deleterious phases, and optimizes for performance objectives. However, the previous methodology only samples the interior of a composition space, meaning designed gradients must include all elements in the space throughout the gradient. Because even small amounts of additional alloying elements can introduce new deleterious phases, this characteristic often neglects potentially simpler solutions to otherwise unsolvable problems and, consequently, discourages the addition of new elements to the state space. The present work improves upon the previous methodology by introducing a sampling method that includes subspaces with fewer elements in the design search. The new method samples within an artificially expanded form of the state space and projects samples outside the true region to the nearest true subspace. This method is evaluated first by observing the sample distribution in each subspace of a 3D, 4D, and 5D state space. Next, a parametric study in a synthetic 3D problem compares the performance of the new sampling scheme to the previous methodology. Lastly, the updated methodology is applied to design a gradient from stainless steel to equiatomic NiTi that has practical uses such as embedded shape memory actuation and for which the previous methodology fails to find a feasible path.

Engineering↗
DOE OSTI2015

Four-Dimensional Magnetic Resonance Imaging With 3-Dimensional Radial Sampling and Self-Gating–Based K-Space Sorting: Early Clinical Experience on Pancreatic Cancer Patients

Purpose: To apply a novel self-gating k-space sorted 4-dimensional MRI (SG-KS-4D-MRI) method to overcome limitations due to anisotropic resolution and rebinning artifacts and to monitor pancreatic tumor motion. Methods and Materials: Ten patients were imaged using 4D-CT, cine 2-dimensional MRI (2D-MRI), and the SG-KS-4D-MRI, which is a spoiled gradient recalled echo sequence with 3-dimensional radial-sampling k-space projections and 1-dimensional projection-based self-gating. Tumor volumes were defined on all phases in both 4D-MRI and 4D-CT and then compared. Results: An isotropic resolution of 1.56 mm was achieved in the SG-KS-4D-MRI images, which showed superior soft-tissue contrast to 4D-CT and appeared to be free of stitching artifacts. The tumor motion trajectory cross-correlations (mean ± SD) between SG-KS-4D-MRI and cine 2D-MRI in superior–inferior, anterior–posterior, and medial–lateral directions were 0.93 ± 0.03, 0.83 ± 0.10, and 0.74 ± 0.18, respectively. The tumor motion trajectories cross-correlations between SG-KS-4D-MRI and 4D-CT in superior–inferior, anterior–posterior, and medial–lateral directions were 0.91 ± 0.06, 0.72 ± 0.16, and 0.44 ± 0.24, respectively. The average standard deviation of gross tumor volume calculated from the 10 breathing phases was 0.81 cm{sup 3} and 1.02 cm{sup 3} for SG-KS-4D-MRI and 4D-CT, respectively (P=.012). Conclusions: A novel SG-KS-4D-MRI acquisition method capable of reconstructing rebinning artifact–free, high-resolution 4D-MRI images was used to quantify pancreas tumor motion. The resultant pancreatic tumor motion trajectories agreed well with 2D-cine-MRI and 4D-CT. The pancreatic tumor volumes shown in the different phases for the SG-KS-4D-MRI were statistically significantly more consistent than those in the 4D-CT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation

This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order solution is that reduced order Karush–Kuhn–Tucker conditions accurately represent their full order counterparts. In particular, accurate reduced order approximations are needed for the forward and adjoint dynamical models, as well as for the reduced gradient. New strategies to construct reduced order based are developed for proper orthogonal decomposition (POD) ROM data assimilation using both Galerkin and Petrov–Galerkin projections. For the first time POD, tensorial POD, and discrete empirical interpolation method (DEIM) are employed to develop reduced data assimilation systems for a geophysical flow model, namely, the two dimensional shallow water equations. Numerical experiments confirm the theoretical framework for Galerkin projection. In the case of Petrov–Galerkin projection, stabilization strategies must be considered for the reduced order models. The new reduced order shallow water data assimilation system provides analyses similar to those produced by the full resolution data assimilation system in one tenth of the computational time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Symmetry restoration in mixed-spin paired heavy nuclei

The nature of the nuclear pairing condensates in heavy nuclei, specifically neutron-proton (spin-triplet), versus identical-particle (spin-singlet) pairing has been an active area of research for quite some time. In this work, we probe three candidates that should display spin-triplet, spin-singlet, and mixed-spin pairing. Using theoretical approaches such as the gradient method and symmetry-restoration techniques, we find the ground state of these nuclei in Hartree–Fock–Bogoliubov theory and compute ground state to ground state pair-transfer amplitudes to neighboring isotopes while simultaneously projecting to specific particle number and nuclear-spin values. We identify specific reactions for future experimental research that could shed light on spin-triplet and mixed-spin pairing.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Numerical Experiments and Identification of Areas for Further Consideration (B639388 Subcontract Quarter II Report)

The second quarter of the project was spent carrying out numerical experiments on a variety of test matrices, using a combination of precisions, with the intent to study the numerical properties (namely, accuracy and convergence behavior) of the Conjugate Gradient (CG) method. We summarize our findings in the remainder of the document. Other activities include attending biweekly xSDK meetings. We are also currently collaborating with Steven Thomas (NREL) on the numerical stability analysis of “low-synch” Gram-Schmidt routines, for potential application within high-performance GMRES variants. This work is in progress. The subsequent quarter will be spent delving into the numerical analysis in order to provide theoretical explanation for the behavior observed in our experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Investigation of Scanning Droplet Cell Technology for Electrochemical Deposition of Custom Three-Dimensional Alloys

The goal of this project was to assess the feasibility of a new method of electroplating, which we have termed “electroprinting”, for fabricating millimeter to centimeter metal parts with full density, and eventually, with bespoke 3D internal density patterns. Alloys, gradients and varying density is beyond the scope of this work, and efforts were focused on developing the technology to be capable of printing solid parts, beyond the lines and columns previously reported in the literature. Enabling this technology would expand the design space possible for the WPD program, allowing for smooth and complex density gradients in parts rather than discrete density steps between multilayers. We successfully designed and built an electroprinting apparatus, capable of printing copper in customizable 1-D patterns, which can be printed in stacked layers to form 3D parts. We successfully characterized the flat printed patterns, however, have encountered difficulty in characterizing multilayer prints. We have partially addressed the feasibility question, by developing the method for electroprinting 3D parts, however, some questions about the internal porosity and density of these parts still remain.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Efficient Generalizable Deep Learning

Stochastic optimization is a fundamental field of research for machine learning. Stochastic gradient descent (SGD) and related methods provide a feasible means to train complicated prediction models over large datasets. SGD, however, does not explicitly address the problem of overfitting, which can lead to predictions that perform poorly on new data. This difference between loss performance on unseen testing data verses that of training data defines the generalization gap of a model. We introduce a new computational kernel called Stochastic Hessian Projection (SHP) that uses a maximum likelihood framework to simultaneously estimate gradient noise covariance and local curvature of the loss function. Our analysis illustrates that these quantities affect the evolution of parameter uncertainty and therefore generalizability. We show how these computations allow us to predict the generalization gap without requiring holdout data. Explicitly assessing this metric for generalizability during training may improve machine learning predictions when data is scarce and understanding prediction variability is critical.

42 ENGINEERING↗
DOE OSTI2015

WE-AB-BRA-12: Virtual Endoscope Tracking for Endoscopy-CT Image Registration

Purpose: The use of endoscopy in radiotherapy will remain limited until we can register endoscopic video to CT using standard clinical equipment. In this phantom study we tested a registration method using virtual endoscopy to measure CT-space positions from endoscopic video. Methods: Our phantom is a contorted clay cylinder with 2-mm-diameter markers in the luminal surface. These markers are visible on both CT and endoscopic video. Virtual endoscope images were rendered from a polygonal mesh created by segmenting the phantom’s luminal surface on CT. We tested registration accuracy by tracking the endoscope’s 6-degree-of-freedom coordinates frame-to-frame in a video recorded as it moved through the phantom, and using these coordinates to measure CT-space positions of markers visible in the final frame. To track the endoscope we used the Nelder-Mead method to search for coordinates that render the virtual frame most similar to the next recorded frame. We measured the endoscope’s initial-frame coordinates using a set of visible markers, and for image similarity we used a combination of mutual information and gradient alignment. CT-space marker positions were measured by projecting their final-frame pixel addresses through the virtual endoscope to intersect with the mesh. Registration error was quantified as the distance between this intersection and the marker’s manually-selected CT-space position. Results: Tracking succeeded for 6 of 8 videos, for which the mean registration error was 4.8±3.5mm (24 measurements total). The mean error in the axial direction (3.1±3.3mm) was larger than in the sagittal or coronal directions (2.0±2.3mm, 1.7±1.6mm). In the other 2 videos, the virtual endoscope got stuck in a false minimum. Conclusion: Our method can successfully track the position and orientation of an endoscope, and it provides accurate spatial mapping from endoscopic video to CT. This method will serve as a foundation for an endoscopy-CT registration framework that is clinically valuable and requires no specialized equipment.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Seismic Spatial Gradients and Machine Learning-Based Classifiers for Explosion Monitoring (LDRD 218327)

This final report summarizes the work completed under the Laboratory Directed Research and Development (LDRD) project “Seismic Spatial Gradients as a Machine Learning-Based Classifier for Explosion Monitoring.” The overarching goal of the project was to explore the efficacy of using machine learning-based classification algorithms where the input data are the spatial gradient of the seismic wavefield collected at a single point on the Earth’s surface. The methods that I describe here are in direct contrast to conventional methods of seismic discrimination which typically rely on a spatially extended network of instruments and physics-based wavefield attributes such as, for example, the ratio between $\textit{P}$ and $\textit{S}$ waves. Rather, we use the spatial gradient of the seismic wavefield observed at a single point on the Earth’s surface and data processing approaches inspired by the machine learning community. We tested two algorithms, a neural network and a modified version of principal component analysis termed Spectrally Filtered Principal Component Analysis (SFPCA). To test these algorithms, we first conducted a series of numerical tests using synthetic data and then conducted a small-scale controlled field experiment. The tests using synthetic data showed that both algorithms had high success rates on gradiometric data, even when simulated noise was added to the signal. Furthermore, we found that using seismic spatial gradients increased the performance of our discrimination algorithms when compared to using just the traditional translational motion seismic data. The tests with field data also showed a high degree of discriminative success.

58 GEOSCIENCES↗
DOE OSTI2018

SUPG stabilization for the nonconforming virtual element method for advection–diffusion–reaction equations

We present here the design, convergence analysis and numerical investigations of the nonconforming virtual element method with Streamline Upwind/Petrov–Galerkin (VEM-SUPG) stabilization for the numerical resolution of convection–diffusion–reaction problems in the convective-dominated regime. According to the virtual discretization approach, the bilinear form is split as the sum of a consistency and a stability term. The consistency term is given by substituting the functions of the virtual space and their gradients with their polynomial projection in each term of the bilinear form (including the SUPG stabilization term). Polynomial projections can be computed exactly from the degrees of freedom. The stability term is also built from the degrees of freedom by ensuring the correct scalability properties with respect to the mesh size and the equation coefficients. The nonconforming formulation relaxes the continuity conditions at cell interfaces and a weaker regularity condition is considered involving polynomial moments of the solution jumps at cell interface. Optimal convergence properties of the method are proved in a suitable norm, which includes contribution from the advective stabilization terms. Experimental results confirm the theoretical convergence rates.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

MO-FG-CAMPUS-JeP3-03: Detection of Unpredictable Patient Movement During SBRT Using a Single KV Projection of An On-Board CBCT System: Simulation Study

Purpose: An unpredictable movement of a patient can occur during SBRT even when immobilization devices are applied. In the SBRT treatments using a conventional linear accelerator detection of such movements relies heavily on human interaction and monitoring. This study aims to detect such positional abnormalities in real-time by assessing intra-fractional gantry mounted kV projection images of a patient’s spine. Methods: We propose a self-CBCT image based spine tracking method consisting of the following steps: (1)Acquire a pre-treatment CBCT image; (2)Transform the CBCT volume according to the couch correction; (3)Acquire kV projections during treatment beam delivery; (4)Simultaneously with each acquisition generate a DRR from the CBCT volume based-on the current projection geometry; (5)Perform an intensity gradient-based 2D registration between spine ROI images of the projection and the DRR images; (6)Report an alarm if the detected 2D displacement is beyond a threshold value. To demonstrate the feasibility, retrospective simulations were performed on 1,896 projections from nine CBCT sessions of three patients who received lung SBRT. The unpredictable movements were simulated by applying random rotations and translations to the reference CBCT prior to each DRR generation. As the ground truth, the 3D translations and/or rotations causing >3 mm displacement of the midpoint of the thoracic spine were regarded as abnormal. In the measurements, different threshold values of 2D displacement were tested to investigate sensitivity and specificity of the proposed method. Results: A linear relationship between the ground truth 3D displacement and the detected 2D displacement was observed (R{sup 2} = 0.44). When the 2D displacement threshold was set to 3.6 mm the overall sensitivity and specificity were 77.7±5.7% and 77.9±3.5% respectively. Conclusion: In this simulation study, it was demonstrated that intrafractional kV projections from an on-board CBCT system have a potential to detect unpredictable patient movement during SBRT. This research is funded by Interfractional Imaging Research Grant from Elekta.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Extending Parsimonious Bayesian Inference

Parsimonious Bayesian inference is a theoretical framework for efficient data assimilation that seeks to balance increased consistency between predictions and training data against corresponding increases in model complexity. Within this framework, over-training is understood as optimization that encodes excessive information within model parameters while only achieving small improvements between predictions and training data. This project aims to develop practical methods of limiting excess model information during optimization. One key observation is that practical heuristics for parsimonious learning in high-dimensions must balance expressivity, i.e. the ability of the model to capture diverse predictions with only a few non-zero parameters, against discoverability, i.e. the ability to train the model with gradient-based optimization and drive parameters to low information states. As such, we developed logical activation functions that are able to adaptively approximate arbitrary truth tables that define Boolean logic operations within a probabilistic framework. These functions have demonstrated the ability to learn exclusive disjunction (XOR) and conditioned disjunction (if [condition] then [result_if_true] else [result_if_false]) within a single layer of a neural network. To efficiently exploit these activation functions to drive parsimonious learning required several other advances within the domain of variational inference. The most efficient form of complexity suppression is structured sparsification, driving most model parameters to zero while achieving the structural coherence among nonzeros needed for bandwidth reduction. Such models are not only far more efficient at suppressing information-theoretic complexity, they also reduce the other forms of complexity (computations, communication, storage, and the number of dependencies needed to evaluate predictions). Aiming to support enhanced sparsification, this project examined new approaches to high-dimensional variational inference that allow us to calibrate and control parameter uncertainty during optimization. By identifying which parameters can sustain sparsifying perturbations with little impact on prediction quality, we can develop better pruning strategies by framing them as approximate Bayesian inference. These advances also open paths to mitigate concerns with deploying advanced learning methods in resource-constrained environments, such as running models on power-limited or communication-limited devices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Development of an Ultrahigh-bandwidth Phase Contrast Imaging System for detection of electron scale turbulence and Gigahertz Radio-Frequency Waves

The study of waves and turbulence is vital to the development of future reactor-grade plasma devices developed in the quest for fusion energy. These fluctuations are responsible for moving heat and particles across the magnetic field, and a predictive understanding of them is needed to achieve the density and temperature required to sustain a plasma fusion reaction. While many techniques have been developed for measuring waves and fluctuations, every measurement method has limitations. There are relatively few techniques for measuring very high frequency fluctuations, such as radio frequency waves injected to heat the plasma, unstable waves driven by suprathermal particles, or short wavelength electrostatic waves driven by electron temperature or density gradients. The present project builds upon the proven phase contrast imaging (PCI) technique to extend the response of the diagnostic by orders of magnitude in frequency and almost a factor of ten in spatial resolution. PCI provides a measurement of electron density based on small angle scattering of a CO-2 laser beam by using optical techniques to render a phase shift as an intensity change on a detector. Due to the telecommunications revolution, technological development by manufacturers has focused on components in the near -infrared, so that high- quality lasers and detectors at 1.55 µm are readily available. Shifting PCI design to a new, shorter wavelength has numerous advantages and challenges. Similar detector performance is available with room-temperature arrays with GHz bandwidth, while the detector arrays for 10.6 µm required liquid nitrogen cooling and were therefore limited to a bandwidth of about 1 MHz. Shifting to a shorter wavelength reduces the angle at which the laser beam scatters off of plasma waves, allowing more such scattered components to pass through the aperture of the vacuum vessel port and be collected by the PCI, which increases the spatial resolution. Concomitant with these benefits, various questions of performance arise. At shorter laser wave- length, the sensitivity to mirror and lens quality is increased, the contribution of the laser to the overall system noise is increased, and the sensitivity to vibrations is increased. The custom optical components at the heart of the PCI technique were required to be properly scaled for the shorter wavelength, so fabrication technologies needed to be explored. This project was designed to show that a low noise, high response PCI system at 1.55 µm could be constructed and operated, and then to quantify potential issues to allow extrapolation to a full-size production system providing physics measurements on a large plasma device. The first stage, producing the custom optical component called a Phase Plate, was successfully achieved using two methods. First, an easily reproduced masking and coating technique was able to produce good phase plates with the required parameters. Second, a nanofabrication technique was found to produce extremely high quality phase plates at a competitive price. The PCI constructed with the new phase plates and 1.55 µm laser was found to provide excellent wavelength measurements with the theoretically expected response. The sensitivity to optical surface quality was found to be in line with previous measurements at 10.6 µm. The observed signal-to-noise ratio was similar to the theoretically expected value. The effect of vibrations on PCI was studied with the first measurement of the effect of beam motion on PCI response and comparison to theory, allowing for a quantitative prediction of the effect of vibrations on a production PCI system and the requirements for improved beam stabilization. PCI is an extremely cost-effective method to provide a low noise, absolutely calibrated measurement of plasma fluctuations across a wide spatial scale. This project has shown that a 1.55 µm PCI using modern techniques and components is less expensive than the 10.6 µm PCI of a few years ago, with the largest savings in phase plate fabrication and the infrared detector array.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Metagenome-assembled genomes from topsoils along a hillslope water gradient across early snowmelt to late summer in East River, CO

Drought is changing the American Mountain West at unprecedented rates with unknown consequences to soil microbiome composition and function. As a part of LBNL Watershed Science Focus Area (SFA), we investigated shifts in microbial community and transcriptional activity on a subalpine conifer-meadow transition zone throughout the summer of 2023 as soil dried down. This work took place in Crested Butte, CO on Snodgrass mountain, using a proxy for drought conditions.Here we present metagenome assembled genomes (MAGs) for the bacterial and archaeal community at 0-10cm from three sites along a hillslope water gradient across five timepoints from early snowmelt to late summer. 42 metagenomes were sequenced at Joint Genome Institute (JGI) and can be found under the JGI GOLD (Genomes Online Database) sequencing project Gs0166660. Metagenomes were assembled through an inhouse pipeline (see methods), binned using four autobinners (concoct, maxbin2, metabat2, and vamb) and consolidated using dastool. The consolidated bins from all metagenomes were pooled, filtered by completeness (>70%) and contamination (<10%), and dereplicated at 95% ANI using drep. This dataset (1) a zip file of 157 MAGs (as fasta files, Gs0166660_bins_tar.gz), (2) sample metadata file with sample IGSNs (International Generic Sample Numbers) (samples.csv), (3) bounding box coordinates for the sampled locations (Gs0166660.kml), (4) metagenome assembly and coassembly metadata file listing IMG/M (Integrated Microbial Genomes/Metagenomes) metagenome accessions linking samples to metagenomes (EastRiver_Drought_ESSDive_Metadata.csv), (5) location metadata file (locations.csv), (6) file-level metadata file (flmd.csv) and (7) data dictionary (dd.csv) file.This work was supported by the Watershed Function Science Focus Area at Lawrence Berkeley National Laboratory funded by the US Department of Energy, Office of Science, Biological and Environmental Research under Contract No. DE-AC02-05CH11231.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

Quantifying Carbon-Climate Processes at the Regional Scale Using Atmospheric Carbonyl Sulfide

Atmospheric carbonyl sulfide (COS) analysis has the potentially transformative capability for partitioning the regional carbon flux into respiration and photosynthesis components. This emerging approach is based on the observation that continental atmospheric CO2 gradients are dominated by net ecosystem fluxes while continental atmospheric COS gradients are dominated by photosynthesis-related plant uptake. Regional flux partitioning represents a critical knowledge gap due to a lack of robust methods for regional-scale flux partitioning and large uncertainties in forecasting carbon-climate feedbacks. Our completed project characterized the relationship between COS and CO2 surface fluxes using a novel measurement and modeling system in a winter wheat field at the U.S. Department of Energy?s Atmospheric and Radiation Measurement program Central Facility (DOE-ARM CF). The scope of this project included canopy flux measurements, soil flux measurements, regional atmospheric modeling, and analysis of COS and CO2 airborne observations at SGP. Three critical discoveries emerged from this investigation: (1) the new measurement system provided the first field evidence of a robust relationship between COS leaf fluxes and GPP; (2) a previously unknown seasonal soil source of COS was observed and characterized; (3) the regional atmospheric analysis of airborne measurements provided the first COS-based constraints on GPP parameterizations used in earth systems models. Dissemination of these results includes three publications [Billesbach et al., In Press; Campbell et al., In Preparation; Seibt et al., In Review], three presentations at the AGU Fall Meeting (2012), and four invited presentations to department seminars. We have leveraged this foundational project to continue our work on understanding carbon cycle processes at large scales through one funded project (DOE Lab Fee, 2012-2015) and one proposal that is under review (DOE/NASA/USDA/NOAA, 2014-2016).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Train Like a (Var)Pro: Efficient Training of Neural Networks with Variable Projection

Deep neural networks (DNNs) have achieved state-of-the-art performance across a variety of traditional machine learning tasks, e.g., speech recognition, image classification, and segmentation. The ability of DNNs to efficiently approximate high-dimensional functions has also motivated their use in scientific applications, e.g., to solve partial differential equations and to generate surrogate models. In this paper, we consider the supervised training of DNNs, which arises in many of the above applications. We focus on the central problem of optimizing the weights of the given DNN such that it accurately approximates the relation between observed input and target data. Devising effective solvers for this optimization problem is notoriously challenging due to the large number of weights, nonconvexity, data sparsity, and nontrivial choice of hyperparameters. To solve the optimization problem more efficiently, we propose the use of variable projection (VarPro), a method originally designed for separable nonlinear least-squares problems. Our main contribution is the Gauss--Newton VarPro method (GNvpro) that extends the reach of the VarPro idea to nonquadratic objective functions, most notably cross-entropy loss functions arising in classification. These extensions make GNvpro applicable to all training problems that involve a DNN whose last layer is an affine mapping, which is common in many state-of-the-art architectures. In our four numerical experiments from surrogate modeling, segmentation, and classification, GNvpro solves the optimization problem more efficiently than commonly used stochastic gradient descent (SGD) schemes. Finally, GNvpro finds solutions that generalize well, and in all but one example better than well-tuned SGD methods, to unseen data points.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

AMPPED LDRD: Advanced Models of the Physics & Phenomena of Electrical Discharge.

This Laboratory Directed Research and Development (LDRD) project aimed at addressing an unmet need for physics-based models that enable prediction of electrical breakdown in the presence of high voltage gradients and real-world environments. This project focused on understanding coupled plasma-surface feedback phenomena critical to electrical discharge processes and design of breakdown voltages, breakdown times, and breakdown paths. New secondary electron emission and coupled plasma-surface measurement methods and models were developed. Highly reproducible discharge experiments were developed to provide current-voltage data as a function of time, and methods were developed to condition electrodes for predictable discharge. To assess plasma-surface feedback mechanisms, new surface physics capabilities, including measurement systems for local and global photoemission yield and ion-induced secondary electron emission yield were developed. Discharge models were developed to incorporate these yields for predicting discharge behavior to understand influence of surface physics on discharge current and time evolution, and methods to accelerate these simulations were demonstrated. A key finding was that the initiation process of a non-vacuum discharge appears highly dependent on photoemission at the cathode. Advanced diagnostics were developed, including spatial electrical field imaging, spectroscopy of plasmas, and high-speed imaging of discharge event s in metal and dielectric environments. These diagnostics and improved electrical models are a step toward enabling quantitative design margins, assurance of safety architectures, and implementation of novel materials and technologies for wide ranging energy and electronics applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

On convergent finite difference schemes for variational–PDE-based image processing

We study an adaptive anisotropic Huber functional-based image restoration scheme. Using a combination of L2–L1 regularization functions, an adaptive Huber functional-based energy minimization model provides denoising with edge preservation in noisy digital images. We study a convergent finite difference scheme based on continuous piecewise linear functions and use a variable splitting scheme, namely the Split Bregman (In: Goldstein and Osher, SIAM J Imaging Sci 2(2):323–343, 2009) algorithm, to obtain the discrete minimizer. Experimental results are given in image denoising and comparison with additive operator splitting, dual fixed point, and projected gradient schemes illustrates that the best convergence rates are obtained for our algorithm.

97 MATHEMATICS AND COMPUTING↗