Search NASASearch

SEARCH · Search NASA

Results for “kernel methods”

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 217 records · Page 12

A higher order panel method for general analysis and design applications in subsonic flow

A higher-order panel method is described for numerical solution of boundary-value problems relating to steady inviscid irrotational incompressible subsonic fluid flow in a domain. Both Neumann and Dirichlet boundary conditions are treated; two types of auxiliary conditions are used to remove the degrees of freedom that arise from specifying only the derivative of the perturbation velocity potential. Four general network types and two expansions of the induced potential kernel are employed in the numerical solution. Some results are presented which illustrate the modeling options and numerical characteristics of the method.

Johnson, F. T.

Emulation With Uncertainty Quantification of Regional Sea‐Level Change Caused by the Antarctic Ice Sheet

Abstract Projecting regional sea‐level change under various climate‐change scenarios typically involves running forward simulations of the Earth's gravitational, rotational and deformational (GRD) response to ice‐mass change, which requires substantial computational cost if applied to probabilistic frameworks requiring thousands to millions of samples. Here we build emulators of regional sea‐level change at 27 coastal locations, due to the GRD effects associated with future Antarctic Ice Sheet mass change over the 21st century. The emulators are evaluated against a numerical sea‐level model applied to an ensemble of ice‐sheet model simulations of the Antarctic Ice Sheet through 2100. We build a physics‐based emulator using a recent sensitivity kernel approach and compare it to machine learning based emulators (neural network and conditional variational autoencoder methods). In order to quantify uncertainty, we derive well‐calibrated prediction intervals for regional sea‐level change via split‐conformal inference and linear regression, and show that Monte Carlo dropout does not yield well‐calibrated uncertainties in this instance. We also demonstrate substantial gains in computational efficiency using both the physics‐based emulator and neural networks in comparison to the numerical model for the complete regional sea‐level solution. Overall, we find the physics‐based emulator modestly outperforms the machine learning emulators for this problem.

58 GEOSCIENCES

Improved Weld Residual Stress Modeling System in BlackBear

This report presents enhancements to the MOOSE-based BlackBear application aimed at improving its capability to simulate welding and other thermo-mechanical manufacturing processes. Two primary avenues of improvement are pursued. First, to enhance user accessibility, we introduce a centralized default block restriction mechanism that ensures coverage checks are performed within user-specified default blocks. This default setting is applied consistently to all block-describable objects, such as variables, kernels, and more. In addition, we develop a modular action for moving heat source simulations, which integrates path file parsing, subdomain modification, and heat source kernel enforcement into a single, streamlined configuration. Second, to improve solver robustness, we implement an alternative method for assigning initial conditions to the updated active domain during the simulation, thereby enhancing convergence behavior. To validate the framework, we design and conduct several benchmark simulations, including heat conduction with progressive material addition, linear elasticity with time-dependent material deposition, and viscoplasticity model with isotropic hardening under similar conditions. Finally, we demonstrate the effectiveness of the proposed framework through large-scale thermo-mechanical welding simulations in both two and three dimensions.

42 ENGINEERING

Stability, accuracy, and efficiency of some underintegrated methods in finite element computations

In an attempt to increase computational efficiency in the numerical solution of highly nonlinear problems in solid and fluid mechanics, underintegrated finite element methods have been employed by many analysts. Underintegration refers to the use of a rule of an order lower than that required to integrate polynomial integrands exactly. The main drawback of this technique is related to the production of rank-deficient stiffness matrices, or equivalently an expanded kernel of the governing linear momentum operators. Such a development can introduce numerical instabilities. In order to overcome this difficulty, artificial stiffness or viscosity methods, or other stabilization methods have been proposed. One approach involves the elimination of spurious modes in a postprocessing operation. The present study is concerned with this a posteriori elimination method, taking into account the results which can be expected from it, and some of its possible extensions.

Jacquotte, O.-P.

A new method for diagnosing effective radiative forcing from aerosol–cloud interactions in climate models

Aerosol–cloud interactions (ACIs) are a leading source of uncertainty in estimates of the historical effective radiative forcing (ERF). One reason for this uncertainty is the difficulty in estimating the ERF from aerosol–cloud interactions (ERFaci) in climate models, which typically requires multiple calls to the radiation code. Most commonly used methods also cannot disentangle the contributions from different processes to ERFaci. Here, we develop a new, computationally efficient method for estimating the shortwave (SW) ERFaci from liquid clouds using histograms of monthly averaged cloud fraction partitioned by cloud droplet effective radius (r e ) and liquid water path (LWP). Multiplying the histograms with SW cloud radiative kernels gives the total SW ERFaci from liquid clouds, which can be decomposed into contributions from the Twomey effect, LWP adjustments, and cloud fraction (CF) adjustments. We test the method with data from five CMIP6-era models, using the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite instrument simulator to generate the histograms. Our method gives similar total SW ERFaci estimates to other established methods in regions of prevalent liquid cloud and indicates that the Twomey effect, LWP adjustments, and CF adjustments have contributed -0.34 ± 0.23, -0.22 ± 0.13, and -0.09 ± 0.11 W m -2 , respectively, to the effective radiative forcing of the climate since 1850 in the ensemble mean (95 % confidence). These results demonstrate that widespread adoption of a MODIS r e –LWP joint histogram diagnostic would allow the SW ERFaci and its components to be quickly and accurately diagnosed from climate model outputs, a crucial step for reducing uncertainty in the historical ERF.

54 ENVIRONMENTAL SCIENCES

On comparing helioseismic two-dimensional inversion methods

We consider inversion techniques for investigating the structure and dynamics of the solar interior as functions of radius and latitude. In particular, we look at the problem of inferring the radial and latitudinal dependence of the Sun's internal rotation, using a fully two-dimensional least-squares inversion algorithm. Concepts such as averaging kernels, measures of resolution, and trade-off curves, which have previously been used in the one-dimensional case, are generalized to facilitate a comparison of two-dimensional methods. We investigate the weighting given to different modes and discuss the implications of this for observational strategies. As an illustration we use a mode set whose properties are similar to those expected for data from the GONG network.

Schou, J.

Parallel homotopy curve tracking on a hypercube

An investigation is conducted to find good parallel algorithms for solving systems of nonlinear equations using probability-one homotopy methods. Particular attention is paid to algorithms for the hypercube. Methods for one of the most computationally expensive steps of the homotopy approach, the computation of the kernel of the Jacobian matrix of the homotopy map, are studied. General nonlinear systems of equations with small and dense Jacobian matrices are considered, however, polynomial systems are not, since their structure leads to different strategies for parallelism. The mathematics behind the homotopy algorithm is summarized and the use of orthogonal factorizations is discussed. Parallel algorithms for orthogonal factorizations and triangular system solving are described. Computational results are presented and discussed.

Chakraborty, A.

Radiative Heat Transfer in Finite Cylindrical Enclosures with Nonhomogeneous Participating Media

Results of a numerical solution for radiative heat transfer in homogeneous and nonhomogeneous participating media are presented. The geometry of interest is a finite axisymmetric cylindrical enclosure. The integral formulation for radiative transport is solved by the YIX method. A three-dimensional solution scheme is applied to two-dimensional axisymmetric geometry to simplify kernel calculations and to avoid difficulties associated with treating boundary conditions. As part of the effort to improve modeling capabilities for turbulent jet diffusion flames, predicted distributions for flame temperature and soot volume fraction are used to calculate radiative heat transfer from soot particles in such flames. It is shown that the nonhomogeneity of radiative property has very significant effects. The peak value of the divergence of radiative heat flux could be underestimated by 2 factor of 7 if a mean homogeneous radiative property is used. Since recent studies have shown that scattering by soot agglomerates is significant in flames, the effect of magnitude of scattering is also investigated and found to be nonnegligible.

Hsu, Pei-Feng

Measurement of Flaw Size From Thermographic Data

Simple methods for reducing the pulsed thermographic responses of delaminations tend to overestimate the size of the delamination, since the heat diffuses in the plane parallel to the surface. The result is a temperature profile over the delamination which is larger than the delamination size. A variational approach is presented for reducing the thermographic data to produce an estimated size for a flaw that is much closer to the true size of the delamination. The method is based on an estimate for the thermal response that is a convolution of a Gaussian kernel with the shape of the flaw. The size is determined from both the temporal and spatial thermal response of the exterior surface above the delamination and constraints on the length of the contour surrounding the delamination. Examples of the application of the technique to simulation and experimental data are presented to investigate the limitations of the technique.

Winfree, William P.

Spectrally Stabilized Interface Capturing Formulation and Implementation in Nek5000/NekRS

This report documents the formulation of a novel level-set method for incompressible two-phase flows in the continuous Galerkin (CG) high order spectral element framework. The overall method hinges on a novel implementation of the spectral vanishing viscosity (SVV) operator for the stabilization of linear/non-linear hyperbolic problems. The multidimensional SVV convolution kernels, which in essence, have a similar effect as a high pass filter applied to the derivatives, are formulated by exploiting the tensor product form, analogous to the construction of the usual stiffness matrix system. The resulting kernels are directionally decoupled and ensure a linear, symmetric positive definite, elliptic matrix operator. The SVV formulation is demonstrated to provide a robust stabilizing mechanism through challenging linear and non-linear hyperbolic problems, including problems pertinent to the level-set formulation. The two-phase framework conceptualized herein is based on the conservative level-set (CLS) method which represents the interface between the fluids by the 0.5 iso-contour of the smoothed Heaviside function. The CLS method is augmented with a preconditioning procedure for interface normals using the signed distance function which precludes the manifestation of spurious oscillations in the vicinty of the interface. Further, the existing mixed explicit-implicit approach for the solution of Navier-Stokes equations in Nek5000, as described in Tomboulides et al, is augmented with a pressure coefficient splitting approach for the Poisson equation, which greatly accelerated the convergence of pressure solver for two-phase systems with large density ratio. The robustness and accuracy of the overall two-phase method is demonstrated through canonical challenging problems involving high density and viscosity ratios, with and without surface tension. The two-phase formulation is wholly implemented in Nek5000 and the SVV stabilization method is implemented in NekRS, which is the essential precursor to the two-phase framework, undergoing active development.

97 MATHEMATICS AND COMPUTING

Iterative Discrete Ordinates Solution of the Equation for the Surface-Reflected Radiance

This paper presents a new method of numerical solution of the integral equation for the radiance reflected from an anisotropic surface. The equation relates the radiance at the surface level with BRDF and solutions of the standard radiative transfer problems for a slab with no reflection on its surfaces. It is also shown that the kernel of the equation satisfies the condition of the existence of a unique solution and the convergence of the successive approximations to that solution. The developed method features two basic steps: discretization on a 2D quadrature, and solving the resulting system of algebraic equations with successive over-relaxation method based on the Gauss-Seidel iterative process. Presented numerical examples show good coincidence between the surface-reflected radiance obtained with DISORT and the proposed method. Analysis of contributions of the direct and diffuse (but not yet reflected) parts of the downward radiance to the total solution is performed. Together, they represent a very good initial guess for the iterative process. This fact ensures fast convergence. The numerical evidence is given that the fastest convergence occurs with the relaxation parameter of 1 (no relaxation). An integral equation for BRDF is derived as inversion of the original equation. The potential of this new equation for BRDF retrievals is analyzed. The approach is found not viable as the BRDF equation appears to be an ill-posed problem, and it requires knowledge the surface-reflected radiance on the entire domain of both Sun and viewing zenith angles.

Alexander Radkevich

Spatial Signatures of Electron Correlation in Least-Squares Tensor Hypercontraction

Least Squares Tensor Hypercontraction (LS-THC) has received some attention in recent years as an approach to reduce the significant computational costs of wavefunc- tion based methods in quantum chemistry. However, previous work has demonstrated that the LS-THC factorization performs disproportionately worse in the description of wavefunction components (e.g. cluster amplitudes T 2 ) than Hamiltonian compo- nents (e.g. electron repulsion integrals (pq|rs)). This work develops novel theoretical methods to study the source of these errors in the context of the real-space T 2 kernel, and reports, for the first time, the existence of a “correlation feature” in the errors of the LS-THC representation of the “exchange-like” correlation energy EX and T 2 that is remarkably consistent across ten molecular species, three correlated wavefunctions, and four basis sets. This correlation feature portends the existence of a “pair-point kernel” missing in the usual LS-THC representation of the wavefunction, which critically depends upon pairs of grid points situated close to atoms and with inter-pair distances between one and two Bohr radii. These findings point the way for future LS-THC developments to address these shortcomings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Simulation of electron Bernstein waves using FullWave with a 2D non-local hot plasma model

Hot plasma wave simulation capability is expanded in the FullWave code by updating the hybrid iterative solver in the code with a semi-implicit time stepping method. The new approach is used to simulate Electron Bernstein Wave (EBW) heating in over-dense spherical tokamak plasmas. The code’s hybrid iterative solver circumvents the prohibitive memory cost of direct methods by combining a time evolution of Maxwell’s equations with frequency-domain relaxation, while the conductivity kernel, calculated via 3D particle tracking, captures the essential non-local wave–particle interactions. One-dimensional EBW simulations verify the algorithm’s accuracy by demonstrating mode conversion from X-mode wave to EBW at the upper hybrid resonance and a strong cyclotron damping near the plasma core. Two-dimensional simulation reproduces the predicted short EBW wavelength and quantitatively matches the hot-plasma dispersion relation. This study demonstrates the fidelity of the hybrid solver for the electron cyclotron frequency range.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Atwood effects on nonlocality of the scalar transport closure in Rayleigh-Taylor mixing

The importance of nonlocality is assessed in modeling mean scalar transport for turbulent Rayleigh-Taylor (RT) mixing at different Atwood numbers. Building on the two-dimensional incompressible work of Lavacot et al. [J. Fluid Mech. 985, A47 (2024)], the present work extends the macroscopic forcing method to variable density problems in three-dimensional space to measure moments of the generalized eddy diffusivity kernel in RT mixing for increasing Atwood numbers (𝐴 = 0.05, 0.3, 0.5, 0.8). It is found that as 𝐴 increases, (1) the eddy diffusivity moments become asymmetric and (2) the higher-order eddy diffusivity moments become larger relative to the leading-order diffusivity, indicating that nonlocality becomes more important at higher 𝐴. There is a particularly strong temporal nonlocality at higher 𝐴, suggesting stronger history effects. In conclusion, the implications of these findings for closure modeling for finite-Atwood RT are discussed.

general physics

Numerical eigen-spectrum slicing, accurate orthogonal eigen-basis, and mixed-precision eigenvalue refinement using OpenMP data-dependent tasks and accelerator offload

Performing a variety of numerical computations efficiently and, at the same time, in a portable fashion requires both an overarching design followed by a number of implementation strategies. All of these are exemplified below as we present transitioning the PLASMA numerical library from relying on dependence-driven large tasks to achieving utilization of fine grain tasking and offload to hardware accelerators while keeping its core dependence sets: OpenMP source code pragmas and runtime for most system-level functionality and basic low-level numerical kernels provided directly by hardware vendors or open source projects with vendor contributions. We also present new algorithmic methods and their efficient parallel implementations including fine grained tasking for eigen-spectrum slicing and offload for mixed-precision eigenvalue refinement. We provide performance, scaling, and numerical results showing sizable gains over the available solutions from either the open source and vendor-provided packages.

Luszczek, Piotr

Retrieval of aerosol size distribution moments from multiwavelength particulate extinction measurements

Two methods for inferring aerosol size distribution moments from multiwavelength particulate extinction measurements are studied. The methods are an eigenvalue technique that approximates an appropriate moment-weighting function by a linear combination of kernel functions and a conversion ratio approach that uses the ratio of the particulate extinction measurements at two wavelengths to choose a model moment-to-extinction conversion ratio. The techniques are applied to infer the third moment, or volume, of the aerosol size distribution from actual particulate extinction measurements taken as part of the Stratospheric Aerosol and Gas Experiment II during a correlative measurement experiment in Brazil in April 1985.

Livingston, John M.

Enzymic synthesis of indole-3-acetyl-1-O-beta-d-glucose. I. Partial purification and characterization of the enzyme from Zea mays

The first enzyme-catalyzed reaction leading from indole-3-acetic acid (IAA) to the myo-inositol esters of IAA is the synthesis of indole-3-acetyl-1-O-beta-D-glucose from uridine-5'-diphosphoglucose (UDPG) and IAA. The reaction is catalyzed by the enzyme, UDPG-indol-3-ylacetyl glucosyl transferase (IAA-glucose-synthase). This work reports methods for the assay of the enzyme and for the extraction and partial purification of the enzyme from kernels of Zea mays sweet corn. The enzyme has an apparent molecular weight of 46,500 an isoelectric point of 5.5, and its pH optimum lies between 7.3 and 7.6. The enzyme is stable to storage at zero degrees but loses activity during column chromatographic procedures which can be restored only fractionally by addition of column eluates. The data suggest either multiple unknown cofactors or conformational changes leading to activity loss.

NASA Discipline Number 40-10

MOOSE ProbML: Parallelizable Probabilistic Machine Learning and Uncertainty Quantification Capabilities

The Multiphysics Object Oriented Simulation Environment (MOOSE) is a widely used open- source finite element software for performing multiphysics multiscale simulations in a massively parallel fashion. Recently, the computational team at Idaho National Laboratory (INL) has implemented Probabilistic Machine Learning (ProbML) capabilities in MOOSE—in a parallelized fashion—and enable active learning with large-scale computational models for tasks such as surrogate model development, scale bridging, forward/inverse uncertainty quantification (UQ), Bayesian optimization, etc. This presentation summarizes these developments in MOOSE along with demonstrations on several real applications relevant to nuclear energy. At the fundamental level, samplers like Monte Carlo/Latin Hypercube, variance reduction, parallelized Markov Chain Monte Carlo (MCMC) support uncertainty propagation in both forward and inverse settings. These samplers can be integrated with the Gaussian processes (GP) suite in MOOSE, which offer several variants like scalar GPs, multi-output GPs, and deep GPs, to enable active learning. These GPs can be tuned using gradient-based optimization methods like Adam and its variants or gradient-free methods like the elliptical slice sampler (a variant of MCMC adept under Gaussian settings) for more complex covariance kernels or likelihoods whose gradient computations can be cumbersome. A variety of batch acquisition functions permit parallelized evaluation of the computational model and support different learning objectives with high efficiency like Bayesian inference, global surrogate development, optimization, etc. Furthermore, libtorch integration supports training, evaluation, and re-training of neural networks and other complex machine learning models in active learning settings. The impacts of these developments are shown on several real applications: (1) nuclear fuel inverse UQ and model inadequacy assessment using the Kennedy O’Hagan framework; (2) uncertainty aware surrogate modeling for additive manufacturing to predict field quantities; (3) nuclear reactor rare events analysis; and (4) complex fluid flow prediction using a global surrogate with quantified prediction uncertainty. Finally, the outlook of MOOSE ProbML is discussed for both outer-loop and inner-loop computations in the broad view to accelerate fuels and materials qualification, address gaps in knowledge and data, and assess new reactor/fuel systems.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS