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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Neural Network-Enhanced Reproducing Kernel Particle Method for Image-Based Multiphysics Damage Modeling of Energy Storage Materials

Energy storage materials undergo significant stresses during charge/discharge cycling, which makes understanding their reliability and durability fundamental in predicting performance and service life. Strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking, largely along material interfaces and grain boundaries. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), image-based modeling techniques are used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electrochemical-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in capturing crack propagation due to mesh dependency. Additionally, commonly used damage models, such as the continuous damage model and the cohesive zone model, often have steep tradeoffs between discontinuous field accuracy and computational expense. In this work, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1] is leveraged to accurately capture damage and crack propagation throughout the material by learning the location, orientation, and sharpness of discontinuity while allowing for a coarser nodal distribution than that necessary for capturing sharp solution transitions using traditional mesh-based methods. NN-RKPM is used to inform how crack opening and closure in turn affect the coupled chemical equations and material microstructure. Reference: [1] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, https://doi.org/10.1002/nme.7040, 2022.

damage modeling↗
DOE OSTI2021

Simple, low-cost and accurate data-driven geophysical forecasting with learned kernels

Modelling geophysical processes as low-dimensional dynamical systems and regressing their vector field from data is a promising approach for learning emulators of such systems. We show that when the kernel of these emulators is also learned from data (using kernel flows, a variant of cross-validation), then the resulting data-driven models are not only faster than equation-based models but are easier to train than neural networks such as the long short-term memory neural network. In addition, they are also more accurate and predictive than the latter. When trained on geophysical observational data, for example the weekly averaged global sea-surface temperature, considerable gains are also observed by the proposed technique in comparison with classical partial differential equation-based models in terms of forecast computational cost and accuracy. When trained on publicly available re-analysis data for the daily temperature of the North American continent, we observe significant improvements over classical baselines such as climatology and persistence-based forecast techniques. Although our experiments concern specific examples, the proposed approach is general, and our results support the viability of kernel methods (with learned kernels) for interpretable and computationally efficient geophysical forecasting for a large diversity of processes.

58 GEOSCIENCES↗
NASA NTRS1977

On the logarithmic-singularity correction in the kernel function method of subsonic lifting-surface theory

A logarithmic-singularity correction factor is derived for use in kernel function methods associated with Multhopp's subsonic lifting-surface theory. Because of the form of the factor, a relation was formulated between the numbers of chordwise and spanwise control points needed for good accuracy. This formulation is developed and discussed. Numerical results are given to show the improvement of the computation with the new correction factor.

Lan, C. E.↗
DOE OSTI2022

A neural network‐enhanced reproducing kernel particle method for modeling strain localization

Abstract Modeling the localized intensive deformation in a damaged solid requires highly refined discretization for accurate prediction, which significantly increases the computational cost. Although adaptive model refinement can be employed for enhanced effectiveness, it is cumbersome for the traditional mesh‐based methods to perform while modeling the evolving localizations. In this work, neural network‐enhanced reproducing kernel particle method (NN‐RKPM) is proposed, where the location, orientation, and shape of the solution transition near a localization is automatically captured by the NN approximation via a block‐level neural network (NN) optimization. The weights and biases in the blocked parameterization network control the location and orientation of the localization. The designed basic four‐kernel NN block is capable of capturing a triple junction or a quadruple junction topological pattern, while more complicated localization topological patters are captured by the superposition of multiple four‐kernel NN blocks. The standard RK approximation is then utilized to approximate the smooth part of the solution, which permits a much coarser discretization than the high‐resolution discretization needed to capture sharp solution transitions with the conventional methods. A regularization of the NN approximation is additionally introduced for discretization‐independent material responses. The effectiveness of the proposed NN‐RKPM is verified by a series of numerical verifications.

Baek, Jonghyuk↗
DOE OSTI2020

Connecting quasinormal modes and heat kernels in 1-loop determinants

We connect two different approaches for calculating functional determinants on quotients of hyperbolic spacetime: the heat kernel method and the quasinormal mode method. For the example of a rotating BTZ background, we show how the image sum in the heat kernel method builds up the logarithms in the quasinormal mode method, while the thermal sum in the quasinormal mode method builds up the integrand of the heat kernel. More formally, we demonstrate how the heat kernel and quasinormal mode methods are linked via the Selberg zeta function. We show that a 1-loop partition function computed using the heat kernel method may be cast as a Selberg zeta function whose zeros encode quasinormal modes. We discuss how our work may be used to predict quasinormal modes on more complicated spacetimes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Kernel polynomial method for linear spin wave theory

Calculating dynamical spin correlations is essential for matching model magnetic exchange Hamiltonians to momentum-resolved spectroscopic measurements. A major numerical bottleneck is the diagonalization of the dynamical matrix, especially in systems with large magnetic unit cells, such as those with incommensurate magnetic structures or quenched disorder. In this paper, we demonstrate an efficient scheme based on the kernel polynomial method for calculating dynamical correlations of relevance to inelastic neutron scattering experiments. This method reduces the scaling of numerical cost from cubic to linear in the magnetic unit cell size.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

A kernel function method for computing steady and oscillatory supersonic aerodynamics with interference.

The method presented uses a collocation technique with the nonplanar kernel function to solve supersonic lifting surface problems with and without interference. A set of pressure functions are developed based on conical flow theory solutions which account for discontinuities in the supersonic pressure distributions. These functions permit faster solution convergence than is possible with conventional supersonic pressure functions. An improper integral of a 3/2 power singularity along the Mach hyperbola of the nonplanar supersonic kernel function is described and treated. The method is compared with other theories and experiment for a variety of cases.

Cunningham, A. M., Jr.↗
NASA NTRS1989

Dicke narrowing of the polarized Stokes-Raman Q branch of the v = 0-1 transition of D2 in He

Results are presented from calculations of several Stokes-Raman Q branch line shapes of the v = 0-1 transition of D2 in He in the low pressure regime where Dicke narrowing is observed. Consideration is given to five different approximations: a form of the generalized Hess theory (Monchick and Hunter, 1987), two high pressure asymptotes of Hess's method, the moment method of Corey and McCourt (1984), and a collision kernel method. It is found that the generalized Hess and the collision kernel methods have the best agreement with experiments.

Blackmore, Robert↗
DOE OSTI2022

Importance of kernel bandwidth in quantum machine learning

Quantum kernel methods are considered a promising avenue for applying quantum computers to machine learning problems. Identifying hyperparameters controlling the inductive bias of quantum machine learning models is expected to be crucial given the central role hyperparameters play in determining the performance of classical machine learning methods. In this work we introduce the hyperparameter controlling the bandwidth of a quantum kernel and show that it controls the expressivity of the resulting model. We use extensive numerical experiments with multiple quantum kernels and classical data sets to show consistent change in the model behavior from underfitting (bandwidth too large) to overfitting (bandwidth too small), with optimal generalization in between. We draw a connection between the bandwidth of classical and quantum kernels and show analogous behavior in both cases. Furthermore, we show that optimizing the bandwidth can help mitigate the exponential decay of kernel values with qubit count, which is the cause behind recent observations that the performance of quantum kernel methods decreases with qubit count. Here, we reproduce these negative results and show that if the kernel bandwidth is optimized, the performance instead improves with growing qubit count and becomes competitive with the best classical methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1974

Oscillatory supersonic kernel function method for interfering surfaces

In the method presented in this paper, a collocation technique is used with the nonplanar supersonic kernel function to solve multiple lifting surface problems with interference in steady or oscillatory flow. The pressure functions used are based on conical flow theory solutions and provide faster solution convergence than is possible with conventional functions. In the application of the nonplanar supersonic kernel function, an improper integral of a 3/2 power singularity along the Mach hyperbola is described and treated. The method is compared with other theories and experiment for two wing-tail configurations in steady and oscillatory flow.

Cunningham, A. M., Jr.↗
DOE OSTI2022

Cross Inference of Throughput Profiles Using Micro Kernel Network Method

Dedicated network connections are being increasingly deployed in cloud, centralized and edge computing and data infrastructures, whose throughput profiles are critical indicators of the underlying data transfer performance. Due to the cost and disruptions to physical infrastructures, network emulators, such as Mininet, are often used to generate measurements needed to estimate throughput profiles, typically expressed as a function of the connection round trip time. The profiles estimated using measurements from such emulated networks are usually inaccurate for high bandwidth and high latency connections, since they do not accurately reflect the critical network transport dynamics mainly due to computing and memory constraints of the host. We present a machine learning (ML) method to estimate the throughput profiles using emulation measurements to closely match the testbed and production network profiles. In particular, we propose a micro Kernel Network (mKN) that provides baseline throughput measurements on the host running Mininet emulations, which are used to learn a regression map that converts them to the corresponding testbed measurement estimates. Once initially learned, this map is applied to measurements from subsequent network emulations on the same host. We present experimental measurements to illustrate this approach, and derive generalization equations for the proposed mKN-ML method. Using a four-site scenario emulation, we show the effectiveness of this method in providing accurate concave throughput profiles from inaccurate convex or non-smooth ones indicated by Mininet emulation.

Rao, Nageswara↗
DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

Inversion of the Solar Rotation Rate Versus Depth and Latitude

Three differential inversion techniques were used to compute the internal solar rotation rate from several sets of n-averaged frequency splittings. An iterative variation of the spectral expansion method; the optimal averaging kernel method; and a piecewise constant constrained least square method were used to invert the data. Each computation was carried out independently. While they present similar trends, each of the solutions differs in detail. A consistent feature in all the inversions is the disappearance of differential rotation below the base of the convection zone. Also, a strong differential signature in the deeper part of the convection zone is present in most of the solutions. A slow decrease of the rotation rate with depth for the equatorial and midlatitude curves is significant in the spectral expansion and the least square results but only marginally apparent in the averaging kernel results.

Korzennik, Sylvain G.↗
NASA NTRS1974

An oscillatory kernel function method for lifting surfaces in mixed transonic flow

A study was conducted on the use of combined subsonic and supersonic linear theory to obtain economical and yet realistic solutions to unsteady transonic flow problems. With some modification, existing linear theory methods were combined into a single computer program. The method was applied to problems for which measured steady Mach number distributions and unsteady pressure distributions were available. By comparing theory and experiment, the transonic method showed a significant improvement over uniform flow methods. The results also indicated that more exact local Mach number effects and normal shock boundary conditions on the perturbation potential were needed. The validity of these improvements was demonstrated by application to steady flow.

Cunningham, A. M., Jr.↗
NASA NTRS2004

Virtual Sensors: Using Data Mining to Efficiently Estimate Spectra

Detecting clouds within a satellite image is essential for retrieving surface geophysical parameters, such as albedo and temperature, from optical and thermal imagery because the retrieval methods tend to be valid for clear skies only. Thus, routine satellite data processing requires reliable automated cloud detection algorithms that are applicable to many surface types. Unfortunately, cloud detection over snow and ice is difficult due to the lack of spectral contrast between clouds and snow. Snow and clouds are both highly reflective in the visible wavelen,ats and often show little contrast in the thermal Infrared. However, at 1.6 microns, the spectral signatures of snow and clouds differ enough to allow improved snow/ice/cloud discrimination. The recent Terra and Aqua Moderate Resolution Imaging Spectro-Radiometer (MODIS) sensors have a channel (channel 6) at 1.6 microns. Presently the most comprehensive, long-term information on surface albedo and temperature over snow- and ice-covered surfaces comes from the Advanced Very High Resolution Radiometer ( AVHRR) sensor that has been providing imagery since July 1981. The earlier AVHRR sensors (e.g. AVHRR/2) did not however have a channel designed for discriminating clouds from snow, such as the 1.6 micron channel available on the more recent AVHRR/3 or the MODIS sensors. In the absence of the 1.6 micron channel, the AVHRR Polar Pathfinder (APP) product performs cloud detection using a combination of time-series analysis and multispectral threshold tests based on the satellite's measuring channels to produce a cloud mask. The method has been found to work reasonably well over sea ice, but not so well over the ice sheets. Thus, improving the cloud mask in the APP dataset would be extremely helpful toward increasing the accuracy of the albedo and temperature retrievals, as well as extending the time-series of albedo and temperature retrievals from the more recent sensors to the historical ones. In this work, we use data mining methods to construct a model of MODIS channel 6 as a function of other channels that are common to both MODIS and AVHRR. The idea is to use the model to generate the equivalent of MODIS channel 6 for AVHRR as a function of the AVHRR equivalents to MODIS channels. We call this a Virtual Sensor because it predicts unmeasured spectra. The goal is to use this virtual channel 6. to yield a cloud mask superior to what is currently used in APP . Our results show that several data mining methods such as multilayer perceptrons (MLPs), ensemble methods (e.g., bagging), and kernel methods (e.g., support vector machines) generate channel 6 for unseen MODIS images with high accuracy. Because the true channel 6 is not available for AVHRR images, we qualitatively assess the virtual channel 6 for several AVHRR images.

Srivastava, Ashok↗