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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Accurate Ultrasonic Thickness Measurement for Arbitrary Time-Variant Thermal Profile

Ultrasonic thickness measurement of mechanical structures is one of the most popular and commonly used nondestructive methods for various kinds of process control and corrosion monitoring. With ultrasonic propagation speed being temperature-dependent, the thickness measurement can be performed reliably only when the thermal profile is completely known. Most conventional techniques assume the temperature of the test structure is uniform and at room temperature across its thickness. Such assumptions may lead to large errors in the thickness measurement, especially when there are significant temperature variations across the thickness. State-of-the-art techniques use external temperature measurements or implement iterative methods to compensate for the unknown thermal profiles. However, such techniques produce unsatisfactory results when the heat distribution is complex or varies rapidly with time. In this work, we propose a two-sensors technique, using both compressive and shear excitations, with a non-iterative rapid data processing method for accurate thickness measurement under arbitrary time-variant thermal profile. The independent behavior of shear and compressive waves is used to formulate a real-time thickness estimation technique. The developed technique is experimentally validated on a steel plate with fixed acoustic sensors. Test results show that the error in thickness estimation can be reduced by up to 98% compared to conventional thickness gauging methods.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Equilibrium core modeling of a pebble bed reactor similar to the Xe-100 with SCALE

As the nuclear industry moves towards licensing and constructing advanced reactors, new attention has been focused on the advanced reactor designs that have past operational experience, such as pebble-bed high-temperature gas-cooled reactors (PB-HTGRs). Pebble-bed reactor designs have many advantages, such as their higher operating temperatures and online refueling capabilities. However, high-fidelity computational modeling of pebble-bed reactor designs, from reactor startup to operation at equilibrium, is more challenging compared to conventionally fueled reactors due to the continuous movement of the fuel pebbles through the reactor during operation. In previous work at Oak Ridge National Laboratory (ORNL), the SCALE Leap-In method for Cores at Equilibrium (SLICE) was developed around tools within the SCALE code system. This iterative method can effectively generate pebble-bed reactor zone-wise fuel inventories at equilibrium core operation within a reasonable computational time. The objective of this work was to further verify the ORNL SLICE method and to investigate the impact of considering temperature profiles during the application of the method. The SLICE method was applied to a modular high-temperature gas-cooled reactor design based upon publicly available design specifications of the Xe-100 pebble-bed reactor. Upon comparing the results from the SLICE method to published literature, the differences in the eigenvalue k effective were on the order of several hundred pcm (percent millirho). To investigate one possible cause of these differences, a study looking at the sensitivity of the full-core equilibrium k effective and discharge nuclide inventory to temperature was performed by developing equilibrium cores of two additional temperature profiles. From this temperature study, differences on the order of hundreds of pcm for the full-core equilibrium k effective , and up to 15% difference for the discharge inventories were found. In conclusion, these results indicated the strong dependence on temperature that needs to be considered for future work in equilibrium modeling of PB-HTGRs.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Super Resolving Unrolled Neural Networks for Remote Sensing

In remote sensing systems, the capabilities of the system are constrained by the complex interactions between size, weight, and power (SWAP) of potential designs. In electro-optical (EO) systems, examples of these critical parameters include the system’s sensitivity and resolution. Those parameters can be increased by ever larger optical apertures and focal planes but at the cost of more SWAP. Multi-image super resolution (MISR) techniques allow resolution to be enhanced via computation rather than more sophisticated optical hardware. These algorithms combine multiple images together into a single, higher resolution image, trading temporal resolution and computation for spatial resolution. Fielded MISR techniques, such as Drizzle, can require several hundred images to create a single super resolved image, implying reduced temporal resolution, increased data acquisition load, and limiting mission applications. Iterative techniques, such as model-based image reconstruction and compressive sensing, have been shown to create super resolved images using fewer images than Drizzle. They do this by posing an optimization problem that balances accuracy between a highly accurate physical model and an image model. In the case of super resolution, the physical model is defined by the relation between low resolution input images and the desired high resolution output image. The image model encodes some assumptions about the super resolved image. These assumptions are meant to suppress reconstruction artifacts that arise due to deterministic physical model error, stochastic measurement noise, and potential undersampling. In practice, the performance of iterative methods are limited by imaging models compatible with optimization. Deep learning-based methods can effectively learn image models of arbitrary complexity, but lack the theoretical explainability and robustness of iterative techniques. Consensus equilibrium (CE) generalizes the iterative techniques beyond optimization, enabling blackbox algorithms such as traditional and neural image denoisers to be used as the image model. CE-based approaches retain much of the explainability and robustness of iterative techniques while allowing the expressiveness of machine learning image models to be used. Additionally, by unrolling iterations of CE with an embedded image denoiser, the image denoiser can be further trained and specialized to the specific application with potentially higher quality reconstructions. Under this project, we demonstrated the feasibility of training an unrolled neural network based upon CE. While we didn’t train one, we showed that the CE process is differentiable and its gradient can be tractably computed. We also explored the usage of a variants of CE akin to generative neural works. Most importantly, we applied the CE framework to a number of problems including non-blind deconvolution, upsampling, single-image super resolution, MISR, event-based sensing, and saturated deconvolution. Our MISR prototype creates high quality reconstructions with an order of magnitude fewer images than previous approaches and, critically, produces these reconstructions fast enough for practical usage.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Newton trust-region methods with primary variable switching for simulating high temperature multiphase porous media flow

Coupling multiphase flow with energy transport due to high temperature heat sources introduces significant new challenges since boiling and condensation processes can lead to dry-out conditions with subsequent re-wetting. The transition between two-phase and single-phase behavior can require changes to the primary dependent variables adding discontinuities as well as extending constitutive nonlinear relations to extreme physical conditions. Practical simulations of large-scale engineered domains lead to Jacobian systems with a very large number of unknowns that must be solved efficiently using iterative methods in parallel on high-performance computers. Performance assessment of potential nuclear repositories, carbon sequestration sites and geothermal reservoirs can require numerous Monte-Carlo simulations to explore uncertainty in material properties, boundary conditions, and failure scenarios. Due to the numerical challenges, standard NR iteration may not converge over the range of required simulations and require more sophisticated optimization method like trust-region. In this study, we use the open-source simulator PFLOTRAN for the important practical problem of the safety assessment of future nuclear waste repositories in the U.S. DOE geologic disposal safety assessment Framework. The simulator applies the PETSc parallel framework and a backward Euler, finite volume discretization. We demonstrate failure of the conventional NR method and the success of trust-region modifications to Newton’s method for a series of test problems of increasing complexity. Trust-region methods essentially modify the Newton step size and direction under some circumstances where the standard NR iteration can cause the solution to diverge or oscillate. Furthermore, we show how the Newton Trust-Region method can be adapted for Primary Variable Switching (PVS) when the multiphase state changes due to boiling or condensation. The simulations with high-temperature heat sources which led to extreme nonlinear processes with many state changes in the domain did not converge with NR, but they do complete successfully with the trust-region methods modified for PVS. This implementation effectively decreased weeks of simulation time needing manual adjustments to complete a simulation down to a day. Finally, we show the strong scalability of the methods on a single node and multiple nodes in an HPC cluster.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Lyapunov-Based Iterative Learning of Regions of Attraction for Autonomous Systems

This paper proposes a novel algorithm for estimating the region of attraction of equilibrium points for nonlinear discrete-time autonomous systems. The method iteratively expands an initial estimate of the region of attraction by constructing unions of sublevel sets of learned functions parametrized as neural networks. Unlike conventional techniques that rely on a single global Lyapunov function, the proposed approach provides a collection of local Lyapunov-like functions, enabling richer representations and potentially larger region of attraction estimates. These functions are trained using sampled state-space data, and their Lipschitz continuity ensures that desirable properties extend beyond the training samples. The devised strategy is tested via numerical simulations, demonstrating the effectiveness of the proposed approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Lyapunov-Based Iterative Learning of the Region of Attraction for Autonomous Systems

This presentation introduces a novel algorithm for estimating the region of attraction of equilibrium points for nonlinear discrete-time autonomous systems. The method iteratively expands an initial estimate of the region of attraction by constructing unions of sublevel sets of learned functions parametrized as neural networks. Unlike conventional techniques that rely on a single global Lyapunov function, the proposed approach provides a collection of local Lyapunov-like functions, enabling richer representations and potentially larger region of attraction estimates. These functions are trained using sampled state-space data, and their Lipschitz continuity ensures that desirable properties extend beyond the training samples. The devised strategy is tested via numerical simulations, demonstrating the effectiveness of the proposed approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

How to detect lensing rotation

Gravitational lensing rotation of images is predicted to be negligible at linear order in density perturbations, but can be produced by the post-Born lens-lens coupling at second order. This rotation is somewhat enhanced for Cosmic Microwave Background (CMB) lensing due to the large source path length, but remains small and very challenging to detect directly by CMB lensing reconstruction alone. We show the rotation may be detectable at high significance as a cross-correlation signal between the curl reconstructed with Simons Observatory (SO) or CMB-S4 data, and a template constructed from quadratic combinations of large-scale structure (LSS) tracers. Equivalently, the lensing rotation-tracer-tracer bispectrum can also be detected, where LSS tracers considered include the CMB lensing convergence, galaxy density, and the Cosmic Infrared Background (CIB), or optimal combinations thereof. We forecast that an optimal combination of these tracers can probe post-Born rotation at the level of 5.7σ–6.1σ with SO and 13.6σ–14.7σ for CMB-S4, depending on whether standard quadratic estimators or maximum a posteriori iterative methods are deployed. We also show possible improvement up to 21.3σ using a CMB-S4 deep patch observation with polarization-only iterative lensing reconstruction. However, these cross-correlation signals have non-zero bias because the rotation template is quadratic in the tracers, and exists even if the lensing is rotation free. We estimate this bias analytically, and test it using simple null-hypothesis simulations to confirm that the bias remains subdominant to the rotation signal of interest. Detection and then measurement of the lensing rotation cross-spectrum is therefore a realistic target for future observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Iterated Gauss-Seidel GMRES

The GMRES algorithm of Saad and Schultz [SIAM J. Sci. Stat. Comput., 7 (1986), pp. 856-869] is an iterative method for approximately solving linear systems Ax = b, with initial guess x0 and residual r0 = b Ax0. The algorithm employs the Arnoldi process to generate the Krylov basis vectors (the columns of Vk ). It is well known that this process can be viewed as a QR factorization of the matrix Bk = [r0, AVk] at each iteration. Despite an O (..epsilon..)..kappa.. (Bk ) loss of orthogonality, for unit roundoff ..epsilon..and condition number ..kappa.. , the modified Gram-Schmidt formulation was shown to be backward stable in the seminal paper by Paige et al. [SIAM J. Matrix Anal.Appl., 28 (2006), pp. 264-284]. We present an iterated Gauss-Seidel formulation of the GMRES algorithm (IGS-GMRES) based on the ideas of Ruhe [Linear Algebra Appl., 52 (1983), pp. 591-601] and Swirydowicz et al. [Numer. Linear Algebra Appl., 28 (2020), pp. 1-20]. IGS-GMRES maintains orthogonality to the level O (..epsilon..)..kappa.. (Bk ) or O (..epsilon..), depending on the choice of one or two iterations; for two Gauss-Seidel iterations, the computed Krylov basis vectors remain orthogonal to working accuracy and the smallest singular value of Vk remains close to one. The resulting GMRES method is thus backward stable. We show that IGS-GMRES can be implemented with only a single synchronization point per iteration, making it relevant to large-scale parallel computing environments. We also demonstrate that, unlike MGS-GMRES, in IGS-GMRES the relative Arnoldi residual corresponding to the computed approximate solution no longer stagnates above machine precision even for highly nonnormal systems.

Arnoldi-QR↗
DOE OSTI2023

An implicit particle code with exact energy and charge conservation for electromagnetic studies of dense plasmas

A collisional particle code based on implicit energy- and charge-conserving methods is presented. A modified version of the particle-suppressed Jacobian-Free Newton-Krylov method that can enhance the solver efficiency is introduced. Mathematically, it is shown that this new approach can be viewed as a fixed-point iteration method for the particle positions. The model can exactly conserve global energy and local charge and can efficiently use time steps larger than the plasma period. In conclusion, the algorithm's ability to simulate dense plasmas accurately and efficiently is quantified by simulating the dynamic compression of a plasma slab via a magnetic piston in 1D planar geometry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Joint state-parameter estimation for the reduced fracture model via the united filter

Here, in this paper, we introduce an effective United Filter method for jointly estimating the solution state and physical parameters in flow and transport problems within fractured porous media. Fluid flow and transport in fractured porous media are critical in subsurface hydrology, geophysics, and reservoir geomechanics. Reduced fracture models, which represent fractures as lower-dimensional interfaces, enable efficient multi-scale simulations. However, reduced fracture models also face accuracy challenges due to modeling errors and uncertainties in physical parameters such as permeability and fracture geometry. To address these challenges, we propose a United Filter method, which integrates the Ensemble Score Filter (EnSF) for state estimation with the Direct Filter for parameter estimation. EnSF, based on a score-based diffusion model framework, produces ensemble representations of the state distribution without deep learning. Meanwhile, the Direct Filter, a recursive Bayesian inference method, estimates parameters directly from state observations. The United Filter combines these methods iteratively: EnSF estimates are used to refine parameter values, which are then fed back to improve state estimation. Numerical experiments demonstrate that the United Filter method surpasses the state-of-the-art Augmented Ensemble Kalman Filter, delivering more accurate state and parameter estimation for reduced fracture models. This framework also provides a robust and efficient solution for PDE-constrained inverse problems with uncertainties and sparse observations.

Bayesian inference↗
DOE OSTI2023

On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF

This study presents the development and evaluation of a fully-implicit variational multiscale (VMS) stabilized unstructured finite element (FE) formulation for compressible magnetohydrodynamics (MHD) model, at low Mach number regime. The model describes the dynamics of a compressible conducting fluid in the low Mach number limit in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics phenomena. The specific applications that motivate this study are macroscopic simulations of the longer time-scale stability and disruptions of magnetic confinement fusion (MCF) devices, specifically the ITER tokamak. The discussion considers the development of the VMS FE representation, the structure of the stabilizing terms that deal with significant convective flows, the stabilization of the nearly incompressible response of the fluid flow, and the stabilization of the constraint that enforces the solenoidal involution on the magnetic field. The nonlinear discretized system is solved with scalable preconditioned Newton–Krylov iterative methods, which employs a multiphysics block preconditioning method based on approximate block factorizations and Schur complements. The study presents an evaluation of the VMS method on a 2D cartesian tearing mode instability, and illustrates the scalability of the solvers on MCF relevant problems. A set of results are also presented for longer time-scale stability and disruptions for the ITER tokamak. These include a vertical displacement event (VDE), and a (1,1) internal kink mode. Here, the formulation is demonstrated to be scalable and also reasonably robust with respect to the Lundquist number scaling.

42 ENGINEERING↗
DOE OSTI2024

Large-scale harmonic balance simulations with Krylov subspace and preconditioner recycling

The multi-harmonic balance method combined with numerical continuation provides an efficient framework to compute a family of time-periodic solutions, or response curves, for large-scale, nonlinear mechanical systems. The predictor and corrector steps repeatedly solve a sequence of linear systems that scale by the model size and number of harmonics in the assumed Fourier series approximation. In this paper, a novel Newton–Krylov iterative method is embedded within the multi-harmonic balance and continuation algorithm to efficiently compute the approximate solutions from the sequence of linear systems that arise during the prediction and correction steps. Further, the method recycles, or reuses, both the preconditioner and the Krylov subspace generated by previous linear systems in the solution sequence. A delayed frequency preconditioner refactorizes the preconditioner only when the performance of the iterative solver deteriorates. The GCRO-DR iterative solver recycles a subset of harmonic Ritz vectors to initialize the solution subspace for the next linear system in the sequence. The performance of the iterative solver is demonstrated on two exemplars with contact-type nonlinearities and benchmarked against a direct solver with traditional Newton–Raphson iterations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Simulation of an inductively coupled plasma with a two-dimensional Darwin particle-in-cell code

A two-dimensional particle-in-cell code for the simulation of low-frequency electromagnetic processes in laboratory plasmas has been developed. The code uses the Darwin method omitting the electromagnetic wave propagation. The Darwin method separates the electric field into solenoidal and irrotational parts. The solenoidal electric field is calculated with a new algorithm based on the equation for the electric field vorticity. The system of linear equations in the new algorithm is readily solved using a standard iterative method. The irrotational electric field is the electrostatic field calculated with the direct implicit algorithm. The code is verified by reproducing the two-stream instability, electron electromagnetic waves, and shear Alfvén waves. The code is applied to simulate an inductively coupled plasma with the driving current flowing around the plasma region. In this simulation, a ring of dense plasma forms at the initial stage but then the density becomes maximal in the center and decays monotonically toward the walls. The skin effect is in the transitional mode between local and non-local, and the electron velocity distribution function is non-Maxwellian.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Fermilab Booster loss modelling and rebalancing using Bayesian methods

Fermilab Booster is being upgraded for the PIP-II project to support 20Hz ramp rate at higher intensities. Loss trip limits determine the achievable peak power. To meet PIP-II requirements, losses need to be halved as compared to current levels. Losses primarily occur at injection and transition crossing, with both gradually increasing and threshold-like intensity-dependent behaviors. The existing simulation models are not yet good enough for quantitative loss predictions. In practice, it will be necessary to tune up the Booster using iterative methods and operator intuition. In this paper we present an effort to systematically model Booster losses using active learning (Bayesian exploration) techniques, and subsequently to rebalance them for higher trip limit margins. We first created several sets of spatially and temporally isolated orbit and optics knobs, and trained Gaussian process models for each beam loss monitor as well as beam current. This is a complex task due to safety and timing requirements – we discuss mitigations such as uncertainty constraints and approximate fitting. Once models are stable, we perform large-scale single and multi-objective tuning using scalarized objectives made up of critical beam loss locations. Our results demonstrate significant rebalancing of losses, increasing trip margins, as well as an overall improvement in beam transmission efficiency. We are exploring how to combine existing simulations with experimental data and automate the collection procedure so that more advanced surrogate models can be created over time.

Kuklev, Nikita [Fermilab]↗
DOE OSTI2024

Score-based denoising for atomic structure identification

We propose an effective method for removing thermal vibrations that complicate the task of analyzing complex dynamics in atomistic simulation of condensed matter. Our method iteratively subtracts thermal noises or perturbations in atomic positions using a denoising score function trained on synthetically noised but otherwise perfect crystal lattices. The resulting denoised structures clearly reveal underlying crystal order while retaining disorder associated with crystal defects. Purely geometric, agnostic to interatomic potentials, and trained without inputs from explicit simulations, our denoiser can be applied to simulation data generated from vastly different interatomic interactions. The denoiser is shown to improve existing classification methods, such as common neighbor analysis and polyhedral template matching, reaching perfect classification accuracy on a recent benchmark dataset of thermally perturbed structures up to the melting point. Demonstrated here in a wide variety of atomistic simulation contexts, the denoiser is general, robust, and readily extendable to delineate order from disorder in structurally and chemically complex materials.

36 MATERIALS SCIENCE↗
DOE OSTI2025

An FFT-based micromechanical model for gradient enhanced brittle fracture

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

36 MATERIALS SCIENCE↗
DOE OSTI2025

Random Phase Approximation Correlation Energy Using Real-Space Density Functional Perturbation Theory

We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn–Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In particular, we employ a cubic-scaling formalism based on density functional perturbation theory that circumvents the calculation of the response function matrix, instead relying on the ability to compute its product with a vector through the solution of the associated Sternheimer linear systems. We develop a large-scale parallel implementation of this formalism using the subspace iteration method in conjunction with the spectral quadrature method while employing the Kronecker product-based method for the application of the Coulomb operator and the conjugate orthogonal conjugate gradient method for the solution of the linear systems. We demonstrate convergence with respect to key parameters and verify the method’s accuracy by comparing with plane-wave results. We show that the framework achieves good strong scaling to many thousands of processors, reducing the time to solution for a lithium hydride system with 128 electrons to around 150 s on 4608 processors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

TTDFT: A GPU accelerated Tucker tensor DFT code for large-scale Kohn-Sham DFT calculations

We present the Tucker tensor DFT (TTDFT) code which uses a tensor-structured algorithm with graphic processing unit (GPU) acceleration for conducting ground-state DFT calculations on large-scale systems. The Tucker tensor DFT algorithm uses a localized Tucker tensor basis computed from an additive separable approximation to the Kohn-Sham Hamiltonian. The discrete Kohn-Sham problem is solved using Chebyshev filtered subspace iteration method that relies on matrix-matrix multiplications of a sparse symmetric Hamiltonian matrix and a dense wavefunction matrix, expressed in the localized Tucker tensor basis. These matrix-matrix multiplication operations, which constitute the most computationally intensive step of the solution procedure, are GPU accelerated providing ~8-fold GPU-CPU speedup for these operations on the largest systems studied. In conclusion, the computational performance of the TTDFT code is presented using benchmark studies on aluminum nano-particles and silicon quantum dots with system sizes ranging up to ~7,000 atoms.

97 MATHEMATICS AND COMPUTING↗