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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

WE-EF-207-09: Single-Scan Dual-Energy CT Using Primary Modulation

Purpose: Compared with conventional CT, dual energy CT (DECT) provides better material differentiation but requires projection data with two different effective x-ray spectra. Current DECT scanners use either a two-scan setting or costly imaging components, which are not feasible or available on open-gantry cone-beam CT systems. We propose a hardware-based method which utilizes primary modulation to enable single-scan DECT on a conventional CT scanner. The CT imaging geometry of primary modulation is identical to that used in our previous method for scatter removal, making it possible for future combination with effective scatter correction on the same CT scanner. Methods: We insert an attenuation sheet with a spatially-varying pattern - primary modulator-between the x-ray source and the imaged object. During the CT scan, the modulator selectively hardens the x-ray beam at specific detector locations. Thus, the proposed method simultaneously acquires high and low energy data. High and low energy CT images are then reconstructed from projections with missing data via an iterative CT reconstruction algorithm with gradient weighting. Proof-of-concept studies are performed using a copper modulator on a cone-beam CT system. Results: Our preliminary results on the Catphan(c) 600 phantom indicate that the proposed method for single-scan DECT is able to successfully generate high-quality high and low energy CT images and distinguish different materials through basis material decomposition. By applying correction algorithms and using all of the acquired projection data, we can reconstruct a single CT image of comparable image quality to conventional CT images, i.e., without primary modulation. Conclusion: This work shows great promise in using a primary modulator to perform high-quality single-scan DECT imaging. Future studies will test method performance on anthropomorphic phantoms and perform quantitative analyses on image qualities and DECT decomposition accuracy. We will use simulations to optimize the modulator material and geometry parameters.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Intercomparison of methods of coupling between convection and large-scale circulation. 1. Comparison over uniform surface conditions

Here, as part of an international intercomparison project, a set of single-column models (SCMs) and cloud-resolving models (CRMs) are run under the weak-temperature gradient (WTG) method and the damped gravity wave (DGW) method. For each model, the implementation of the WTG or DGW method involves a simulated column which is coupled to a reference state defined with profiles obtained from the same model in radiative-convective equilibrium. The simulated column has the same surface conditions as the reference state and is initialized with profiles from the reference state. We performed systematic comparison of the behavior of different models under a consistent implementation of the WTG method and the DGW method and systematic comparison of the WTG and DGW methods in models with different physics and numerics. CRMs and SCMs produce a variety of behaviors under both WTG and DGW methods. Some of the models reproduce the reference state while others sustain a large-scale circulation which results in either substantially lower or higher precipitation compared to the value of the reference state. CRMs show a fairly linear relationship between precipitation and circulation strength. SCMs display a wider range of behaviors than CRMs. Some SCMs under the WTG method produce zero precipitation. Within an individual SCM, a DGW simulation and a corresponding WTG simulation can produce different signed circulation. When initialized with a dry troposphere, DGW simulations always result in a precipitating equilibrium state. The greatest sensitivities to the initial moisture conditions occur for multiple stable equilibria in some WTG simulations, corresponding to either a dry equilibrium state when initialized as dry or a precipitating equilibrium state when initialized as moist. Multiple equilibria are seen in more WTG simulations for higher SST. In some models, the existence of multiple equilibria is sensitive to some parameters in the WTG calculations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

CRCNS22 Learning Rules in the Hippocampus and their Mapping to Neuromorphic Systems (Final Technical Report)

Large scale biologically-realistic computational models are key to investigating the interplay between structure and function in nervous systems, thus paving the way to new clinical methods and neuro-inspired computing solutions. This project focuses on the hippocampus, in particular the CA3-CA1 regions, due to their role in associative learning and memory, pattern separation and completion, and spatial navigation. Investigations into the neuronal organization and learning rule(s) of this circuit can shed light into how declarative memories are formed, stored, recalled and forgotten and inform computational, experimental and clinical neuroscience work. Our project aims at developing a novel data-driven methodology supported by a broad heterogeneous base of neuroscience experimental knowledge and inspired from advances in computer science and engineering. Specifically, this work will benchmark existing and new learning rules within a full-scale spiking neural network simulation of the CA3-CA1 region. The model will be based on an open-source repository, called the Hippocampome, which contains neuronal morphologies, firing patterns, synapse probabilities, and most other required parameters for all known neuron types in the rodent hippocampal formation. The model will be first trained in a supervised fashion for associative memory tasks using backpropagation through time traditionally used in computer science, enhanced with a new technique called the surrogate gradient method. This optimization method will be used to obtain a global loss minimization, but it is not biologically inspired as it assumes the use of data not locally available to the synapses. However, we propose its use as a benchmarking tool, to compare the training performance of local biologically plausible and hardware-mappable learning rules at scale. New rules or combinations will be proposed and tested as needed, based on the obtained results. Progress in this area will also drive the development of novel hardware-mappable algorithms for continual lifelong learning and categorization of new events from few presented examples. This project goes beyond the existing state-of-the-art by looking at large scale realistic neuronal circuits as networks trainable via global optimization methods such as surrogate gradient descent. The objective function of the brain that supports learning is largely unknown, but it is likely that it operates through local learning rules. Studying network trajectories around local minima as proposed in this work represents a useful strategy for understanding whether a network is training by using a specific (set of) learning rule(s). Starting from a completely untrained network is a challenging test since it is difficult to determine how the learning rule affects the trajectory of the network. This interdisciplinary project will help understand what rule governs learning in these regions or if multiple learning rules are involved. The work will develop a robust methodology to measure if the network is converging to the target solution, oscillating around it, or diverging away.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

Geometric validation of self-gating k-space-sorted 4D-MRI vs 4D-CT using a respiratory motion phantom

Purpose: MRI is increasingly being used for radiotherapy planning, simulation, and in-treatment-room motion monitoring. To provide more detailed temporal and spatial MR data for these tasks, we have recently developed a novel self-gated (SG) MRI technique with advantage of k-space phase sorting, high isotropic spatial resolution, and high temporal resolution. The current work describes the validation of this 4D-MRI technique using a MRI- and CT-compatible respiratory motion phantom and comparison to 4D-CT. Methods: The 4D-MRI sequence is based on a spoiled gradient echo-based 3D projection reconstruction sequence with self-gating for 4D-MRI at 3 T. Respiratory phase is resolved by using SG k-space lines as the motion surrogate. 4D-MRI images are reconstructed into ten temporal bins with spatial resolution 1.56 × 1.56 × 1.56 mm{sup 3}. A MRI-CT compatible phantom was designed to validate the performance of the 4D-MRI sequence and 4D-CT imaging. A spherical target (diameter 23 mm, volume 6.37 ml) filled with high-concentration gadolinium (Gd) gel is embedded into a plastic box (35 × 40 × 63 mm{sup 3}) and stabilized with low-concentration Gd gel. The phantom, driven by an air pump, is able to produce human-type breathing patterns between 4 and 30 respiratory cycles/min. 4D-CT of the phantom has been acquired in cine mode, and reconstructed into ten phases with slice thickness 1.25 mm. The 4D images sets were imported into a treatment planning software for target contouring. The geometrical accuracy of the 4D MRI and CT images has been quantified using target volume, flattening, and eccentricity. The target motion was measured by tracking the centroids of the spheres in each individual phase. Motion ground-truth was obtained from input signals and real-time video recordings. Results: The dynamic phantom has been operated in four respiratory rate (RR) settings, 6, 10, 15, and 20/min, and was scanned with 4D-MRI and 4D-CT. 4D-CT images have target-stretching, partial-missing, and other motion artifacts in various phases, whereas the 4D-MRI images are visually free of those artifacts. Volume percentage difference for the 6.37 ml target ranged from 5.3% ± 4.3% to 10.3% ± 5.9% for 4D-CT, and 1.47 ± 0.52 to 2.12 ± 1.60 for 4D-MRI. With an increase of respiratory rate, the target volumetric and geometric deviations increase for 4D-CT images while remaining stable for the 4D-MRI images. Target motion amplitude errors at different RRs were measured with a range of 0.66–1.25 mm for 4D-CT and 0.2–0.42 mm for 4D-MRI. The results of Mann–Whitney tests indicated that 4D-MRI significantly outperforms 4D-CT in phase-based target volumetric (p = 0.027) and geometric (p < 0.001) measures. Both modalities achieve equivalent accuracy in measuring motion amplitude (p = 0.828). Conclusions: The k-space self-gated 4D-MRI technique provides a robust method for accurately imaging phase-based target motion and geometry. Compared to 4D-CT, the current 4D-MRI technique demonstrates superior spatiotemporal resolution, and robust resistance to motion artifacts caused by fast target motion and irregular breathing patterns. The technique can be used extensively in abdominal targeting, motion gating, and toward implementing MRI-based adaptive radiotherapy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Scalable and Energy-Efficient Methods for Interactive Exploration of Scientific Data

The main scientific contributions of this project are the following novel concepts for multidimensional arrays: shape-based similarity join (SIGMOD 2016), incremental view maintenance (SIGMOD 2017), user-defined stencil functions (HPDC 2017), and distributed caching for in-situ processing (SSDBM 2018). Building on our collaboration with the astrophysics group at LBNL, we applied these techniques to the data generated in the Palomar Transient Factory (PTF) astronomical survey. They played a pivotal role in the first-ever observation of a neutron star merger, which produces gravitational waves and turns out to be the origin of heavy elements, including gold. This has lead to a Science magazine article that has received extensive media coverage on ACM TechNews, Slashdot, FiveThirtyEight, and Quanta Magazine, among others. Additionally, two other articles detailing related aspects of the same discovery have been published in the Astrophysical Journal Letters journal. These publications have more than 3,000 citations according to Google Scholar (as of February 2022). This cross-disciplinary collaboration provided very good opportunities to apply database techniques to real-life scientific problems. The fact that they facilitated major discoveries in astrophysics proves the importance of our research. In addition to the work on multidimensional array databases, this project has also developed stochastic gradient descent (SGD) optimization algorithms for training large scale machine learning models, methods for querying in-situ data, and a database query optimizer based on sketch synopses.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Stochastic projective splitting

Here, we present a new, stochastic variant of the projective splitting (PS) family of algorithms for inclusion problems involving the sum of any finite number of maximal monotone operators. This new variant uses a stochastic oracle to evaluate one of the operators, which is assumed to be Lipschitz continuous, and (deterministic) resolvents to process the remaining operators. Our proposal is the first version of PS with such stochastic capabilities. We envision the primary application being machine learning (ML) problems, with the method’s stochastic features facilitating “mini-batch” sampling of datasets. Since it uses a monotone operator formulation, the method can handle not only Lipschitz-smooth loss minimization, but also min–max and noncooperative game formulations, with better convergence properties than the gradient descent-ascent methods commonly applied in such settings. The proposed method can handle any number of constraints and nonsmooth regularizers via projection and proximal operators. We prove almost-sure convergence of the iterates to a solution and a convergence rate result for the expected residual, and close with numerical experiments on a distributionally robust sparse logistic regression problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Implementation and Exploration of Parameterizations of Large-Scale Dynamics in NCAR's Single Column Atmosphere Model SCAM6

A single column model with parameterized large-scale (LS) dynamics is used to better understand the response of steady-state tropical precipitation to relative sea surface temperature under various representations of radiation, convection, and circulation. The large-scale dynamics are parametrized via the weak temperature gradient (WTG), damped gravity wave (DGW), and spectral weak temperature gradient (Spectral WTG) method in NCAR's Single Column Atmosphere Model (SCAM6). Radiative cooling is either specified or interactive, and the convective parameterization is run using two different values of a parameter that controls the degree of convective inhibition. Results are interpreted in the context of the Global Atmospheric System Studies -Weak Temperature Gradient (GASS-WTG) Intercomparison project. Using the same parameter settings and simulation configuration as in the GASS-WTG Intercomparison project, SCAM6 under the WTG and DGW methods produces erratic results, suggestive of numerical instability. However, when key parameters are changed to weaken the large-scale circulation's damping of tropospheric temperature variations, SCAM6 performs comparably to single column models in the GASS-WTG Intercomparison project. The Spectral WTG method is less sensitive to changes in convection and radiation than are the other two methods, performing qualitatively similarly across all configurations considered. Under all three methods, circulation strength, represented in 1D by grid-scale vertical velocity, is decreased when barriers to convection are reduced. This effect is most extreme under specified radiative cooling, and is shown to come from increased static stability in the column's reference radiative-convective equilibrium profile. This argument can be extended to interactive radiation cases as well, though perhaps less conclusively.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions

Neural network wavefunctions optimized using the variational Monte Carlo method have been shown to produce highly accurate results for the electronic structure of atoms and small molecules, but the high cost of optimizing such wavefunctions prevents their application to larger systems. We propose the Subsampled Projected-Increment Natural Gradient Descent (SPRING) optimizer to reduce this bottleneck. SPRING combines ideas from the recently introduced minimum-step stochastic reconfiguration optimizer (MinSR) and the classical randomized Kaczmarz method for solving linear least-squares problems. We demonstrate that SPRING outperforms both MinSR and the popular Kronecker-Factored Approximate Curvature method (KFAC) across a number of small atoms and molecules, given that the learning rates of all methods are optimally tuned. For example, on the oxygen atom, SPRING attains chemical accuracy after forty thousand training iterations, whereas both MinSR and KFAC fail to do so even after one hundred thousand iterations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

SU-D-206-03: Segmentation Assisted Fast Iterative Reconstruction Method for Cone-Beam CT

Purpose: Total Variation (TV) based iterative reconstruction (IR) methods enable accurate CT image reconstruction from low-dose measurements with sparse projection acquisition, due to the sparsifiable feature of most CT images using gradient operator. However, conventional solutions require large amount of iterations to generate a decent reconstructed image. One major reason is that the expected piecewise constant property is not taken into consideration at the optimization starting point. In this work, we propose an iterative reconstruction method for cone-beam CT (CBCT) using image segmentation to guide the optimization path more efficiently on the regularization term at the beginning of the optimization trajectory. Methods: Our method applies general knowledge that one tissue component in the CT image contains relatively uniform distribution of CT number. This general knowledge is incorporated into the proposed reconstruction using image segmentation technique to generate the piecewise constant template on the first-pass low-quality CT image reconstructed using analytical algorithm. The template image is applied as an initial value into the optimization process. Results: The proposed method is evaluated on the Shepp-Logan phantom of low and high noise levels, and a head patient. The number of iterations is reduced by overall 40%. Moreover, our proposed method tends to generate a smoother reconstructed image with the same TV value. Conclusion: We propose a computationally efficient iterative reconstruction method for CBCT imaging. Our method achieves a better optimization trajectory and a faster convergence behavior. It does not rely on prior information and can be readily incorporated into existing iterative reconstruction framework. Our method is thus practical and attractive as a general solution to CBCT iterative reconstruction. This work is supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LR16F010001), National High-tech R&D Program for Young Scientists by the Ministry of Science and Technology of China (Grant No. 2015AA020917).

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

High Gradient Magnetic Simulation Final Report 2025

Over the course of nearly 2 years, the goal of this project has been to identify methods for the separation of uranium oxide particles from other geologic materials. The primary motivation is to assess methods for enhancing the extraction and throughput of actinide particles from environmental samples, enabling the evaluation of these trace actinides through more traditional methods such as thermal ionization mass spectrometry or secondary ion mass spectrometry.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2025

Reliable and Efficient Machine Learning (Final Technical Report)

Modern scientific experiments generate massive amounts of data at a pace much faster than humans can manually analyze. While machine learning has revolutionized commercial data analysis (such as recommending movies or recognizing faces), applying these tools to complex scientific discovery is challenging because scientific answers must be precise, interpretable, and adhere to physical laws. The research under this project aims to develop new mathematical tools and computer algorithms specifically designed for scientific applications. Major progress has been made in automatically cleaning and deconstructing messy experimental data, analyzing the visual information of physical phenomena, determining the underlying physical variables, and providing rig orous mathematical analysis of interesting algorithms and concepts widely used in machine learning. This project addressed the critical gap between our ability to generate massive scientific data and our ability to extract interpretable information from it. We established mathematical foundations for Scientific Machine Learning (SciML) aimed at effective data analytics and automated discovery. Our work focused on three core objectives: (1) developing reliable feature extraction methods for dynamic high-dimensional data, (2) establishing mathematical foundations for discovering dynamics via neural networks, and (3) creating rigorous optimization techniques for these models. Key outcomes come from two fronts. On the practical side, they include the development of algorithms that significantly enhance the extraction of signals from field data, as well as the capability to handle situations that exhibit smooth variations or physical stretching due to temperature changes. They also include the creation of an automated framework for discovering fundamental state variables from raw experimental data, demonstrating the ability to identify intrinsic physical dimensions without prior knowledge of the governing laws. On the theoretical front, the research results in theoretical advances in Optimal Transport, a widely used notion in SciML, specifically regarding functions with fixed-size nodal sets, provide sharp bounds relevant to uncertainty quantification. Meanwhile, the outcomes also include the establishment of convergence theories for nonlocal gradient descent methods, enabling robust optimization with noisy data in high-dimensional settings commonly encountered in scientific modeling. The project also helps creating opportunities to train the next generation of researchers, equipping them with the necessary technical skills for today’s workplace and preparing them for future advances.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Systematic study of target localization for bioluminescence tomography guided radiation therapy

Purpose: To overcome the limitation of CT/cone-beam CT (CBCT) in guiding radiation for soft tissue targets, the authors developed a spectrally resolved bioluminescence tomography (BLT) system for the small animal radiation research platform. The authors systematically assessed the performance of the BLT system in terms of target localization and the ability to resolve two neighboring sources in simulations, tissue-mimicking phantom, and in vivo environments. Methods: Multispectral measurements acquired in a single projection were used for the BLT reconstruction. The incomplete variables truncated conjugate gradient algorithm with an iterative permissible region shrinking strategy was employed as the optimization scheme to reconstruct source distributions. Simulation studies were conducted for single spherical sources with sizes from 0.5 to 3 mm radius at depth of 3–12 mm. The same configuration was also applied for the double source simulation with source separations varying from 3 to 9 mm. Experiments were performed in a standalone BLT/CBCT system. Two self-illuminated sources with 3 and 4.7 mm separations placed inside a tissue-mimicking phantom were chosen as the test cases. Live mice implanted with single-source at 6 and 9 mm depth, two sources at 3 and 5 mm separation at depth of 5 mm, or three sources in the abdomen were also used to illustrate the localization capability of the BLT system for multiple targets in vivo. Results: For simulation study, approximate 1 mm accuracy can be achieved at localizing center of mass (CoM) for single-source and grouped CoM for double source cases. For the case of 1.5 mm radius source, a common tumor size used in preclinical study, their simulation shows that for all the source separations considered, except for the 3 mm separation at 9 and 12 mm depth, the two neighboring sources can be resolved at depths from 3 to 12 mm. Phantom experiments illustrated that 2D bioluminescence imaging failed to distinguish two sources, but BLT can provide 3D source localization with approximately 1 mm accuracy. The in vivo results are encouraging that 1 and 1.7 mm accuracy can be attained for the single-source case at 6 and 9 mm depth, respectively. For the 2 sources in vivo study, both sources can be distinguished at 3 and 5 mm separations, and approximately 1 mm localization accuracy can also be achieved. Conclusions: This study demonstrated that their multispectral BLT/CBCT system could be potentially applied to localize and resolve multiple sources at wide range of source sizes, depths, and separations. The average accuracy of localizing CoM for single-source and grouped CoM for double sources is approximately 1 mm except deep-seated target. The information provided in this study can be instructive to devise treatment margins for BLT-guided irradiation. These results also suggest that the 3D BLT system could guide radiation for the situation with multiple targets, such as metastatic tumor models.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Efficient optimization method for finding minimum energy paths of magnetic transitions

Here, efficient algorithms for the calculation of minimum energy paths of magnetic transitions are implemented within the geodesic nudged elastic band (GNEB) approach. While an objective function is not available for GNEB and a traditional line search can, therefore, not be performed, the use of limited memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) and conjugate gradient algorithms in conjunction with orthogonal spin optimization (OSO) approach is shown to greatly outperform the previously used velocity projection and dissipative Landau–Lifschitz dynamics optimization methods. The implementation makes use of energy weighted springs for the distribution of the discretization points along the path and this is found to improve performance significantly. The various methods are applied to several test problems using a Heisenberg-type Hamiltonian, extended in some cases to include Dzyaloshinskii–Moriya and exchange interactions beyond nearest neighbours. Minimum energy paths are found for magnetization reversals in a nano-island, collapse of skyrmions in two-dimensional layers and annihilation of a chiral bobber near the surface of a three-dimensional magnet. The LBFGS-OSO method is found to outperform the dynamics based approaches by up to a factor of 8 in some cases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

WE-AB-BRA-08: Correction of Patient Motion in C-Arm Cone-Beam CT Using 3D-2D Registration

Purpose: Intraoperative C-arm cone-beam CT (CBCT) is subject to artifacts arising from patient motion during the fairly long (∼5–20 s) scan times. We present a fiducial free method to mitigate motion artifacts using 3D-2D image registration that simultaneously corrects residual errors in geometric calibration. Methods: A 3D-2D registration process was used to register each projection to DRRs computed from the 3D image by maximizing gradient orientation (GO) using the CMA-ES optimizer. The resulting rigid 6 DOF transforms were applied to the system projection matrices, and a 3D image was reconstructed via model-based image reconstruction (MBIR, which accommodates the resulting noncircular orbit). Experiments were conducted using a Zeego robotic C-arm (20 s, 200°, 496 projections) to image a head phantom undergoing various types of motion: 1) 5° lateral motion; 2) 15° lateral motion; and 3) 5° lateral motion with 10 mm periodic inferior-superior motion. Images were reconstructed using a penalized likelihood (PL) objective function, and structural similarity (SSIM) was measured for axial slices of the reconstructed images. A motion-free image was acquired using the same protocol for comparison. Results: There was significant improvement (p < 0.001) in the SSIM of the motion-corrected (MC) images compared to uncorrected images. The SSIM in MC-PL images was >0.99, indicating near identity to the motion-free reference. The point spread function (PSF) measured from a wire in the phantom was restored to that of the reference in each case. Conclusion: The 3D-2D registration method provides a robust framework for mitigation of motion artifacts and is expected to hold for applications in the head, pelvis, and extremities with reasonably constrained operative setup. Further improvement can be achieved by incorporating multiple rigid components and non-rigid deformation within the framework. The method is highly parallelizable and could in principle be run with every acquisition. Research supported by National Institutes of Health Grant No. R01-EB-017226 and academic-industry partnership with Siemens Healthcare (AX Division, Forcheim, Germany).

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

DEVELOPMENT AND APPLICATION OF RISK ANALYSIS TOOLKIT FOR PLANT RESOURCE OPTIMIZATION

This paper presents the development of methods and tools that are being designed to optimize plant operations (e.g., maintenance/replacement schedules and optimal maintenance postures for plant components) in a manner that is more cost effective than current approaches and makes better use of available component health and cost data. These methods include both data- and model-based optimization methods. Model-based optimization methods directly include reliability and cost models to determine an optimal plant operational strategy. We consider gradient-based and evolutionary (based on genetic algorithms) optimization methods. The second class of methods target more specific use cases (e.g., project schedule optimization) and are not based on reliability models directly, but they require specific component reliability and cost data. This class of methods is based on variants of the knapsack problem with an aim to determine an optimal project schedule that maximizes the overall NPV. This paper also presents multi-objective methods designed to identify an optimal maintenance posture based on a Pareto frontier analysis. Rather than dictating the “right” tradeoff (i.e., identify the absolute best posture), we show how it is possible to perform a trade space exploration approach (i.e., identify value and costs of several postures and let the analysis account for desired value and cost metrics). This is performed by identifying maintenance postures that maximize value (e.g., system availability) and minimize operational costs, i.e., the Pareto frontier in a value-cost trade space. For all these methods we present detailed applicative examples that show their validity from a decision-making perspective.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Sensitivity of magnetic islands in permanent magnet stellarators using the gradient and Hessian methods

Stellarator plasmas are known to be very sensitive to perturbations in the magnetic field. The permanent magnet stellarator was in part developed as a solution to high machining tolerances placed on the shape properties of electromagnetic coils in traditional stellarators. However, as a consequence of this high sensitivity to the field structure, sensitivities of permanent magnet stellarator plasmas to perturbations of permanent magnet properties must necessarily be well-understood. The gradient and Hessian matrix methods have been previously demonstrated to be useful sensitivity analysis methods for modular coils. We apply these two methods to the study of island width sensitivities in both the MUSE and PM4STELL permanent magnet stellarator projects. These sensitivity methods were used to determine the relative impacts of permanent magnet parameter perturbations on island widths in the vacuum field approximation of both stellarator equilibria. The square of resonant magnetic field perturbation is used here as a proxy for island width. In particular, gradients of magnetizations of individual magnets were examined in MUSE, as well as gradients of magnet group displacements informed by device design. Three different forms of permanent magnet magnetization perturbations are investigated for MUSE, and the flux surface response to perturbations is demonstrated. The Hessian matrix method is applied to PM4STELL, illustrating the sensitivity of dominant island widths to displacements of toroidal wedge structures. These methods allow for selective direction of experimental resources toward regions of heightened sensitivity, while constraints on less impactful permanent magnet parameters can be relaxed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Bayesian 3D X-ray computed tomography image reconstruction with a scaled Gaussian mixture prior model

In order to improve quality of 3D X-ray tomography reconstruction for Non Destructive Testing (NDT), we investigate in this paper hierarchical Bayesian methods. In NDT, useful prior information on the volume like the limited number of materials or the presence of homogeneous area can be included in the iterative reconstruction algorithms. In hierarchical Bayesian methods, not only the volume is estimated thanks to the prior model of the volume but also the hyper parameters of this prior. This additional complexity in the reconstruction methods when applied to large volumes (from 512{sup 3} to 8192{sup 3} voxels) results in an increasing computational cost. To reduce it, the hierarchical Bayesian methods investigated in this paper lead to an algorithm acceleration by Variational Bayesian Approximation (VBA) [1] and hardware acceleration thanks to projection and back-projection operators paralleled on many core processors like GPU [2]. In this paper, we will consider a Student-t prior on the gradient of the image implemented in a hierarchical way [3, 4, 1]. Operators H (forward or projection) and H{sup t} (adjoint or back-projection) implanted in multi-GPU [2] have been used in this study. Different methods will be evalued on synthetic volume 'Shepp and Logan' in terms of quality and time of reconstruction. We used several simple regularizations of order 1 and order 2. Other prior models also exists [5]. Sometimes for a discrete image, we can do the segmentation and reconstruction at the same time, then the reconstruction can be done with less projections.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗