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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2014

TH-C-BRD-04: Beam Modeling and Validation with Triple and Double Gaussian Dose Kernel for Spot Scanning Proton Beams

Purpose: To present the validity of our beam modeling with double and triple Gaussian dose kernels for spot scanning proton beams in Nagoya Proton Therapy Center. This study investigates the conformance between the measurements and calculation results in absolute dose with two types of beam kernel. Methods: A dose kernel is one of the important input data required for the treatment planning software. The dose kernel is the 3D dose distribution of an infinitesimal pencil beam of protons in water and consists of integral depth doses and lateral distributions. We have adopted double and triple Gaussian model as lateral distribution in order to take account of the large angle scattering due to nuclear reaction by fitting simulated inwater lateral dose profile for needle proton beam at various depths. The fitted parameters were interpolated as a function of depth in water and were stored as a separate look-up table for the each beam energy. The process of beam modeling is based on the method of MDACC [X.R.Zhu 2013]. Results: From the comparison results between the absolute doses calculated by double Gaussian model and those measured at the center of SOBP, the difference is increased up to 3.5% in the high-energy region because the large angle scattering due to nuclear reaction is not sufficiently considered at intermediate depths in the double Gaussian model. In case of employing triple Gaussian dose kernels, the measured absolute dose at the center of SOBP agrees with calculation within ±1% regardless of the SOBP width and maximum range. Conclusion: We have demonstrated the beam modeling results of dose distribution employing double and triple Gaussian dose kernel. Treatment planning system with the triple Gaussian dose kernel has been successfully verified and applied to the patient treatment with a spot scanning technique in Nagoya Proton Therapy Center.

07 ISOTOPE AND RADIATION SOURCES↗
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 OSTI2018

Toward precision holography in type IIA with Wilson loops

We study the one-loop effective action of certain classical type IIA string configurations in AdS 4 × CP 3 . These configurations are dual to Wilson loops in the N = 6 U( N ) k × U( N ) –k Chern-Simons theory coupled to matter whose expectation values are known via supersymmetric localization. We compute the one-loop effective actions using two methods: perturbative heat kernel techniques and full ζ-function regularization. We find that the result of the perturbative heat kernel method matches the field theory prediction at the appropriate order while the ζ-function approach seems to lead to a disagreement.

't Hooft and Polyakov loops↗
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↗
DOE OSTI2019

Treatment of near-incompressibility in meshfree and immersed-particle methods

We propose here new projection methods for treating near-incompressibility in small and large deformation elasticity and plasticity within the framework of particle and meshfree methods. Using the $\bar{B}$ and $\bar{F}$ techniques as our point of departure, we develop projection methods for the conforming reproducing kernel method and the immersed-particle or material point-like methods. The methods are based on the projection of the dilatational part of the appropriate measure of deformation onto lower-dimensional approximation spaces, according to the traditional $\bar{B}$ and $\bar{F}$ approaches, but tailored to meshfree and particle methods. The presented numerical examples exhibit reduced stress oscillations and are free of volumetric locking and hourglassing phenomena.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗