Search NASA⌕ Search

SEARCH · Search NASA

Results for “Kernel function”

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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A generalized Selberg zeta function for flat space cosmologies

Flat space cosmologies (FSCs) are time dependent solutions of three-dimensional (3D) gravity with a vanishing cosmological constant. They can be constructed from a discrete quotient of empty 3D flat spacetime and are also called shifted-boost orbifolds. Using this quotient structure, we build a new and generalized Selberg zeta function for FSCs, and show that it is directly related to the scalar 1-loop partition function. We then propose an extension of this formalism applicable to more general quotient manifolds $\mathcal{M}$/ℤ, based on representation theory of fields propagating on this background. Our prescription constitutes a novel and expedient method for calculating regularized 1-loop determinants, without resorting to the heat kernel. We compute quasinormal modes in the FSC using the zeroes of a Selberg zeta function, and match them to known results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Exact calculation of the time convolutionless master equation generator: Application to the nonequilibrium resonant level model

The generalized quantum master equation provides a powerful tool to describe the dynamics in quantum impurity models driven away from equilibrium. Two complementary approaches, one based on Nakajima–Zwanzig–Mori time-convolution (TC) and the other on the Tokuyama–Mori time-convolutionless (TCL) formulations provide a starting point to describe the time-evolution of the reduced density matrix. A key in both approaches is to obtain the so called “memory kernel” or “generator,” going beyond second or fourth order perturbation techniques. While numerically converged techniques are available for the TC memory kernel, the canonical approach to obtain the TCL generator is based on inverting a super-operator in the full Hilbert space, which is difficult to perform and thus, nearly all applications of the TCL approach rely on a perturbative scheme of some sort. Here, the TCL generator is expressed using a reduced system propagator which can be obtained from system observables alone and requires the calculation of super-operators and their inverse in the reduced Hilbert space rather than the full one. This makes the formulation amenable to quantum impurity solvers or to diagrammatic techniques, such as the nonequilibrium Green’s function. We implement the TCL approach for the resonant level model driven away from equilibrium and compare the time scales for the decay of the generator with that of the memory kernel in the TC approach. Furthermore, the effects of temperature, source-drain bias, and gate potential on the TCL/TC generators are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A functional global sensitivity measure and efficient reliability sensitivity analysis with respect to statistical parameters

Sensitivity analysis and reliability assessment are two important aspects of structural and system safety. Epistemic uncertainty with respect to probabilistic model of input parameters due to lack of knowledge is present in many scarce-data applications and complicates the characterization of uncertainty in model response. In this article, we present two importance measures to evaluate the impact of distribution parameters on the probability distribution function (PDF) of the output and the failure probability. The epistemic uncertainty associated with the distribution parameters is modeled as random variables. Additionally, a modified extended polynomial chaos expansion (MEPCE) approach is introduced in which aleatory and epistemic random variables are modeled and propagated simultaneously while allowing the separate assessment for any single epistemic variable. A MEPCE-based kernel density estimation (KDE) construction provides a composite map from each epistemic variable to the response PDF. The functional global sensitivity index of the PDF with respect to the distribution parameters is thus derived, as a function of output, which is both more informative and more efficient than standard scalar sensitivity measures. Reliability sensitivity indices can be readily evaluated by integrating the global sensitivity index function over the failure zone. Three illustrative examples are used to demonstrate the proposed methodology.

42 ENGINEERING↗
DOE OSTI2019

Design and analysis of machine learning exchange-correlation functionals via rotationally invariant convolutional descriptors

Here, we explore the potential of a data-driven approach to the design of exchange-correlation (xc) functionals. The approach, inspired by convolutional filters in computer vision and surrogate functions from optimization, utilizes convolutions of the electron density to form a feature space to represent local electronic environments and neural networks to map the features to the exchange-correlation energy density. These features are orbital free, and provide a systematic route to including information at various length scales. This work shows that convolutional descriptors are theoretically capable of an exact representation of the electron density, and proposes Maxwell-Cartesian spherical harmonic kernels as a class of rotationally invariant descriptors for the construction of machine learned functionals. The approach is demonstrated using data from the B3LYP functional on a number of small molecules containing C, H, O, and N along with a neural network regression model. The machine learned functionals are compared to standard physical approximations and the accuracy is assessed for the absolute energy of each molecular system as well as formation energies. The results indicate that it is possible to reproduce the exchange-correlation portion of B3LYP formation energies to within chemical accuracy using orbital-free descriptors with a spatial extent of 0.2 Å. The findings provide empirical insight into the spatial range of electron exchange, and suggest that the combination of convolutional descriptors and machine learning regression models is a promising framework for xc functional design, although challenges remain in obtaining training data and generating models consistent with pseudopotentials.

36 MATERIALS SCIENCE↗
DOE OSTI2020

nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius δ goes to zero, and to the fractional Laplacian as δ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We provide theoretical convergence rates with respect to δ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, δ and α, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order α(γ), which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as δ. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius $\delta$ goes to zero, and to the fractional Laplacian as $\delta$ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We also provide theoretical convergence rates with respect to $\delta$ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, $\delta$ and $\alpha$, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order $\alpha(y)$, which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as $\delta$. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Probabilistic Solar Power Forecasting Using Bayesian Model Averaging

There is rising interest in probabilistic forecasting to mitigate risks from solar power uncertainty, but the numerical weather prediction (NWP) ensembles readily available to system operators are often biased and underdispersed. We propose a Bayesian model averaging (BMA) post-processing method suitable for forecasting power from utility-scale photovoltaic (PV) plants at multiple time horizons up to at least the day-ahead timescale. BMA is a kernel dressing technique for NWP ensembles in which the forecast is a weighted sum of member-specific probability density functions. We tailor BMA for utility-scale PV forecasting by modeling power clipping at the AC inverter rating and advance the theory of BMA with a new beta kernel parameterization that accommodates theoretical constraints not previously addressed. BMA is demonstrated for a case study of 11 utility-scale PV plants in Texas, forecasting at hourly resolution for the complete year 2018. BMA's mixture-model approach mitigates underdispersion of the raw ensemble to significantly improve forecast calibration, while consistently outperforming an ensemble model output statistics (EMOS) parametric approach from the literature. At 4-hour lead time, the BMA post-processing achieves continuous ranked probability skill scores of 2--36% over the raw ensemble, with consistent performance at multiple lead times suitable for power system operations.

14 SOLAR ENERGY↗
DOE OSTI2022

3D analysis of TRISO fuel compacts via X-ray computed tomography

In this study, low-enriched uranium oxycarbide (LEUCO) and surrogate tristructural isotropic (TRISO)- coated-particle compacts with particle volumetric packing fractions of 25%, 40%, and 48% were imaged utilizing X-ray-computed tomography. Subsequent 3D image analysis identified and further quantified kernel size, sphericity, and observed porosity. In addition, the spatial distribution, coordination number, and kernel-nearest neighbors were analyzed and compared for the different packing fractions. Metrics such as observed porosity and sphericity enabled quantification and screening for abnormal kernels within TRISO compacts. Assessment of TRISO particle location confirmed and further quantified a non-uniform distribution of TRISO particles with the spatial distribution in the radial direction being roughly described as a dampened sinusoidal function. The amplitude and frequency of this non-uniform distribution increased with increasing packing fraction. Measured kernel-nearest neighbor distances indicated two regions along the radial surfaces of compacts where TRISO particles are more likely to be in intimate contact with one another. These regions were found: (1) at upper and lower faces of compacts (i.e., corners); (2) offset ~10% of a compact's length from the axial center near the exterior surface. Within these regions, small quantities of defective TRISO surrogate particles (48% packing fraction) and defective LEUCO TRISO particles (40% packing fraction) were found. No defective particles were found within 25% packing fraction LEUCO TRISO compacts.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Efficient simulations of charge density waves in the transition metal Dichalcogenide TiSe 2

Charge density waves (CDWs) in transition metal dichalcogenides are the subject of growing scientific interest due to their rich interplay with exotic phases of matter and their potential technological applications. Here, using density functional theory with advanced meta-generalized gradient approximations (meta-GGAs) and linear response time-dependent density functional theory (TDDFT) with state-of-the-art exchange-correlation kernels, we investigate the electronic, vibrational, and optical properties in 1T-TiSe 2 with and without CDW. In both bulk and monolayer TiSe 2 , the electronic bands and phonon dispersions in either normal or CDW (semiconducting) phase are described well via meta-GGAs, which separate the valence and conduction bands just as HSE06 does but with significantly more computational feasibility. The experimentally observed humps of electron energy loss spectroscopy are successfully reproduced in TDDFT. Our work opens the door to simulating these complexities in CDW compounds from first principles by revealing meta-GGAs as an accurate low-cost alternative to HSE06.

Electronic properties and materials↗
DOE OSTI2022

Performance portability study of epistasis detection using SYCL on NVIDIA GPU

We describe the experience of converting a CUDA implementation of a high-order epistasis detection algorithm to SYCL. The goals are for our work to be useful to application and compiler developers with a detailed description of migration paths between CUDA and SYCL. Evaluating the CUDA and SYCL applications on an NVIDIA V100 GPU, we find that the optimization of loop unrolling needs to be applied manually to the SYCL kernel for obtaining comparable performance. The performance of the SYCL group reduce function, an alternative to the CUDA warp-based reduction, depends on the problem and work group sizes. The 64-bit popcount operation implemented with tree of adders is slightly faster than the built-in popcount operation. When the number of OpenMP threads is four, the highest performance of the SYCL and CUDA applications are comparable.

Jin, Zheming↗
DOE OSTI2019

A Novel Statistical Method for Measuring the Temperature–Density Relation in the IGM Using the b – N Hi Distribution of Absorbers in the Ly α Forest

We propose a new method for determining the thermal state of the intergalactic medium based on Voigt profile decomposition of the Lyα forest. The distribution of Doppler parameter and column density (b–N H i distribution) is sensitive to the temperature–density relation T = T 0 (ρ/ρ 0 ) γ-1 , and previous work has inferred T 0 and γ by fitting its low-b cutoff. This approach discards the majority of available data and is susceptible to systematics related to cutoff determination. We introduce an approach that exploits all information encoded in the b – N H i distribution by modeling its entire shape. We apply kernel density estimation to discrete absorption lines to generate model probability density functions, and then we use principal component decomposition to create an emulator that can be evaluated anywhere in thermal parameter space. We introduce a Bayesian likelihood based on these models enabling parameter inference via Markov Chain Monte Carlo. The method's robustness is tested by applying it to a large grid of thermal history simulations. By conducting 160 mock measurements, we establish that our approach delivers unbiased estimates and valid uncertainties for a 2D ( T 0 , γ) measurement. Furthermore, we conduct a pilot study applying this methodology to real observational data at z = 2. Using 200 absorbers, equivalent in path length to a single Lya forest spectrum, we measure $\mathrm{log}{T}_{0}={4.092}_{-0.055}^{+0.050}$ and $\gamma ={1.49}_{-0.074}^{+0.073}$ in excellent agreement with cutoff fitting determinations using the same data. Our method is far more sensitive than cutoff fitting, enabling measurements of log T 0 and γ with precision on $\mathrm{log}{T}_{0}$ (γ) nearly two (three) times higher for current data set sizes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Hierarchical Particle Mesh: An FFT-accelerated Fast Multipole Method

I observe a modification to the original Fast Multipole Method (FMM) of Greengard & Rokhlin that approximates the gravitation field of an FMM cell as a small uniform grid (a “gridlet”) of effective masses. The effective masses on a gridlet are set from the requirement that the multipole moments of the FMM cells are reproduced exactly, thus preserving the accuracy of the gravitational field representation. The measurement of the gravitational field from a multipole expansion can then be computed for all multipole orders simultaneously, with a single Fast Fourier Transform, significantly reducing the computational cost at a given value of the required accuracy. The described approach belongs to the class of “kernel independent” variants of the FMM method and works with any Green function.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2014

Visible Motion Blur

A method of measuring motion blur is disclosed comprising obtaining a moving edge temporal profile r(sub 1)(k) of an image of a high-contrast moving edge, calculating the masked local contrast m(sub1)(k) for r(sub 1)(k) and the masked local contrast m(sub 2)(k) for an ideal step edge waveform r(sub 2)(k) with the same amplitude as r(sub 1)(k), and calculating the measure or motion blur Psi as a difference function, The masked local contrasts are calculated using a set of convolution kernels scaled to simulate the performance of the human visual system, and Psi is measured in units of just-noticeable differences.

Watson, Andrew B.↗
DOE OSTI2015

Decomposition of the polynomial kernel of arbitrary higher spin Dirac operators

In a series of recent papers, we have introduced higher spin Dirac operators, which are generalisations of the classical Dirac operator. Whereas the latter acts on spinor-valued functions, the former acts on functions taking values in arbitrary irreducible half-integer highest weight representations for the spin group. In this paper, we describe how the polynomial kernel spaces of such operators decompose in irreducible representations of the spin group. We will hereby make use of results from representation theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Anisotropic hydrodynamics with number-conserving kernels

We compare anisotropic hydrodynamics (aHydro) results obtained using the relaxation-time approximation (RTA) and leading-order (LO) scalar λΦ 4 collisional kernels. We extend previous work by explicitly enforcing number conservation through the incorporation of a dynamical chemical potential (fugacity) in the underlying aHydro distribution function. We focus on the case of a transversally homogenous and boost-invariant system obeying classical statistics and compare the relevant moments of the two collisional kernels. We then compare the time evolution of the aHydro microscopic parameters and components of the energy-momentum tensor. We also determine the nonequilibrium attractor using both the RTA and LO massless λΦ 4 number-conserving kernels. Furthermore, we find that the aHydro dynamics receives quantitatively important corrections when enforcing number conservation; however, the aHydro attractor itself is not modified substantially.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Optimizing Kernel Machines Using Deep Learning

Building highly non-linear and non-parametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring non-linear models through the construction of similarity functions from data. These methods are particularly preferred in cases where the training data sizes are limited and when prior knowledge of the data similarities is available. Despite their usefulness, they are limited by the computational complexity and their inability to support end-to-end learning with a task specific objective. On the other hand, deep neural networks have become the de facto solution for end-to-end inference in several learning paradigms. In this article, we explore the idea of using deep architectures to perform kernel machine optimization, for both computational efficiency and end-to-end inferencing. To this end, we develop the DKMO (Deep Kernel Machine Optimization) framework, that creates an ensemble of dense embeddings using Nystrõm kernel approximations and utilizes deep learning to generate task-specific representations through the fusion of the embeddings. Intuitively, the filters of the network are trained to fuse information from an ensemble of linear subspaces in the RKHS. Furthermore, we introduce the kernel dropout regularization to enable improved training convergence. Finally, we extend this framework to the multiple kernel case, by coupling a global fusion layer with pre-trained deep kernel machines for each of the constituent kernels. Using case studies with limited training data, and lack of explicit feature sources, we demonstrate the effectiveness of our framework over conventional model inferencing techniques.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Conserved Function of RNA Binding Motif Protein48 (RBM48) and Armadillo Repeat Containing 7 (ARMC7) in Maize and Human U12 Splicing

Splicing of pre-mRNA is fundamental for genes containing introns. Emerging data points to a deeply conserved role of this process in eukaryotic cell differentiation and proliferation. The vast majority of introns termed U2-type introns are spliced by a major spliceosome; however, there also exist rare and more conserved U12-type introns that are spliced by a minor spliceosome. Mutations that disrupt U12 splicing inhibit cell differentiation in both maize endosperm and human blood cells. However, the mechanism underlying this process is not well understood. The maize RNA Binding Motif Protein 48 (RBM48) plays an essential role as a U12 splicing factor and is required for proper maize kernel development. Using human cell lines, CRISPR-Cas9 knockdown of RBM48 demonstrated a conserved function in human U12 intron splicing. RBM48 and Armadillo Repeat Containing 7 (ARMC7) protein interact in both maize and human as part of the activated minor spliceosome. Here we show RBM48 and ARMC7 co-localization in the nucleus of human cell lines. Vertebrate ARMC7 is normally localized in the cytosol, whereas RBM48 is found in the nucleus. Our data suggests that the interaction plays a role in regulating ARMC7 localization or the efficiency of U12 intron splicing. We also performed comprehensive transcriptome profiling and identified a common subset of conserved Minor Intron Containing Genes (MIGs) impacted in both human and maize RBM48 knockout mutants. Of importance, the vast majority of these MIGs are associated with developmental defects in both plants and animals. This suggests that aberrant splicing of these targets has a high likelihood of mediating abnormal cell phenotypes. These data support evolutionarily conserved U12 splicing mechanisms between maize and humans with both RBM48 and ARMC7 having roles in the activated spliceosome.

maize↗
DOE OSTI2019

Spectrum and structure of octet and decuplet baryons and their positive-parity excitations

A continuum approach to the three-valence-quark bound-state problem in quantum field theory, employing parametrizations of the necessary kernel elements, is used to compute the spectrum and Poincare-covariant wave functions for all flavor- SU (3) octet and decuplet baryons and their first positive-parity excitations. Such analyses predict the existence of nonpointlike, dynamical quark-quark (diquark) correlations within all baryons; and a uniformly sound description of the systems studied is obtained by retaining flavor-antitriplet-scalar and flavor-sextet-pseudovector diquarks. Thus constituted, the rest-frame wave function of every system studied is primarily S wave in character; and the fast positive-parity excitation of each octet or decuplet baryon exhibits the characteristics of a radial excitation. Importantly, every ground-state octet and decuplet baryon possesses a radial excitation. Hence, the analysis predicts the existence and masses of positive-parity excitations of the Ξ, Ξ*, and Ω baryons, states which have not yet been empirically identified. This body of analysis suggests that the expression of emergent mass generation is the same in all u , d , and s baryons and, notably, that dynamical quark-quark correlations play an essential role in the structure of each one. Furthermore, it also provides the basis for developing an array of predictions that can be tested in new generation experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗