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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

The Collins-Soper Kernel from Lattice QCD

I will present the first complete determination of the quark Collins-Soper kernel, which relates TMDs at different rapidity scales, using lattice QCD and including systematic control of quark mass, operator mixing, and discretization effects. Next-to-next-to-leading logarithmic matching is used to match lattice-calculable distributions to the corresponding TMDs. The continuum-extrapolated lattice QCD results are consistent with several recent phenomenological parametrizations of the Collins-Soper kernel and are precise enough to disfavor other parametrizations. I will also discuss a first exploration of the gluon Collins-Soper kernel.

Wagman, Michael [Fermilab]↗
DOE OSTI2019

Spectral convergence of the stochastic galerkin approximation to the boltzmann equation with multiple scales and large random perturbation in the collision kernel

In a 2018 article, spectral convergence and long-time decay of the numerical solution towards the global equilibrium of the stochastic Galerkin approximation for the Boltzmann equation with random inputs in the initial data and collision kernel for hard potentials and Maxwellian molecules under Grad's angular cutoff were established using the hypocoercive properties of the collisional kinetic model. One assumption for the random perturbation of the collision kernel is that the perturbation is in the order of the Knudsen number, which can be very small in the fluid dynamical regime. In this article, we remove this smallness assumption, and establish the same results but now for random perturbations of the collision kernel that can be of order one. The new analysis relies on the establishment of a spectral gap for the numerical collision operator.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2018

Surface and top-of-atmosphere radiative feedback kernels for CESM-CAM5

Radiative kernels at the top of the atmosphere are useful for decomposing changes in atmospheric radiative fluxes due to feedbacks from atmosphere and surface temperature, water vapor, and surface albedo. Here we describe and validate radiative kernels calculated with the large-ensemble version of CAM5, CESM1.1.2, at the top of the atmosphere and the surface. Estimates of the radiative forcing from greenhouse gases and aerosols in RCP8.5 in the CESM large-ensemble simulations are also diagnosed. As an application, feedbacks are calculated for the CESM large ensemble. The kernels are freely available at https://doi.org/10.5065/D6F47MT6 , and accompanying software can be downloaded from https://github.com/apendergrass/cam5-kernels .

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Evaluating HPC Kernels for Processing in Memory

Memory subsystems contribute significantly to the performance and energy efficiency of high-performance computing (HPC) applications. Traditional memory technologies with conventional organization (e.g., DRAM) are struggling to keep up with the increasing memory requirements of modern applications. Techniques such as multilayer cache hierarchy and out-of-order execution are still falling short of mitigating the penalty incurred by memory accesses. Processing-in-memory (PIM), which involves moving memory-intensive kernels to memory for execution instead of bringing the data to the processing unit, is emerging as a promising technique. PIM has recently received traction among computer architecture researchers, and the increasing research activity surrounding this technique indicates its potential to alleviate main memory performance bottlenecks. In this paper, we characterize and identify memory-intensive HPC kernels, perform a first-order evaluation of the PIM technique for selected HPC kernels, quantify performance deviation, and analyze the key factors that affect PIM efficiency.

Asifuzzaman, Kazi↗
DOE OSTI2016

Nuclear Forensics for Irradiated Materials using Kernel Regression Models

The ultimate purpose of nuclear forensics is to locate the origin of nuclear and other radioactive materials out of regulatory control used in nuclear security events such as classical forensics. For this purpose, some specific characteristics of interdicted materials (referred to as 'signatures') should be defined to compare the known sample database. In some cases, involved with irradiated material, the signatures could be specific amount of fission product inventory depending on reactor operational histories such as reactor type, initial enrichment, burn up rate of nuclear fuel and cooling period after irradiation in the reactor. In order to make inference model for irradiated material for nuclear forensics, we suggested 3 ways as follows; (i) analyzing ORIGEN produced nuclear substances for the fission product inventory, (ii) classifying the range of reactor type, (iii) predicting the operational history from the fission product inventory. In terms of nuclear substance analysis, the construction of spent fuel database has been internationally carried out since ITWG (Nuclear Smuggling International Technical Working Group) was established in 1995. However, enough sample data cannot be obtained in Korea to determine reactor type and operational histories because analyzing nuclear substances have been limited due to the international regulation. Thus, this study does not mention how to obtain mass or ratios of nuclides for the spent fuel. We just have generated simulation sample data as a fission product inventory using ORIGEN to construct spent fuel database. When unidentified radioactive materials are discovered, it is assumed that mass or ratios of the nuclides are analyzed by certain methods which are available in Korea as well as other countries. Then, a reactor type is determined, and finally, regression model can locate the origin or source of the radioactive materials by inferring operational histories using the fission product inventory. There are some studies on the classification of reactor type using statistical methods. As a part of predicting the operational history, this paper focuses on the development of spent fuel inference algorithm for nuclear forensics to estimate reactor operational histories that reflect characteristics of a reactor from the fission product inventory. The spent fuel inference algorithm for nuclear forensics has been developed on the basis of Kernel Regression (KR) which can conditionally generate the estimated output data by giving weight depending on geometric distance between sample data and input data. Also the KR which comprises Auto-Associative KR and Inferential KR have some benefits that can estimate only using data without assumption for specific physical model and re-learning process. Auto-associative KR (AAKR) was used to sort out outliers of input data and Inferential KR (IKR) was carried out to predict the operational histories for spent fuel. All of regression algorithms were performed in R programming tool. From the validation of both AAKR and IKR, it is expected that kernel regression has enough accuracy to be applied to nuclear forensics for spent fuel. Once the nuclear substance is measured to fill the fission product inventory with a certain reactor type, this kernel regression algorithm would predict the operational histories of spent fuel with high accuracy. Finally, this information is expected to be useful to find the origin of irradiated materials. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2015

Three-dimensional Fréchet sensitivity kernels for electromagnetic wave propagation

Electromagnetic imaging methods are useful tools for monitoring subsurface changes in pore-fluid content and the associated changes in electrical permittivity and conductivity. The most common method for georadar tomography uses a high frequency ray-theoretic approximation that is valid when material variations are sufficiently small relative to the wavelength of the propagating wave. Georadar methods, however, often utilize electromagnetic waves that propagate within heterogeneous media at frequencies where ray theory may not be applicable. In this paper we describe the 3-D Fréchet sensitivity kernels for EM wave propagation. Various data functional types are formulated that consider all three components of the electric wavefield and incorporate near-, intermediate-, and far-field contributions. We show that EM waves exhibit substantial variations for different relative source-receiver component orientations. The 3-D sensitivities also illustrate out-of-plane effects that are not captured in 2-D sensitivity kernels and can influence results obtained using 2-D inversion methods to image structures that are in reality 3-D.

58 GEOSCIENCES↗
DOE OSTI2018

On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model

We present some estimates for the memory kernel function in the generalized Langevin equation, derived using the Mori–Zwanzig formalism from a one-dimensional lattice model, in which the particles interactions are through nearest and second nearest neighbors. The kernel function can be explicitly expressed in a matrix form. The analysis focuses on the decay properties, both spatially and temporally, revealing a power-law behavior in both cases. The dependence on the level of coarse-graining is also studied.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

An Analog of the Hyperbolic Metric Generated by a Hilbert Space with the Schwarz–Pick Kernel

It is proved that a Hilbert function space on a set X with the Schwarz–Pick kernel (this is a wider class than the class of Hilbert spaces with the Nevanlinna–Pick kernel) generates a metric on the set X which is an analog of the hyperbolic metric in the unit disk. For a sequence satisfying an abstract Blaschke condition, it is proved that the associated infinite Blaschke product converges uniformly on any fixed bounded set and in the strong operator topology of the multiplier space. Bibliography: 8 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Using a meshless kernel-based method to solve the Black–Scholes variational inequality of American options

Under the Black–Scholes model, the value of an American option solves a free boundary problem which is equivalent to a variational inequality problem. Using positive definite kernels, we discretize the variational inequality problem in spatial direction and derive a sequence of linear complementarity problems (LCPs) in a finite-dimensional euclidean space. We use special kind of kernels to impose homogeneous boundary conditions and to obtain LCPs with positive definite coefficient matrices to guarantee the existence and uniqueness of the solution. The LCPs are then successfully solved iteratively by the projected SOR algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Determining the memory kernel from a fixed point measurement data for a parabolic equation with memory effect

We consider an inverse problem for a parabolic equation with memory effect. This inverse problem aims to identify the memory kernel function from a fixed point measurement data. Based on the fixed point arguments, we derive the global in time existence and uniqueness of our inverse problem. Moreover, we present a numerical algorithm to reconstruct the memory kernel function. Numerical simulations show the effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Application of mixed kernels function (MKF) based support vector regression model (SVR) for CO 2 – Reservoir oil minimum miscibility pressure prediction

Carbon dioxide (CO 2 ) injection into oil reservoirs is considered a mature enhanced oil recovery (EOR) technique for conventional reservoirs. The local displacement efficiency of the CO 2 -EOR process is highly dependent on the minimum miscibility pressure (MMP), estimating this parameter is critical to design of the CO 2 injection process. Traditional empirical methods to test the CO 2 -oil MMP are time consuming and expensive; derived correlations are fast but not accurate. Therefore, an efficient and reliable method to determine MMP is beneficial. Here in this study, a mixed kernels function (MKF) based support vector regression (SVR) model was developed and used to predict the MMP for both pure and impure CO 2 injection cases. Four parameters were chosen as input parameters: (1) reservoir temperature; (2) average critical temperature; (3) molecular weight of pentane plus (C 5+ ) fraction of crude oil, and; (4) the ratio of volatile components to intermediate components in crude oil. MMP was selected as the desired output parameter to train and test this newly developed model. The performance of basic kernels function based SVR model is compared with that of this newly developed MKF-SVR model. The well-trained MFK-SVR was compared with three well-established published correlations, demonstrated the highest correlation coefficient (R of 0.9381), lowest root mean square error (RMSE of 1.9151), smallest average absolute error (AAE of 1.1406) and maximum absolute error (MAE of 4.6291). We believe that the proposed MFK-SVM model is a more reliable and stable regression model to predict MMP. In addition, a sensitivity analysis was conducted to evaluate the physical correctness. It indicates that the predicted results from the newly developed model are in excellent agreement with previous empirical work.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Kernel-based global sensitivity analysis obtained from a single data set

Results from global sensitivity analysis (GSA) often guide the understanding of complicated input–output systems. Kernel-based GSA methods have recently been proposed for their capability of treating a broad scope of complex systems. In this paper, we develop a new set of kernel GSA tools when only a single set of input–output data is available. Three key advances are made: (1) A new numerical estimator is proposed that demonstrates an empirical improvement over previous procedures. (2) A computational method for generating inner statistical functions from a single data set is presented. (3) A theoretical extension is made to define conditional sensitivity indices, which reveal the degree that the inputs carry shared information about the output when inherent input–input correlations are present. Utilizing these conditional sensitivity indices, a decomposition is derived for the output uncertainty based on what is called the optimal learning sequence of the input variables, which remains consistent when correlations exist between the input variables. Further, while these advances cover a range of GSA subjects, a common single data set numerical solution is provided by a technique known as the conditional mean embedding of distributions. The new methodology is implemented on benchmark systems to demonstrate the provided insights.

42 ENGINEERING↗
DOE OSTI2015

Reproducing kernel potential energy surfaces in biomolecular simulations: Nitric oxide binding to myoglobin

Multidimensional potential energy surfaces based on reproducing kernel-interpolation are employed to explore the energetics and dynamics of free and bound nitric oxide in myoglobin (Mb). Combining a force field description for the majority of degrees of freedom and the higher-accuracy representation for the NO ligand and the Fe out-of-plane motion allows for a simulation approach akin to a mixed quantum mechanics/molecular mechanics treatment. However, the kernel-representation can be evaluated at conventional force-field speed. With the explicit inclusion of the Fe-out-of-plane (Fe-oop) coordinate, the dynamics and structural equilibrium after photodissociation of the ligand are correctly described compared to experiment. Experimentally, the Fe-oop coordinate plays an important role for the ligand dynamics. This is also found here where the isomerization dynamics between the Fe–ON and Fe–NO state is significantly affected whether or not this co-ordinate is explicitly included. Although the Fe–ON conformation is metastable when considering only the bound {sup 2}A state, it may disappear once the {sup 4}A state is included. This explains the absence of the Fe–ON state in previous experimental investigations of MbNO.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

SU-F-T-672: A Novel Kernel-Based Dose Engine for KeV Photon Beams

Purpose: Mimicking state-of-the-art patient radiotherapy with high precision irradiators for small animals allows advanced dose-effect studies and radiobiological investigations. One example is the implementation of pre-clinical IMRT-like irradiations, which requires the development of inverse planning for keV photon beams. As a first step, we present a novel kernel-based dose calculation engine for keV x-rays with explicit consideration of energy and material dependencies. Methods: We follow a superposition-convolution approach adapted to keV x-rays, based on previously published work on micro-beam therapy. In small animal radiotherapy, we assume local energy deposition at the photon interaction point, since the electron ranges in tissue are of the same order of magnitude as the voxel size. This allows us to use photon-only kernel sets generated by MC simulations, which are pre-calculated for six energy windows and ten base materials. We validate our stand-alone dose engine against Geant4 MC simulations for various beam configurations in water, slab phantoms with bone and lung inserts, and on a mouse CT with (0.275mm)3 voxels. Results: We observe good agreement for all cases. For field sizes of 1mm{sup 2} to 1cm{sup 2} in water, the depth dose curves agree within 1% (mean), with the largest deviations in the first voxel (4%) and at depths>5cm (<2.5%). The out-of-field doses at 1cm depth agree within 8% (mean) for all but the smallest field size. In slab geometries, the mean agreement was within 3%, with maximum deviations of 8% at water-bone interfaces. The γ-index (1mm/1%) passing rate for a single-field mouse irradiation is 71%. Conclusion: The presented dose engine yields an accurate representation of keV-photon doses suitable for inverse treatment planning for IMRT. It has the potential to become a significantly faster yet sufficiently accurate alternative to full MC simulations. Further investigations will focus on energy sampling as well as calculation times. Research at ICR is also supported by Cancer Research UK under Programme C33589/A19727 and NHS funding to the NIHR Biomedical Research Centre at RMH and ICR. MFF is supported by Cancer Research UK under Programme C33589/A19908.

43 PARTICLE ACCELERATORS↗
DOE OSTI2015

GPU Acceleration of Mean Free Path Based Kernel Density Estimators for Monte Carlo Neutronics Simulations

Kernel Density Estimators (KDEs) are a non-parametric density estimation technique that has recently been applied to Monte Carlo radiation transport simulations. Kernel density estimators are an alternative to histogram tallies for obtaining global solutions in Monte Carlo tallies. With KDEs, a single event, either a collision or particle track, can contribute to the score at multiple tally points with the uncertainty at those points being independent of the desired resolution of the solution. Thus, KDEs show potential for obtaining estimates of a global solution with reduced variance when compared to a histogram. Previously, KDEs have been applied to neutronics for one-group reactor physics problems and fixed source shielding applications. However, little work was done to obtain reaction rates using KDEs. This paper introduces a new form of the MFP KDE that is capable of handling general geometries. Furthermore, extending the MFP KDE to 2-D problems in continuous energy introduces inaccuracies to the solution. An ad-hoc solution to these inaccuracies is introduced that produces errors smaller than 4% at material interfaces.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Digital Modeling on Large Kernel Metamaterial Neural Network

Deep neural networks (DNNs) utilized recently are physically deployed with computational units (e.g., CPUs and GPUs). Such a design might lead to a heavy computational burden, significant latency, and intensive power consumption, which are critical limitations in applications such as Internet of Things (IoT), edge computing, and usage of drones. Recent advances in optical computational units (e.g., metamaterial) have shed light on energy-free and light-speed neural networks. However, the digital design of the metamaterial neural network (MNN) is fundamentally limited by its physical limitations, such as precision, noise, and bandwidth during fabrication. Moreover, the unique advantages of MNN’s (e.g., light-speed computation) are not fully explored via standard 3×3 convolution kernels. In this paper, we propose a novel large kernel metamaterial neural network (LMNN) that maximizes the digital capacity of the state-of-the-art (SOTA) MNN with model re-parametrization and network compression, while also considering the optical limitation explicitly. The new digital learning scheme can maximize the learning capacity of MNN while modeling the physical restrictions of meta-optics. With the proposed LMNN, the computation cost of the convolutional front-end can be offloaded to fabricated optical hardware. The experimental results on two publicly available datasets demonstrate that the optimized hybrid design improved classification accuracy while reducing computational latency. In conclusion, the development of the proposed LMNN is a promising step towards the ultimate goal of energy-free and light-speed AI.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Gaussian Kernel Methods for Seismic Fragility and Risk Assessment of Mid-Rise Buildings

Seismic fragility functions can be evaluated using the cloud analysis method with linear regression which makes three fundamental assumptions about the relation between structural response and seismic intensity: log-linear median relationship, constant standard deviation, and Gaussian distributed errors. While cloud analysis with linear regression is a popular method, the degree to which these individual and compounded assumptions affect the fragility and the risk of mid-rise buildings needs to be systematically studied. This paper conducts such a study considering three building archetypes that make up a bulk of the building stock: RC moment frame, steel moment frame, and wood shear wall. Gaussian kernel methods are employed to capture the data-driven variations in the median structural response and standard deviation and the distributions of residuals with the intensity level. With reference to the Gaussian kernels approach, it is found that while the linear regression assumptions may not affect the fragility functions of lower damage states, this conclusion does not hold for the higher damage states (such as the Complete state). In addition, the effects of linear regression assumptions on the seismic risk are evaluated. For predicting the demand hazard, it is found that the linear regression assumptions can impact the computed risk for larger structural response values. However, for predicting the loss hazard with downtime as the decision variable, linear regression can be considered adequate for all practical purposes.

58 GEOSCIENCES↗