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NASA NTRS1973

Derivation of aerodynamic kernel functions

The method of Fourier transforms is used to determine the kernel function which relates the pressure on a lifting surface to the prescribed downwash within the framework of Dowell's (1971) shear flow model. This model is intended to improve upon the potential flow aerodynamic model by allowing for the aerodynamic boundary layer effects neglected in the potential flow model. For simplicity, incompressible, steady flow is considered. The proposed method is illustrated by deriving known results from potential flow theory.

Dowell, E. H.↗

DOE OSTI2020

Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation

Here, we study reproducing kernel (RK) collocation method for peridynamic Navier equation. In the first part, we apply a linear RK approximation to both displacement and dilatation, and then back-substitute dilatation and solve the peridynamic Navier equation in a pure displacement form. The RK collocation scheme converges to the nonlocal limit for a fixed nonlocal interaction length and also to the local limit as nonlocal interactions vanish. The stability is shown by comparing the collocation scheme with the standard Galerkin scheme using Fourier analysis. In the second part, we apply the RK collocation to the quasi-discrete peridynamic Navier equation and show its convergence to the correct local limit when the ratio between the nonlocal length scale and the discretization parameter is fixed. The analysis is carried out on a special family of rectilinear Cartesian grids for the RK collocation method with a designated kernel with finite support. We assume the Lamé parameters satisfy λ ≥ μ to avoid extra assumptions on the nonlocal kernel. Finally, numerical experiments are conducted to validate the theoretical results.

42 ENGINEERING↗

DOE OSTI2019

Combining the mapping Hamiltonian linearized semiclassical approach with the generalized quantum master equation to simulate electronically nonadiabatic molecular dynamics

The generalized quantum master equation (GQME) provides a powerful framework for simulating electronically nonadiabatic molecular dynamics. Within this framework, the effect of the nuclear degrees of freedom on the time evolution of the electronic reduced density matrix is fully captured by a memory kernel superoperator. In this paper, we consider two different procedures for calculating the memory kernel of the GQME from projection-free inputs obtained via the combination of the mapping Hamiltonian (MH) approach and the linearized semiclassical (LSC) approximation. Here, the accuracy and feasibility of the two procedures are demonstrated on the spin-boson model. We find that although simulating the electronic dynamics by direct application of the two LSC-based procedures leads to qualitatively different results that become increasingly less accurate with increasing time, restricting their use to calculating the memory kernel leads to an accurate description of the electronic dynamics. Comparison with a previously proposed procedure for calculating the memory kernel via the Ehrenfest method reveals that MH/LSC methods produce memory kernels that are better behaved at long times and lead to more accurate electronic dynamics

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Angular oversampling with temporally offset layers on multilayer detectors in computed tomography

Purpose: Today’s computed tomography (CT) scanners operate at an increasingly high rotation speed in order to reduce motion artifacts and to fulfill the requirements of dynamic acquisition, e.g., perfusion and cardiac imaging, with lower angular sampling rate as a consequence. In this paper, a simple method for obtaining angular oversampling when using multilayer detectors in continuous rotation CT is presented. Methods: By introducing temporal offsets between the measurement periods of the different layers on a multilayer detector, the angular sampling rate can be increased by a factor equal to the number of layers on the detector. The increased angular sampling rate reduces the risk of producing aliasing artifacts in the image. A simulation of a detector with two layers is performed to prove the concept. Results: The simulation study shows that aliasing artifacts from insufficient angular sampling are reduced by the proposed method. Specifically, when imaging a single point blurred by a 2D Gaussian kernel, the method is shown to reduce the strength of the aliasing artifacts by approximately an order of magnitude. Conclusions: The presented oversampling method is easy to implement in today’s multilayer detectors and has the potential to reduce aliasing artifacts in the reconstructed images.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2024

Meshfree Methods

Meshfree methods have undergone substantial development and have received much attention in the last two decades. This new family of numerical methods is designed to inherit the main advantages of the finite element method such as compact supports of shape functions and good approximation properties while, at the same time, overcome the main disadvantages of the finite element method caused by the mesh dependence. The meshfree methods share a common feature that no mesh is needed and shape functions are constructed from sets of points, thus eliminating the need for time consuming mesh generation. The most significant advantage of meshfree methods is the flexibility in customizing approximation functions for desired regularity and for capturing essential physics and features of the particular problems of interest. Adaptivity formulation and multiple-scale solution strategies also can be implemented with relative ease. It has become clear that the meshfree methods provide considerable advantages over the conventional finite element methods in solving problems involving moving discontinuities, evolving material interfaces, multiple-scale phenomena, large material distortion and structural deformation, and fracture and damage processes. This Chapter gives an overview of many classes of meshfree methods, with more detailed discussions on Smoothed Particle Hydrodynamics (SPH), the Reproducing Kernel Particle Method (RKPM), Peridynamics (PD), the Material Point Method (MPM), as well as their applications in various challenging engineering problems.2

Chen, Jiun-Shyan↗

DOE OSTI2013

A method for removing arm backscatter from EPID images

Purpose: To develop a method for removing the support arm backscatter from images acquired using current Varian electronic portal imaging devices (EPIDs).Methods: The effect of arm backscatter on EPID images was modeled using a kernel convolution method. The parameters of the model were optimized by comparing on-arm images to off-arm images. The model was used to develop a method to remove the effect of backscatter from measured EPID images. The performance of the backscatter removal method was tested by comparing backscatter corrected on-arm images to measured off-arm images for 17 rectangular fields of different sizes and locations on the imager. The method was also tested using on- and off-arm images from 42 intensity modulated radiotherapy (IMRT) fields.Results: Images generated by the backscatter removal method gave consistently better agreement with off-arm images than images without backscatter correction. For the 17 rectangular fields studied, the root mean square difference of in-plane profiles compared to off-arm profiles was reduced from 1.19% (standard deviation 0.59%) on average without backscatter removal to 0.38% (standard deviation 0.18%) when using the backscatter removal method. When comparing to the off-arm images from the 42 IMRT fields, the mean {gamma} and percentage of pixels with {gamma} < 1 were improved by the backscatter removal method in all but one of the images studied. The mean {gamma} value (1%, 1 mm) for the IMRT fields studied was reduced from 0.80 to 0.57 by using the backscatter removal method, while the mean {gamma} pass rate was increased from 72.2% to 84.6%.Conclusions: A backscatter removal method has been developed to estimate the image acquired by the EPID without any arm backscatter from an image acquired in the presence of arm backscatter. The method has been shown to produce consistently reliable results for a wide range of field sizes and jaw configurations.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2025

Kernel Manifolds: Nonlinear‐Augmentation Dimensionality Reduction Using Reproducing Kernel Hilbert Spaces

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections, augment linear dimensionality reduction with a nonlinear correction term in the reconstruction map to overcome approximation accuracy limitations of purely linear approaches. While feature map-based approaches typically learn a least squares optimal polynomial correction term, we generalize this approach by learning an optimal nonlinear correction from a user-defined reproducing kernel Hilbert space. Our approach allows one to impose arbitrary nonlinear structure on the correction term, including polynomial structure, and includes feature map and radial basis function-based corrections as special cases. Furthermore, our method has relatively low training cost and has monotonically decreasing error as the latent space dimension increases. In conclusion, we compare our approach to proper orthogonal decomposition and several recent QM approaches on data from several example problems.

kernel methods↗

DOE OSTI2016

Accelerated Monte Carlo Fission Source Convergence with Fission Matrix and Kernel Density Estimators

Accurate solution of the k-eigenvalue form of the Boltzmann radiation transport equation is required in many application areas, including nuclear reactor analysis and criticality safety. Monte Carlo calculations are free of the discretization errors inherent to deterministic methods and therefore offer the most accurate solutions. However, converging the fission source can be difficult for many problems, resulting in either a substantial computational overhead or potential inaccuracies that negate many of the benefits of using Monte Carlo methods. Difficulty in converging the fission source occurs for two distinct reasons. The first is the existence of a high dominance ratio in the problem (i.e. the largest and second largest eigenvalues have approximately the same magnitude). The second difficulty arises due to undersampling of the fission source because an insufficient number of particle histories are simulated. The first difficulty is shared by deterministic solvers when using power iteration, while the second difficulty is unique to Monte Carlo solvers. In practice, both difficulties may be present in the same problem, compounding the difficulty in achieving a converged distribution. In this paper, we consider a new approach to accelerate the convergence of the fission source based on combining the use of fission matrix methods with kernel density estimators (KDEs). It has been observed that deterministic fission matrix methods show the potential to accelerate the convergence of the fission source in Monte Carlo criticality calculations but may introduce significant additional noise for difficult problems. In this paper, we have demonstrated the use of a KDE approach in combination with the fission matrix acceleration. Although the addition of the KDE initially slows the convergence of the fission matrix acceleration, it decreases the magnitude of the noise while still offering significantly improved convergence relative to analog Monte Carlo. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Cholesky-based experimental design for Gaussian process and kernel-based emulation and calibration.

Gaussian processes and other kernel-based methods are used extensively to construct approximations of multivariate data sets. The accuracy of these approximations is dependent on the data used. This paper presents a computationally efficient algorithm to greedily select training samples that minimize the weighted L p error of kernel-based approximations for a given number of data. The method successively generates nested samples, with the goal of minimizing the error in high probability regions of densities specified by users. The algorithm presented is extremely simple and can be implemented using existing pivoted Cholesky factorization methods. Training samples are generated in batches which allows training data to be evaluated (labeled) in parallel. For smooth kernels, the algorithm performs comparably with the greedy integrated variance design but has significantly lower complexity. Numerical experiments demonstrate the efficacy of the approach for bounded, unbounded, multi-modal and non-tensor product densities. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data using Bayesian inference.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Quality Control Methods for Measurement of UCO Kernel Composition and SiC Microstructure

Quality control (QC) is critically important to tristructural-isotropic (TRISO) particle fuels owing to the complexity of and reliance on the fuel form to contain fission products during irradiation. Characterization methods for particle fuel QC have decades of history and have continued to develop as new insights into fuel performance inform revised fuel specifications and as advances in underlying technologies expand the possibilities of what may be characterized. Two relatively new methods for characterization of TRISO fuels have been published in open literature: optical microscopy image analysis for mixed uranium carbide/uranium oxide (UCO) kernel composition analysis and automated grain boundary detection in backscattered electron (BSE) images of the silicon carbide (SiC) layer in TRISO particles for grain size characterization. Suggestions and guidelines for the application of these methods to TRISO fuel qualification are provided in this report.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2018

CFD-DEM solution verification: Fixed-bed studies

Fixed (frozen) particle configurations are used to study CFD-DEM convergence behavior in the limit of infinite grid resolution. A filtering scheme based on solving a diffusion equation, i.e., a Gaussian kernel, is used to interpolate particle information to the continuum grid, free of cell size limitations. A regression method is used for Richardson extrapolation of the discrete solutions to the grid-free solution. The regression method is shown to predict accurate extrapolation curves in the presence of the observed oscillatory convergence behavior. The extrapolation curve is used to complete the solution verification process by quantifying the numerical uncertainty present in the calculations. Several numerical and model parameters are studied including the spatial discretization method, the kernel width and the mean drag law. Here, a manageable level of discretization error is found with relative discretization errors generally <4%.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Bayesian Active Learning for Scanning Probe Microscopy: From Gaussian Processes to Hypothesis Learning

Recent progress in machine learning methods and the emerging availability of programmable interfaces for scanning probe microscopes (SPMs) have propelled automated and autonomous microscopies to the forefront of attention of the scientific community. However, enabling automated microscopy requires the development of task-specific machine learning methods, understanding the interplay between physics discovery and machine learning, and fully defined discovery workflows. This, in turn, requires balancing the physical intuition and prior knowledge of the domain scientist with rewards that define experimental goals and machine learning algorithms that can translate these to specific experimental protocols. Here, we discuss the basic principles of Bayesian active learning and illustrate its applications for SPM. We progress from the Gaussian process as a simple data-driven method and Bayesian inference for physical models as an extension of physics-based functional fits to more complex deep kernel learning methods, structured Gaussian processes, and hypothesis learning. These frameworks allow for the use of prior data, the discovery of specific functionalities as encoded in spectral data, and exploration of physical laws manifesting during the experiment. Here, the discussed framework can be universally applied to all techniques combining imaging and spectroscopy, SPM methods, nanoindentation, electron microscopy and spectroscopy, and chemical imaging methods and can be particularly impactful for destructive or irreversible measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Meshfree Methods for Modeling Chemo-Mechanical Cathode Cracking in Li-Ion Batteries

Through repeated charging and discharging, the electrodes of a Li-ion battery experience cyclic loading causing swelling and contraction due to the movement of lithium, also known as intercalation. This research focuses specifically on the chemo-mechanical cracking in the cathode. Because cathode particles are comprised of many randomly-oriented grains, which have highly anisotropic material properties, the expansion and contraction is very non-uniform. As a result, stress concentrations tend to form between grains, which necessitates the modeling of crack propagation largely along grain boundaries. Chemo-mechanical models are simulated mainly by two methods: the cohesive zone model (CZM) and the continuous damage model (CDM). The CZM is more accurate at capturing the sharp discontinuities of a crack but is very computationally expensive and intractable for large-scale models as a result. Conversely, the CDM is easily computed but not well-suited to easily allow for discontinuous field variables, which are inherent across a crack. This study aims to improve the CDM's ability to capture discontinuous cracks. Current versions of the CDM use the finite element method (FEM), which is one of the most widely used approaches for spatial discretization. This research investigates the use of the Reproducing Kernel Particle Method (RKPM), a meshfree method, for spatial discretization and aims to achieve a chemo-mechanical crack propagation model that achieves both intermediate accuracy and computational time between a CDM and CZM. To gain a better understanding of how the meshfree model compares to the current FEM model in capturing cathode crack propagation, further investigation is needed.

cathode cracking↗

DOE OSTI2015

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum. The use of a symmetric Lanczos algorithm only requires half of the memory compared with the nonsymmetric variant of the Lanczos algorithm. The symmetric Lanczos algorithm is also numerically more stable than the nonsymmetric version. The KPM algorithm is also presented as a low-memory alternative to the Lanczos approach, but the algorithm may require more matrix-vector multiplications in practice. We discuss the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost. Applications to a set of small and medium-sized molecules are also presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Machine learning models for volumetric swelling in uranium nitride

Machine learning methods are applied to predict the volumetric swelling rate of the nuclear fuel uranium nitride (UN) over various temperatures, irradiation conditions, and power densities. Both kernel-based methods and symbolic regression models for UN swelling are developed and compared with multiple experimental datasets. We find that the UN pellet geometry and dimensions must be taken into account to accurately model swelling behavior. Strong agreement is observed between the developed machine learning models and the data. The predictive error generated by the machine learning models improves on empirical models taken from the literature. Sensitivity analysis is performed to determine which properties such as temperature, burnup, and power density, are most important in the swelling process. We find that machine learning can be used to quickly develop accurate swelling models for nuclear materials. In conclusion, the presented results illustrate the potential of machine learning to determine volumetric swelling in UN.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2017

Formation enthalpies for transition metal alloys using machine learning

The enthalpy of formation is an important thermodynamic property. Developing fast and accurate methods for its prediction is of practical interest in a variety of applications. Material informatics techniques based on machine learning have recently been introduced in the literature as an inexpensive means of exploiting materials data, and can be used to examine a variety of thermodynamics properties. Here we investigate the use of such machine learning tools for predicting the formation enthalpies of binary intermetallic compounds that contain at least one transition metal. We consider certain easily available properties of the constituting elements complemented by some basic properties of the compounds, to predict the formation enthalpies. We show how choosing these properties (input features) based on a literature study (using prior physics knowledge) seems to outperform machine learning based feature selection methods such as sensitivity analysis and LASSO (least absolute shrinkage and selection operator) based methods. A nonlinear kernel based support vector regression method is employed to perform the predictions. The predictive ability of our model is illustrated via several experiments on a dataset containing 648 binary alloys. We train and validate the model using the formation enthalpies calculated using a model by Miedema, which is a popular semiempirical model used for the prediction of formation enthalpies of metal alloys.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion

Reproducing kernel (RK) approximations are meshfree methods that construct shape functions from sets of scattered data. We present an asymptotically compatible (AC) RK collocation method for nonlocal diffusion models with Dirichlet boundary condition. The numerical scheme is shown to be convergent to both nonlocal diffusion and its corresponding local limit as nonlocal interaction vanishes. The analysis is carried out on a special family of rectilinear Cartesian grids for a linear RK method with designed kernel support. The key idea for the stability of the RK collocation scheme is to compare the collocation scheme with the standard Galerkin scheme, which is stable. In addition, assembling the stiffness matrix of the nonlocal problem requires costly computational resources because high-order Gaussian quadrature is necessary to evaluate the integral. We thus provide a remedy to the problem by introducing a quasi-discrete nonlocal diffusion operator for which no numerical quadrature is further needed after applying the RK collocation scheme. The quasi-discrete nonlocal diffusion operator combined with RK collocation is shown to be convergent to the correct local diffusion problem by taking the limits of nonlocal interaction and spatial resolution simultaneously. The theoretical results are then validated with numerical experiments. We additionally illustrate a connection between the proposed technique and an existing optimization based approach based on generalized moving least squares.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2019

State Predictor of Classification Cognitive Engine Applied to Channel Fading

This study presents the application of machine learning (ML) to a space-to-ground communication link, showing how ML can be used to detect the presence of detrimental channel fading. Using this channel state information, the communication link can be used more efficiently by reducing the amount of lost data during fading. The motivation for this work is based on channel fading observed during on-orbit operations with NASA's Space Communication and Navigation (SCaN) testbed on the International Space Station (ISS). This paper presents the process to extract a target concept (fading and not-fading) from the raw data. The pre-processing and data exploration effort is explained in detail, with a list of assumptions made for parsing and labelling the dataset. The model selection process is explained, specifically emphasizing the benefits of using an ensemble of algorithms with majority voting for binary classification of the channel state. Experimental results are shown, highlighting how an end-to-end communication system can utilize knowledge of the channel fading status to identity fading and take appropriate action. With a laboratory testbed to emulate channel fading, the overall performance is compared to standard adaptive methods without fading knowledge, such as adaptive coding and modulation.

Fading↗