The Top‐of‐Atmosphere, Surface and Atmospheric Cloud Radiative Kernels Based on ISCCP‐H Datasets: Method and Evaluation
Explore the source record for details and available documents.
Yuanchong Zhang↗
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.
New Method for Analysis of Individual UCO Kernel Phase Fractions
Explore the source record for details and available documents.
Helmreich, Grant↗
A simple and fast method for computing the relativistic Compton Scattering Kernel for radiative transfer
The Klein-Nishina differential cross section averaged over a relativistic Maxwellian electron distribution is analytically reduced to a single integral, which can then be rapidly evaluated in a variety of ways. A particularly fast method for numerically computing this single integral is presented. This is, to the authors' knowledge, the first correct computation of the Compton scattering kernel.
Kershaw, David S.↗
A meshless stochastic method for Poisson–Nernst–Planck equations
A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson–Nernst–Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift–diffusion process with time- and space-varying drift. We leverage Green’s functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method’s convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.
Chemistry↗
Advanced stationary and nonstationary kernel designs for domain-aware Gaussian processes
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The mathematical methods we discuss in this paper are an extension of the Gaussian-process framework. We are proposing advanced kernel designs that only allow for functions with certain desirable characteristics to be elements of the reproducing kernel Hilbert space (RKHS) that underlies all kernel methods and serves as the sample space for Gaussian process regression. These desirable characteristics reflect the underlying physics; two obvious examples are symmetry and periodicity constraints. In addition, non-stationary kernel designs can be defined in the same framework to yield flexible multi-task Gaussian processes. We will show the impact of advanced kernel designs on Gaussian processes using several synthetic and two scientific data sets. The results of our research show that including domain knowledge, communicated through advanced kernel designs, has a significant impact on the accuracy and relevance of the function approximation.
97 MATHEMATICS AND COMPUTING↗
SU-E-CAMPUS-I-06: Y90 PET/CT for the Instantaneous Determination of Both Target and Non-Target Absorbed Doses Following Hepatic Radioembolization
Purpose The process of converting Yttrium-90 (Y90) PET/CT images into 3D absorbed dose maps will be explained. The simple methods presented will allow the medical physicst to analyze Y90 PET images following radioembolization and determine the absorbed dose to tumor, normal liver parenchyma and other areas of interest, without application of Monte-Carlo radiation transport or dose-point-kernel (DPK) convolution. Methods Absorbed dose can be computed from Y90 PET/CT images based on the premise that radioembolization is a permanent implant with a constant relative activity distribution after infusion. Many Y90 PET/CT publications have used DPK convolution to obtain 3D absorbed dose maps. However, this method requires specialized software limiting clinical utility. The Local Deposition method, an alternative to DPK convolution, can be used to obtain absorbed dose and requires no additional computer processing. Pixel values from regions of interest drawn on Y90 PET/CT images can be converted to absorbed dose (Gy) by multiplication with a scalar constant. Results There is evidence that suggests the Local Deposition method may actually be more accurate than DPK convolution and it has been successfully used in a recent Y90 PET/CT publication. We have analytically compared dose-volume-histograms (DVH) for phantom hot-spheres to determine the difference between the DPK and Local Deposition methods, as a function of PET scanner point-spread-function for Y90. We have found that for PET/CT systems with a FWHM greater than 3.0 mm when imaging Y90, the Local Deposition Method provides a more accurate representation of DVH, regardless of target size than DPK convolution. Conclusion Using the Local Deposition Method, post-radioembolization Y90 PET/CT images can be transformed into 3D absorbed dose maps of the liver. An interventional radiologist or a Medical Physicist can perform this transformation in a clinical setting, allowing for rapid prediction of treatment efficacy by comparison to published tumoricidal thresholds.
60 APPLIED LIFE SCIENCES↗
Self-consistent Kohn-Sham method based on the adiabatic-connection fluctuation-dissipation theorem and the exact-exchange kernel
A self-consistent Kohn-Sham method based on the adiabatic-connection fluctuation-dissipation (ACFD) theorem, employing the frequency-dependent exact exchange kernel f{sub x} is presented. The resulting SC-exact-exchange-only (EXX)-ACFD method leads to even more accurate correlation potentials than those obtained within the direct random phase approximation (dRPA). In contrast to dRPA methods, not only the Coulomb kernel but also the exact exchange kernel f{sub x} is taken into account in the EXX-ACFD correlation which results in a method that, unlike dRPA methods, is free of self-correlations, i.e., a method that treats exactly all one-electron systems, like, e.g., the hydrogen atom. The self-consistent evaluation of EXX-ACFD total energies improves the accuracy compared to EXX-ACFD total energies evaluated non-self-consistently with EXX or dRPA orbitals and eigenvalues. Reaction energies of a set of small molecules, for which highly accurate experimental reference data are available, are calculated and compared to quantum chemistry methods like Møller-Plesset perturbation theory of second order (MP2) or coupled cluster methods [CCSD, coupled cluster singles, doubles, and perturbative triples (CCSD(T))]. Moreover, we compare our methods to other ACFD variants like dRPA combined with perturbative corrections such as the second order screened exchange corrections or a renormalized singles correction. Similarly, the performance of our EXX-ACFD methods is investigated for the non-covalently bonded dimers of the S22 reference set and for potential energy curves of noble gas, water, and benzene dimers. The computational effort of the SC-EXX-ACFD method exhibits the same scaling of N{sup 5} with respect to the system size N as the non-self-consistent evaluation of only the EXX-ACFD correlation energy; however, the prefactor increases significantly. Reaction energies from the SC-EXX-ACFD method deviate quite little from EXX-ACFD energies obtained non-self-consistently with dRPA orbitals and eigenvalues, and the deviation reduces even further if the Coulomb kernel is scaled by a factor of 0.75 in the dRPA to reduce self-correlations in the dRPA correlation potential. For larger systems, such a non-self-consistent EXX-ACFD method is a competitive alternative to high-level wave-function-based methods, yielding higher accuracy than MP2 and CCSD methods while exhibiting a better scaling of the computational effort than CCSD or CCSD(T) methods. Moreover, EXX-ACFD methods were shown to be applicable in situation characterized by static correlation.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Technical Note: Dose gradients and prescription isodose in orthovoltage stereotactic radiosurgery
Purpose: The purpose of this work is to examine the trade-off between prescription isodose and dose gradients in orthovoltage stereotactic radiosurgery. Methods: Point energy deposition kernels (EDKs) describing photon and electron transport were calculated using Monte Carlo methods. EDKs were generated from 10 to 250 keV, in 10 keV increments. The EDKs were converted to pencil beam kernels and used to calculate dose profiles through isocenter from a 4π isotropic delivery from all angles of circularly collimated beams. Monoenergetic beams and an orthovoltage polyenergetic spectrum were analyzed. The dose gradient index (DGI) is the ratio of the 50% prescription isodose volume to the 100% prescription isodose volume and represents a metric by which dose gradients in stereotactic radiosurgery (SRS) may be evaluated. Results: Using the 4π dose profiles calculated using pencil beam kernels, the relationship between DGI and prescription isodose was examined for circular cones ranging from 4 to 18 mm in diameter and monoenergetic photon beams with energies ranging from 20 to 250 keV. Values were found to exist for prescription isodose that optimize DGI. Conclusions: The relationship between DGI and prescription isodose was found to be dependent on both field size and energy. Examining this trade-off is an important consideration for designing optimal SRS systems.
60 APPLIED LIFE SCIENCES↗
Measurement of the muon anomalous precession frequency in runs 4, 5, and 6 of the muon ${g}-2$ Experiment at Fermilab
The Fermilab E989 Muon $g-2$ experiment measures the muon's anomalous magnetic moment to a precision of 127 parts per billion, as reported in June 2025. The value is proportional to the difference between the muon's cyclotron frequency and the spin precession frequency in the presence of a uniform magnetic field, for muons contained within the $g-2$ storage ring. Spin precession frequency is extracted from the time distribution of the muon's decay positrons recorded by 24 electromagnetic calorimeters positioned around the inner circumference of the storage ring. The anomalous precession frequency is one of the primary experimental inputs necessary to estimate the anomalous magnetic moment, the other being the measurement of the magnetic field. This dissertation details the anomalous precession frequency extraction, including reconstruction, time-distribution fitting, and treatment of systematic uncertainties for the final three data-collection runs: Run-4, Run-5, and Run-6. This data represents a fourfold increase in statistics over the previous analysis release, halving the statistical uncertainty. The residual slow term from previous analyses is now well understood and documented in a systematic treatment. As of the writing of this dissertation, the theoretical prediction for the SM estimate of the muon's anomalous magnetic moment is under debate, with two competing prediction methods, so a definitive comparison with theory is not available. The results submitted for experimental release use the kernel-ratio asymmetry method, contributing 115 parts per billion to the statistical uncertainty and 34 parts per billion to the systematic uncertainty. When combined with the previous analyses in earlier data runs, this thereby improves the measurement beyond the experimental goal and sets the world's most precise measurement of the muon's anomalous magnetic moment.
Israel, Scott Nathan [Boston U.]↗
Measurement of the muon anomalous precession frequency in runs 4, 5, and 6 of the muon ${g}-2$ Experiment at Fermilab
The Fermilab E989 Muon $g-2$ experiment measures the muon's anomalous magnetic moment to a precision of 127 parts per billion, as reported in June 2025. The value is proportional to the difference between the muon's cyclotron frequency and the spin precession frequency in the presence of a uniform magnetic field, for muons contained within the $g-2$ storage ring. Spin precession frequency is extracted from the time distribution of the muon's decay positrons recorded by 24 electromagnetic calorimeters positioned around the inner circumference of the storage ring. The anomalous precession frequency is one of the primary experimental inputs necessary to estimate the anomalous magnetic moment, the other being the measurement of the magnetic field. This dissertation details the anomalous precession frequency extraction, including reconstruction, time-distribution fitting, and treatment of systematic uncertainties for the final three data-collection runs: Run-4, Run-5, and Run-6. This data represents a fourfold increase in statistics over the previous analysis release, halving the statistical uncertainty. The residual slow term from previous analyses is now well understood and documented in a systematic treatment. As of the writing of this dissertation, the theoretical prediction for the SM estimate of the muon's anomalous magnetic moment is under debate, with two competing prediction methods, so a definitive comparison with theory is not available. The results submitted for experimental release use the kernel-ratio asymmetry method, contributing 115 parts per billion to the statistical uncertainty and 34 parts per billion to the systematic uncertainty. When combined with the previous analyses in earlier data runs, this thereby improves the measurement beyond the experimental goal and sets the world's most precise measurement of the muon's anomalous magnetic moment.
Israel, Scott Nathan [Boston U.]↗
Measurement of the muon anomalous precession frequency in Runs 4, 5, and 6 of the Muon g-2 experiment at Fermilab
The Fermilab E989 Muon g − 2 experiment measures the muon’s anomalous magnetic moment to a precision of 127 parts per billion, as reported in June 2025. The value is proportional to the difference between the muon’s cyclotron frequency and the spin precession frequency in the presence of a uniform magnetic field, for muons contained within the g − 2 storage ring. Spin precession frequency is extracted from the time distribution of the muon’s decay positrons recorded by 24 electromagnetic calorimeters positioned around the inner circumference of the storage ring. The anomalous precession frequency is one of the primary experimental inputs necessary to estimate the anomalous magnetic moment, the other being the measurement of the magnetic field. This dissertation details the anomalous precession frequency extraction, including reconstruction, time-distribution fitting, and treatment of systematic uncertainties for the final three data-collection runs: Run-4, Run-5, and Run-6. This data represents a fourfold increase in statistics over the previous analysis release, halving the statistical uncertainty. The residual slow term from previous analyses is now well understood and documented in a systematic treatment. As of the writing of this dissertation, the theoretical prediction for the SM estimate of the muon’s anomalous magnetic moment is under debate, with two competing prediction methods, so a definitive comparison with theory is not available. The results submitted for experimental release use the kernel-ratio asymmetry method, contributing 115 parts per billion to the statistical uncertainty and 34 parts per billion to the systematic uncertainty. When combined with the previous analyses in earlier data runs, this thereby improves the measurement beyond the experimental goal and sets the world’s most precise measurement of the muon’s anomalous magnetic moment.
Israel, Scott Nathan [Boston U.]↗
Advanced Finite-Volume Numerics and Source Term Assumptions for Kernel and G-Equation Modelling of Propane/Air Flames
Here G-Equation models represent propagating flame fronts with an implicit two-dimensional surface representation (level-set). Level-set methods are fast, as transport source terms for the implicit surface can be solved with finite-volume operators on the finite-volume domain, without having to build the actual surface. However, they include approximations whose practical effects are not properly understood. In this study, we improved the numerics of the FRESCO CFD code’s G-Equation solver and developed a new method to simulate kernel growth using signed distance functions and the analytical sphere-mesh overlap. We analyzed their role for simulating propane/air flames, using three well-established constant-volume configurations: a one-dimensional, freely propagating laminar flame; a disc-shaped, constant-volume swirl combustor; and torch-jet flame development through an orifice from a two-chamber device. We tested the explicit (sub-cycled) vs. implicit formulation for the standard transport operators (advection, diffusion, compressibility). In addition to the accurate flame swept-volume method for chemistry and species source term, we developed a more accurate estimator for the burnt/unburnt split cell composition. Then, we developed a signed-distance-function (SDF) based method which provides a more stable reinitialization of the level-set field at every time-step. We found that simplifying assumptions common to several G-Equation implementations, for straightforward terms such as compressibility and advection, lead to large errors in predicting the propagation of even laminar flames, with deviations up to ~300% in simulated vs. formulated flame speed. Conversely, the enhanced numerics enabled through the SDF field reinitialization and improved chemistry source term improve simulation stability and smooth flame propagation even with significantly larger solver time-steps.
42 ENGINEERING↗
Clutter identification based on kernel density estimation and sparse recovery
A cognitive radar framework is being developed to dynamically detect changes in the clutter characteristics, and to adapt to these changes by identifying the new clutter distribution. In our previous work, we have presented a sparse-recovery based clutter identification technique. In this technique, each column of the dictionary represents a specific distribution. More specifically, calibration radar clutter data corresponding to a specific distribution is transformed into a distribution through kernel density estimation. When the new batch of radar data arrives, the new data is transformed to a distribution through the same kernel density estimation method and its distribution characteristics is identified through sparse-recovery. In this paper, we extend our previous work to consider different kernels and kernel parameters for sparse-recovery-based clutter identification and the numerical results are presented as well. The impact of different kernels and kernel parameters are analyzed by comparing the identification accuracy of each scenario.
Wang, Haokun↗
Nuclear rocket shielding methods, modification, updating, and input data preparation. Volume 6 - Point kernel techniques Final progress report
Point kernel techniques for use with nuclear rocket shielding methods, modification, updating, and input data preparation - Vol. 6
Disney, R. K.↗
Density estimation techniques for multiscale coupling of kinetic models of the plasma material interface
In this work we analyze two classes of Density-Estimation techniques which can be used to consistently couple different kinetic models of the plasma-material interface, intended as the region of plasma immediately interacting with the first surface layers of a material wall. In particular, we handle the general problem of interfacing a continuum multi-species Vlasov-Poisson-BGK plasma model to discrete surface erosion models. The continuum model solves for the energy-angle distributions of the particles striking the surface, which are then driving the surface response. A modification to the classical Binary-Collision Approximation (BCA) method is here utilized as a prototype discrete model of the surface, to provide boundary conditions and impurity distributions representative of the material behavior during plasma irradiation. The numerical tests revealed the superior convergence properties of Gaussian Mixture Models over Kernel Density Estimation methods, with Gaussian Mixtures and Epanechnikov-KDEs both being up to two orders of magnitude faster than Gaussian-KDEs. The methodology here presented allows a self-consistent treatment of the plasma-material interface in magnetic fusion devices, including both the near-surface plasma (plasma sheath and presheath) in magnetized conditions, and surface effects such as sputtering, back-scattering, and ion implantation. The same coupling techniques can also be utilized for other discrete material models such as Molecular Dynamics.
42 ENGINEERING↗
Meshless discretization of the discrete-ordinates transport equation with integration based on Voronoi cells
The time-dependent, gray, linear radiation transport equation is discretized using the meshless local Petrov-Galerkin method with reproducing kernels. The integration is performed using a Voronoi tessellation, which creates a partition of unity that only depends on the position and extent of the kernels. The resolution of the integration automatically follows the particles and requires no manual adjustment. The discretization includes streamline-upwind Petrov-Galerkin stabilization to prevent oscillations and improve numerical conditioning. The angular quadrature is selectively refineable to increase angular resolution in chosen directions. The time discretization is done using backward Euler. The transport solve for each direction and the solve for the scattering source are both done using Krylov iterative methods. The results indicate first-order convergence in time and second-order convergence in space for linear reproducing kernels.
97 MATHEMATICS AND COMPUTING↗
SU-E-T-805: Verification of the Simplified Monte Carlo Method for Simulation in An Inhomogeneous Phantom
Purpose: A simplified Monte Carlo (SMC) method has been developed to obtain fast and accurate dose calculation in heterogeneous tissues to improve the accuracy of dose calculation. We have applied the SMC method to calculation of dose kernels for the pencil beam scanning. While the SMC method tracks individual primary protons in medium, it simplifies the dose calculation by using a measured depth-dose distribution instead of considering nuclear reactions and tracking secondary particles. To verify the accuracy of SMC calculation, we compared a dose-calculation Result using the SMC method with that using the Full Monte Carlo (FMC) method in an inhomogeneous phantom. Methods: As a model of the inhomogeneous media, we considered a phantom complied of a rectangular acrylic block of size 150*300*200 mm {sup 3} immersed in water within a virtual container with a size of 300*300*400 mm{sup 3}. Results: We found excellent agreement of overall dose distributions between the SMC and FMC methods. As for the laterally integrated depth-dose distributions, slight difference was found in front of the second Bragg-Peak between the two algorithms. While it took 25717.0 s on 2.7 GHz Intel Core i7 for the FMC method to complete the calculation, it took 15.4 s for the SMC method to complete it. The SMC method can calculate the dose distribution approximately 1675 times faster than the FMC method. Conclusion: The dose distribution obtained by SMC method agreed well that obtained by the FMC method in a simple inhomogeneous phantom. In contrast, calculation time by the SMC method has been reduced by three orders in magnitude compared with the FMC method.
60 APPLIED LIFE SCIENCES↗
Analysis of numerical stability and amplification matrices: Fourth-order Runge-Kutta methods
Amplification matrices, numerical kernels, stable, and exponentially stable numerical solutions are examined. The various techniques involved in these concepts are applied to certain systems that have Jordan forms, which are nondiagonal, with particular interest in the case of imaginary or zero eigenvalues.
Kennedy, E. W.↗