Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Iteration 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Reconstructing cosmic polarization rotation with ResUNet-CMB

Cosmic polarization rotation, which may result from parity-violating new physics or the presence of primordial magnetic fields, converts E-mode polarization of the cosmic microwave background (CMB) into B-mode polarization. Anisotropic cosmic polarization rotation leads to statistical anisotropy in CMB polarization and can be reconstructed with quadratic estimator techniques similar to those designed for gravitational lensing of the CMB. At the sensitivity of upcoming CMB surveys, lensing-induced B-mode polarization will act as a limiting factor in the search for anisotropic cosmic polarization rotation, meaning that an analysis which incorporates some form of delensing will be required to improve constraints on the effect with future surveys. In this study we extend the ResUNet-CMB convolutional neural network to reconstruct anisotropic cosmic polarization rotation in the presence of gravitational lensing and patchy reionization, and we show that the network simultaneously reconstructs all three effects with variance that is lower than that from the standard quadratic estimator nearly matching the performance of an iterative reconstruction method.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Machine learning assisted unfolding for neutrino cross-section measurements with the OmniFold technique

The choice of unfolding method for a cross-section measurement is tightly coupled to the model dependence of the efficiency correction and the overall impact of cross-section modeling uncertainties in the analysis. A key issue is the dimensionality used in unfolding, as the kinematics of all outgoing particles in an event typically affect the reconstruction performance in a neutrino detector. OmniFold is an unfolding method that iteratively reweights a simulated dataset, using machine learning to utilize arbitrarily high-dimensional information, that has previously been applied to proton-proton and proton-electron datasets. This paper demonstrates OmniFold’s application to a neutrino cross-section measurement for the first time using a public T2K near detector simulated dataset, comparing its performance with traditional approaches using a mock data study.

Machine learning↗

An Adaptive Newton-Based Free-Boundary Grad–Shafranov Solver

Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for the poloidal magnetic flux, commonly known as the Grad–Shafranov equation. It is challenging to develop a scalable and accurate free-boundary Grad–Shafranov solver, since it is a fully nonlinear optimization problem that simultaneously solves for the magnetic field coil current outside the plasma to control the plasma shape. In this work, we develop a Newton-based free-boundary Grad–Shafranov solver using adaptive finite elements and preconditioning strategies. The free-boundary interaction leads to the evaluation of a domain-dependent nonlinear form of which its contribution to the Jacobian matrix is achieved through shape calculus. The optimization problem aims to minimize the distance between the plasma boundary and specified control points while satisfying two nontrivial constraints, which correspond to the nonlinear finite element discretization of the Grad–Shafranov equation and a constraint on the total plasma current involving a nonlocal coupling term. The linear system is solved by a block factorization, and AMG is called for subblock elliptic operators. The unique contributions of this work include the treatment of a global constraint, preconditioning strategies, nonlocal reformulation, and the implementation of adaptive finite elements. Furthermore, it is found that the resulting Newton solver is robust, successfully reducing the nonlinear residual to 1e-6 and lower in a small handful of iterations while addressing the challenging case to find a Taylor state equilibrium where conventional Picard-based solvers fail to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Generic Discretization Library

The GenDiL library is a collection of C++ software abstractions designed to discretize and solve partial differential equations (PDEs) for high-performance computing (HPC) applications. Its primary focus is on modern C++ generic programming, which helps ensure portability across various hardware architectures. The central idea behind the library is to provide building blocks for numerical algorithms-such as discretization methods and iteration patterns-so that domain experts can focus on the math, rather than the low-level details of hardware or implementation. By defining abstractions for data types, iteration over computational grids, and scheduling of operations, the library isolates the high-level PDE algorithms from the platform-specific optimizations needed to achieve efficient performance.

Dudouit, Yohann [Lawrence Livermore National Labor↗

Dynamic Graph Sequence Data from Simulated Neutron Reflectometry Measurements

This dataset comprises dynamic graph sequences derived from simulated in-situ neutron reflectometry measurements, capturing the gradual evolution of a layer structure over time. Each graph sequence represents a synthetic sample, with node features detailing the scattering vector and corresponding reflectivity measurements, while adjacency matrices have corresponding reference material parameters attached as metadata. The dataset spans multiple sets, each with a different number of sequences, offering a comprehensive basis for training models that handle dynamic input sequences with embedded physics. This dataset is particularly suited for tackling inverse problems with hidden physical states that evolve over time, challenges that are typically difficult to address using conventional iterative fitting methods.

36 MATERIALS SCIENCE↗

Information content of and the ability to reconstruct dichroic X-ray tomography and laminography

Dichroic tomography is a 3D imaging technique in which the polarization of the incident beam is used to induce contrast due to the magnetization or orientation of a sample. The aim is to reconstruct not only the optical density but the dichroism of the sample. The theory of dichroic tomographic and laminographic imaging in the parallel-beam case is discussed as well as the problem of reconstruction of the sample’s optical properties. The set of projections resulting from a single tomographic/laminographic measurement is not sufficient to reconstruct the magnetic moment for magnetic circular dichroism unless additional constraints are applied or data are taken at two or more tilt angles. For linear dichroism, three polarizations at a common tilt angle are insufficient for unconstrained reconstruction. However, if one of the measurements is done at a different tilt angle than the other, or the measurements are done at a common polarization but at three distinct tilt angles, then there is enough information to reconstruct without constraints. Possible means of applying constraints are discussed. Furthermore, it is shown that for linear dichroism, the basic assumption that the absorption through a ray path is the integral of the absorption coefficient, defined on the volume of the sample, along the ray path, is not correct when dichroism or birefringence is strong. This assumption is fundamental to tomographic methods. An iterative algorithm for reconstruction of linear dichroism is demonstrated on simulated data.

Marcus, Matthew A. (ORCID:0000000325277586)↗

Modeling and Simulation of Xe-100-type Pebble Bed Gas-Cooled Reactor with SCALE

The US Department of Energy (DOE) announced the Advanced Reactor Demonstration Program (ARDP) to accelerate the deployment of advanced reactor concepts. Awardees of ARDP funds are expected to demonstrate the operation of an advanced reactor within 7 years of receiving the award. X-Energy’s advanced reactor concept, the Xe-100, was selected as one of two advanced reactor concepts to receive funding to demonstrate the operation of its high-temperature gas-cooled pebble-bed reactor before the end of this decade. As a result of this push to bring advanced reactors to maturation and commercialization, transition and deployment scenario studies are being performed under the Systems Analysis and Integration (SA&I) campaign within the DOE Office of Nuclear Energy (DOE-NE) to evaluate the transition of the current US commercial fleet of light-water reactors (LWRs) to a future fleet of advanced reactors consisting of a mix of ARDP type reactor concepts and advanced LWRs. To accurately evaluate the front- and back-end resource requirements, it is important to perform reactor physics calculations to determine the discharge burnup and isotopic content, fuel residence time, as well as other parameters. For this purpose, a summer project funded by the SA&I campaign allowed for the setup of SCALE models for full-core Xe-100 type high-temperature gas-cooled pebble-bed reactor and a Xe-100 type slice using publicly available information. The core-averaged equilibrium compositions and zone-wise equilibrium compositions for the slice and 3D models, respectively, were obtained following an iterative depletion method developed by Bostelmann et al. using SCALE’s reactor physics sequence TRITON. The slice model was used with TRITON to generate burnup-dependent cross section libraries at different temperatures which can be used with SCALE’s ORIGAMI code to rapidly determine fuel inventory and therefore to perform quick sensitivity studies on parameters such as the pebble location in the core. The SCALE/TRITON transport and depletion calculation for the Xe-100 type slice model indicates that the isotopic concentrations are in good agreement at 1,300 effective full power days (EFPD) for 235 U. An analysis of 236 U results match 239 Pu results would seem to indicate a typographical error in Mulder and Boyes wherein the reported results of 236 U and 239 Pu are reversed. In addition to SCALE/TRITON calculations, a new capability within SCALE/ORIGAMI for the simulation of pebble-bed reactors was used to study the burnup sensitivity with respect to the pebble pathway through the core. The SCALE/ORIGAMI results show that pebbles that travel closer to the reflector for the entire depletion history have a higher burnup than pebbles that travel through the middle of the core because of the higher thermal to fast flux ratio near the reflector. Consequently, a pebble’s burnup is strongly affected by the pebble’s pathway for each pass. Additional phenomena such as temperature distributions in the core and different travel times of the pebbles in the individual radial zones further affect the burnup distribution. The sensitivity of the discharge vector to the pebble pathways taken during each pass can be evaluated in the future using SCALE/ORIGAMI now that the SCALE inputs have been established.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Impact of Time Dependent Reactor and Sensor Physics on Core Power Synthesis

Online synthesis of the power distribution is critical in the operation and control of nuclear power reactors to ensure that the core is operating within safety margins, and to provide essential knowledge associated with the burnup of the fuel. In light water reactors (LWRs), power synthesis is achieved by using some a priori knowledge of the state of the reactor core and updating based on the signals coming from in-core sensors—namely, self-powered neutron detectors (SPNDs). This report aims to study the effects of fuel burnup and sensor degradation on the ability to accurately synthesize the power distribution in a LWR. Several modeling tools were used to simulate power synthesis based on the responses of SPNDs, with emitters made out of Rh or V. A representative pressurized water reactor low-enriched uranium (LEU) core was modeled using the Polaris/Purdue Advanced Reactor Core Simulator (PARCS) approach. The Monte Carlo N-Particle Transport 6 (MCNP6) code was used, as well, to calculate response functions between different segments of fuel to individual SPNDs; this is a crucial parameter for power synthesis. The Oak Ridge Isotope GENeration (ORIGEN) package in the Standardized Computer Analyses for Licensing Evaluation (SCALE) code was used to model the time-dependent isotopic transmutation in the SPND emitters. All these data were fed into a custom code that enacted the point-based iterative (PBI) method to simulate power synthesis. Developmental work was also performed on high-fidelity SPND models in the GEometry ANd Tracking 4 (Geant4) code, which enables higher-accuracy modeling of the current responses from SPNDs. In this work, five sets of time-dependent power synthesis test cases were conducted. In these test cases, systematic changes in the input conditions enabled an analysis of the effect of (1) slightly inaccurate a priori power distribution assumptions with respect to fuel burnup, (2) highly inaccurate a priori assumptions with respect to fuel burnup (such that burnup is not included in the a priori assumed distribution), and (3) differences between Rh and V SPNDs in terms of downstream consequences of the transmutation in the emitters. The authors discovered that one may permissibly have slightly inaccurate a priori assumptions of the fuel burnup (such that the level of burnup may be slightly under- or over-approximated by the accumulated burnup in approximately 9.3 full power days), but to not account for burnup at all in the a priori assumption leads to severe levels of error, approaching 25% at maximum. The authors also discovered that V SPNDs are extraordinarily robust in the low-enriched uranium fuel cycle considered in this modeling work, whereas Rh SPNDs undergo significant transmutation that can result in large errors in the synthesized power distribution.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications

In this paper, we explore using the Harrow–Hassidim–Lloyd (HHL) algorithm to address scientific and engineering problems through quantum computing, utilizing the NWQSim simulation package on a high-performance computing platform. Focusing on domains such as power-grid management and climate projection, we demonstrate the correlations of the accuracy of quantum phase estimation, along with various properties of coefficient matrices, on the final solution and quantum resource cost in iterative and non-iterative numerical methods such as the Newton–Raphson method and finite difference method, as well as their impacts on quantum error correction costs using the Microsoft Azure Quantum resource estimator. We summarize the exponential resource cost from quantum phase estimation before and after quantum error correction and illustrate a potential way to reduce the demands on physical qubits. This work lays down a preliminary step for future investigations, urging a closer examination of quantum algorithms’ scalability and efficiency in domain applications.

hybrid software for QC-HPC↗

Preliminary Monte Carlo and Thermal Hydraulic Analysis using a Hybrid ETF-Corrected-Diffusion Prediction Block

This paper builds upon previous work to accelerate the Picard iteration (PI) method typically applied for coupled Monte Carlo-Thermal hydraulic (MC-TH) solutions. Previously, the use of the generalized transfer functions (GTFs) to predict variation in macroscopic cross sections following a perturbation in TH properties was demonstrated for a subset of simple 3D problems. In addition, the reduced-order transport prediction block relied on the first order perturbation (FOP) method, which was shown to have computational overheads. Recent work replaced the FOP block with a 1-group nodal diffusion solver to eliminate these overheads. While the use of diffusion is desirable for large-scale problems, the new solver introduces significant homogenization error. This work aims to address this issue by using the Jacobian-Free Newton Krylov (JFNK) method to generate a set of super homogenization (SPH) factors to improve the accuracy of the diffusion solution. The SPH factors will be used in conjunction with an improved cross section prediction method – the expanded transfer function (ETF) method – to produce a highly accurate flux prediction for an axial 1D boiling water reactor (BWR) pincell following a large perturbation in moderator density. The ETF-corrected diffusion (ETF-CD) block is shown to be highly accurate for the 1D test case. Future work will investigate the accuracy of the method for a realistic 3D pressurized water reactor core.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Fourier analysis of continuous fractional diffusion synthetic acceleration schemes in slab geometry

We propose two fractional extensions of continuous diffusion synthetic acceleration (DSA) with fractional derivative order α varying over the interval 2 ≥ α ≥ 1 . We investigate the spectral properties of the corresponding continuous families of fractional preconditioners by performing Fourier analysis for a model infinite homogeneous medium problem in slab geometry. The first family results in a fractional acceleration scheme, FrDSAo, that reduces to traditional DSA for .α = 2 and scattering ratio c limiting to a unit value (c → 1) but is otherwise optimized via the Fourier analysis, to obtain the smallest possible spectral radius, for c < 1 and 2 ≥ α ≥ 1. The second family corresponds to a fractional acceleration scheme, FrDSAs, that reduces to traditional DSA for α = 2 for all values of c. The latter scheme is not optimized but has the advantage of lending itself to a more straightforward implementation. For high values of c, the results of the Fourier analysis point to the existence of an interval 2 > α > ∼1.8 where both FrDSAo and FrDSAs can achieve a lower spectral radius than DSA. For example, DSA has a spectral radius of ∼0.2246 for c = 0.9999 while FrDSAo produces a value of ∼0.1616 at α = 1.92 and FrDSAs results in ∼0.2116 at α =1.93. (author)

97 MATHEMATICS AND COMPUTING↗

Investigating the AGN-201M research reactor's unique dominance ratio

The AGN-201M reactor is a small, thermal spectrum reactor located at the University of New Mexico (UNM). It is moderated by polyethylene, reflected by graphite, with fuel comprised of uranium microspheres embedded in polyethylene plates that are separated by an aluminum baffle. The dominance ratio of a multiplying system is the ratio of the first higher-mode eigenvalue to the fundamental, k{sub 1}/k{sub 0}. It is a key parameter in characterizing the rate of convergence, analyzing system stability, and determining how tightly coupled the system's neutron fission is. The purpose of this paper is to investigate the system's unusually low dominance ratio of 0.632. This investigation varied the reactor's physical parameters, such as the fuel geometry, fuel density, and reflector thickness, and examined their impact on the reactor's dominance ratio. Additionally, this study examined neutronically similar systems in hopes of identifying common causes for systems with low dominance ratios. The reason why the dominance ratio of the reactor is small compared to larger thermal reactors was determined to be because of its significantly smaller geometry and the composition of the fuel plates. The reflector's effect on the dominance ratio is small in comparison to the other factors, but was found to have a non-zero effect. Furthermore, the AGN-201M was found to have a significantly lower dominance ratio than systems in which it shares a very high (c{sub k} >95%) degree of neutronic similarity.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Angular Distribution of Dimuons from Drell-Yan Production in p+Fe Interactions at 120 GeV Beam Energy

In the E906/SeaQuest Fermilab experiment, we report a measurement of the angular distributions by measuring the angular parameters $\lambda$, $\mu$, and $\nu$ of Drell-Yan dimuons produced using a 120 GeV proton beam incident on an iron target. The angular distribution in the naive Drell-Yan model does not show any $\cos2\phi$ dependency, where $\phi$ denotes the azimuthal angle of dimuons in the Collins-Soper frame. However, pion-induced Drell-Yan experiments, such as NA10 and E615, have observed a significant dependence on $\cos2\phi$. The Boer–Mulders function, a transverse momentum-dependent distribution function, represents the correlation between the transverse spin and the transverse momentum of the quark. A non-zero Boer-Mulders function or an improved higher-order Drell-Yan model considering QCD effects can produce a $\cos 2\phi$ modulation in the Drell-Yan angular distribution. To measure the angular distributions, we have used an event mixing method to construct the combin atorial background, which was then subtracted from the data to isolate the Drell-Yan signal. Following this, we corrected the detector, trigger, and reconstruction efficiencies using a doubly-iterative Bayesian Unfolding method. This iterative unfolding technique improves the response matrix based on the results of the previous unfolding step, ensuring robust convergence without exaggeration of uncertainties. The angular distributions of the dimuons were measured over the invariant mass range $5.0 < M_{\mu^+ \mu^-} < 8.0$ $GeV/c^2$, with dimuon transverse momentum $P_T < 2$ GeV/c and Feynman-x $-0.18 < x_F < 0.9$. The measured angular distributions are then compared with the QCD calculations for $p + \text{Fe}$ interactions, and proton-induced angular distribution measurements from other experiments. We have observed weak $\cos 2\phi$ modulations as a function of $P_T$. For $P_T > 1.0 \, \text{GeV}/c$, the predicted NNLO perturbative QCD value of $\nu$ is larger than what we have me asured at E906/SeaQuest. Moreover, we have not observed a strong dependence of $\nu$ on the kinematic variables, such as dimuon mass $M_{\mu^+ \mu^-}$ and Bjorken-$x$. The spin alignment of the virtual photon, $\lambda$, measured from the SeaQuest Drell-Yan $p+\text{Fe}$ data, is found to be strongly dependent on $P_T$, decreasing as $P_T$ increases. $\lambda$ also holds to the upper bound condition $\lambda < 1.0$ within the statistical uncertainty, showing a trend similar to that predicted by NNLO perturbative QCD. However, for $1.0 < P_T < 2.0 \, \text{GeV}/c$, the extracted $\lambda$ value from SeaQuest is smaller than that predicted by perturbative QCD at NNLO.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

SymProp: Scaling Sparse Symmetric Tucker Decomposition via Symmetry Propagation

Sparse symmetric tensors are an important class of tensors, and their decompositions serve as powerful tools for revealing low-rank structures. This paper introduces SymProp, a novel approach for scaling sparse symmetric Tucker decomposition by propagating symmetry through intermediate computations. SymProp optimizes two key computational kernels: Sparse Symmetric Tensor Times Same Matrix chain (S3 TTMc) for Higher-Order Orthogonal Iteration (HOOI) and Sparse Symmetric Tensor Times Same Matrix chain Times Core (S3 TTMcTC) for Higher-Order QR Iteration (HOQRI). Our method employs a metaprogramming-based index iteration approach to efficiently handle the upper triangular parts of intermediate dense symmetric tensors. SymProp achieves up to 50.9× speedup over SPLATT and up to 360.8× over Compressed Sparse Symmetric (CSS) format on the S3 TTMc operation. Moreover, our S3 TTMc and S3 TTMcTC implementations support tensor orders four levels higher than state-of-the-art methods. Our HOQRI demonstrates superior scalability and up to a 33.6× speedup over optimized HOOI. By enabling more scalable Tucker decompositions for higher orders, decomposition ranks, and dimension sizes, SymProp opens new possibilities for analyzing complex hypergraph structures in fields such as network science, data mining, and machine learning.

Li, Zecheng [North Carolina State University]↗

An eigenvalue-based method for computing the relaxed pressure in compressible multiphase flow with N phases

The modeling of compressible multiphase flows is a decades-old area of study with many applications across various fields. Many of these application areas use stiff pressure relaxation. This process involves the solution of a nonlinear system with N + 1 equations and N + 1 unknowns, where N is the number of phases. The resolution of this system with general equations of state (EOSs) is difficult. Furthermore, nonlinear systems can admit multiple solutions, and current solution methods do not address this possibility. Very recently, a thermodynamic relaxation method was introduced, which effectively maps a relatively simple predictor equation of state onto a more complex target equation of state. In this context, the target EOSs are the chosen EOSs for the thermodynamic model. Furthermore, this thermodynamic relaxation has the benefit of simplifying the stiff pressure relaxation system of equations. In this article, we show this system reduces to a polynomial of degree N, which can be recast as an eigenvalue problem through the use of the associated companion matrix. We show that although this eigenvalue method is generally less efficient than Newton–Raphson iteration, it does not suffer from convergence issues and finds all N roots of the polynomial. Hence, the method provides a fail-safe for root-finding iterative methods and a way to address the issue of multiple solutions to the nonlinear system of equations in stiff pressure relaxation.

Eigenvalue algorithm↗

Hierarchical ensemble Kalman methods with sparsity-promoting generalized gamma hyperpriors

This paper introduces a computational framework to incorporate flexible regularization techniques in ensemble Kalman methods, generalizing the iterative alternating scheme to nonlinear inverse problems. The proposed methodology approximates the maximum a posteriori (MAP) estimate of a hierarchical Bayesian model characterized by a conditionally Gaussian prior and generalized gamma hyperpriors. Suitable choices of hyperparameters yield sparsity-promoting regularization. We propose an iterative algorithm for MAP estimation, which alternates between updating the unknown with an ensemble Kalman method and updating the hyperparameters in the regularization to promote sparsity. Here, the effectiveness of our methodology is demonstrated in several computed examples, including compressed sensing and subsurface flow inverse problems.

Ensemble Kalman methods↗

Innovative laser-based methods for monitoring fuel retention in ITER

This paper addresses the challenge of tritium inventory management in ITER and future fusion reactors, highlighting the importance of accurate tritium measurement and its spatial distribution within the vacuum vessel. Given ITER’s operational constraints, especially the limit on tritium retention, precise measurement is essential for both safety and regulatory compliance. To tackle these questions, the paper presents the T-monitor diagnostic system developed by Forschungszentrum Jülich, which uses Laser-Induced Desorption (LID) in combination with Diagnostic Residual Gas Analysis (DRGA) to measure hydrogen isotope concentrations on the surface of divertor tiles. The system integrates a high-power laser, advanced optical components, and a Fast Scanning Mirror Unit (FSMU) for accurate laser spot positioning with rapid response. Designed to measure in situ tritium retention, the diagnostic provides high-resolution spatial mapping, vital for evaluating detritiation strategies. The laser heating process increases the divertor surface temperature to 1600 K within the laser spot, promoting hydrogen isotope desorption. Accurate measurements require the precise control of laser parameters, including pulse duration and spot size, with a target relative accuracy of 20%. The optical design includes both in-vessel and ex-vessel components, such as durable high-reflectivity mirrors made of gold and copper, selected not only for their infrared performance but also for their transmission of visible wavelengths for observation purposes. To protect optical components from contamination, a pneumatic shutter is used.

Hydrogen isotopes↗