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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Collins-Soper kernel and reduced soft function in lattice QCD

We evaluate the Collins-Soper kernel and the reduced soft function in lattice QCD, incorporating 𝒪⁡(𝛼 𝑠 ) matching corrections. The calculation relies on the evaluation of the quasitransverse momentum–dependent wave function with asymmetric staple-shaped quark bilinear operators and four-point meson form factors. These quantities are computed nonperturbatively using two 𝑁 𝑓 =2 + 1 + 1 twisted-mass fermion ensembles with the same lattice spacing of 𝑎 = 0.093 fm: the first ensemble has a lattice size of 24 3 × 48 and a pion mass of 346 MeV, and the second one has a lattice size of 32 3 × 64 and a pion mass of 261 MeV. The Collins-Soper kernel and the soft function are needed for the determination of the transverse momentum–dependent parton distribution functions.

Lattice QCD↗
DOE OSTI2020

Reinforcement Learning via Gaussian Processes with Neural Network Dual Kernels

While deep neural networks (DNNs) and Gaussian Processes (GPs) are both popularly utilized to solve problems in reinforcement learning, both approaches feature undesirable drawbacks for challenging problems. DNNs learn complex non-linear embeddings, but do not naturally quantify uncertainty and are often data-inefficient to train. GPs infer posterior distributions over functions, but popular kernels exhibit limited expressivity on complex and high-dimensional data. Fortunately, recently discovered conjugate and neural tangent kernel functions encode the behavior of overparameterized neural networks in the kernel domain. We demonstrate that these kernels can be efficiently applied to regression and reinforcement learning problems by analyzing a baseline case study.We apply GPs with neural network dual kernels to solve reinforcement learning tasks for the first time. We demonstrate, using the well understood mountain-car problem, that GPs empowered with dual kernels perform at least as well as those using the conventional radial basis function kernel. Finally, we conjecture that by inheriting the probabilistic rigor of GPs and the powerful embedding properties of DNNs, GPs using NN dual kernels will empower future reinforcement learning models on difficult domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Prediction of atomization energy using graph kernel and active learning

Data-driven prediction of molecular properties presents unique challenges to the design of machine learning methods concerning data structure/dimensionality, symmetry adaption, and confidence management. In this paper, we present a kernel-based pipeline that can learn and predict the atomization energy of molecules with high accuracy. The framework employs Gaussian process regression to perform predictions based on the similarity between molecules, which is computed using the marginalized graph kernel. To apply the marginalized graph kernel, a spatial adjacency rule is first employed to convert molecules into graphs whose vertices and edges are labeled by elements and interatomic distances, respectively. We then derive formulas for the efficient evaluation of the kernel. Specific functional components for the marginalized graph kernel are proposed, while the effects of the associated hyperparameters on accuracy and predictive confidence are examined. We show that the graph kernel is particularly suitable for predicting extensive properties because its convolutional structure coincides with that of the covariance formula between sums of random variables. Using an active learning procedure, we demonstrate that the proposed method can achieve a mean absolute error of 0.62 ± 0.01 kcal/mol using as few as 2000 training samples on the QM7 dataset.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Time-dependent orbital-free density functional theory: Background and Pauli kernel approximations

Time-dependent orbital-free density functional theory (DFT) is an efficient method for calculating the dynamic properties of large-scale quantum systems due to the low computational cost compared to standard time-dependent DFT. In this work, we formalize this method by mapping the real system of interacting fermions onto a fictitious system of noninteracting bosons. The dynamic Pauli potential and associated kernel emerge as key ingredients of time-dependent orbital-free DFT. Using the uniform electron gas as a model system, we derive an approximate frequency-dependent Pauli kernel. Pilot calculations suggest that space nonlocality is a key feature for this kernel. Nonlocal terms arise already in the second-order expansion with respect to unitless frequency and reciprocal space variable ($\frac{ω}{qk_F}$ and $\frac{q}{2k_F}$, respectively). Given the encouraging performance of the proposed kernel, we expect it will lead to more accurate orbital-free DFT simulations of nanoscale systems out of equilibrium. Additionally, the proposed path to formulate nonadiabatic Pauli kernels presents several avenues for further improvements which can be exploited in future work to improve the results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Three-dimensional nonlocal anisotropic elasticity: a generalized continuum theory of Ångström-mechanics

In this paper, based on Eringen’s theory of nonlocal anisotropic elasticity, the three-dimensional nonlocal anisotropic elasticity of generalized Helmholtz type is developed. The derivation of a new three-dimensional nonlocal anisotropic kernel, which is the Green function of the three-dimensional anisotropic Helmholtz equation, enables to capture anisotropic length scale effects by means of a length scale tensor, which is a symmetric tensor of rank two. The derived nonlocal kernel function possesses up to six internal characteristic lengths on the Ångström-scale. The presented theory of nonlocal elasticity possesses the appropriate property to be a generalized continuum theory of Ångström-mechanics, since the range of its validity and applicability is up to the Ångström-scale. The connection between the theory of nonlocal anisotropic elasticity and lattice theory is established. The tensor function of nonlocal elastic moduli as well as the nonlocal kernel function is given in terms of the Hessian matrix in the lattice approach. In the framework of the considered theory, the modeling of dislocations in anisotropic materials taking into consideration anisotropic dislocation core effects is presented. Important dislocation key formulas, namely the anisotropic Peach–Koehler stress formula, the Peach–Koehler force and the anisotropic Blin’s formula, are derived. A major tool used in deriving the expression of anisotropic Blin’s formula is Kirchner’s so-called FF-tensor, which is here generalized toward nonlocal anisotropic elasticity. The main feature and advantage of the derived fields, compared with the corresponding ones in classical anisotropic elasticity, is that they are free of singularities. Numerical applications to straight dislocations in bcc Fe are given, revealing the ability and advantage of the considered theory to describe adequately nonsingular anisotropic stress and self-energy fields capturing the effects of anisotropy on the Ångström-scale.

42 ENGINEERING↗
DOE OSTI2020

Normal modes in thermal AdS via the Selberg zeta function

The heat kernel and quasinormal mode methods of computing 1-loop partition functions of spin s s fields on hyperbolic quotient spacetimes \mathbb{H}^{3}/\mathbb{Z} ℍ 3 / ℤ are related via the Selberg zeta function. We extend that analysis to thermal \text{AdS}_{2n+1} AdS 2 n + 1 backgrounds, with quotient structure \mathbb{H}^{2n+1}/\mathbb{Z} ℍ 2 n + 1 / ℤ . Specifically, we demonstrate the zeros of the Selberg function encode the normal mode frequencies of spin fields upon removal of non-square-integrable modes. With this information we construct the 1-loop partition functions for symmetric transverse traceless tensors in terms of the Selberg zeta function and find exact agreement with the heat kernel method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Coarse-Grained Density Functional Theory Predictions via Deep Kernel Learning

Scalable electronic predictions are critical for soft materials design. Recently, the Electronic Coarse-Graining (ECG) method was introduced to renormalize all-atom quantum chemical (QC) predictions to coarse-grained (CG) resolutions using deep neural networks (DNNs). While DNNs can learn complex representations that prove challenging for kernel-based methods, they are susceptible to overfitting and the overconfidence of uncertainty estimations. Here, we develop ECG within a GPU-accelerated Deep Kernel Learning (DKL) framework to enable CG QC predictions using range-separated hybrid density functional theory (DFT), obtaining a 107 speedup relative to naive all-atom QC. By treating the predicted electronic properties as random Gaussian Processes, DKL incorporates CG mapping degeneracy by learning the distribution of electronic energies as a function of CG configuration. DKL-ECG accurately reproduces molecular orbital energies from range-separated DFT while facilitating efficient training via active learning using the uncertainties provided by DKL. Further, we show that while active learning algorithms enable efficient sampling of a more diverse configurational space relative to random sampling, all explored query methods exhibit comparable performance for the examined system. We attribute this result to the significant overlap of the feature space and output property distributions across multiple temperatures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Two new fractional derivatives of variable order with non-singular kernel and fractional differential equation

In this paper, we introduce two new fractional derivatives with non-singular kernel and present a series of other fractional derivatives derived from the new formulations. We present some important results on uniformly convergent sequences of continuous functions with the help of the comparison principle and other results that allow the study of the limitation of the fractional nonlinear differential equation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Imposing correct jellium response is key to predict the density response by orbital-free DFT

Orbital-free density functional theory constitutes a computationally highly effective tool for modeling electronic structures of systems ranging from room-temperature materials to warm dense matter. Its accuracy critically depends on the employed kinetic energy (KE) density functional, which has to be supplied as an external input. In this work we consider several nonlocal and Laplacian-level KE functionals and use an external harmonic perturbation to compute the static density response at T = 0 K in the linear and beyond-linear response regimes. We test for the satisfaction of exact conditions in the limit of uniform densities and for how approximate KE functionals reproduce the density response of realistic materials (e.g., Al and Si) against the Kohn-Sham DFT reference, which employs the exact KE. The results illustrate that several functionals violate exact conditions in the uniform electron gas (UEG) limit. We find a strong correlation between the accuracy of the KE functionals in the UEG limit and in the strongly inhomogeneous case. This empirically demonstrates the importance of imposing the limit of UEG response for uniform densities and validates the use of the Lindhard function in the formulation of kernels for nonlocal functionals. This conclusion is substantiated by additional calculations for bulk aluminum (Al) with a face-centered cubic (fcc) lattice and silicon (Si) with an fcc lattice, body-centered cubic (bcc) lattice, and semiconducting crystal diamond state. The analysis of fcc Al, and fcc as well as bcc Si data follows closely the conclusions drawn for the UEG, allowing us to extend our conclusions to realistic systems that are subject to density inhomogeneities induced by ions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Uncertainty quantification tools for multiphase gas-solid flow simulations using MFIX

Computational fluid dynamics (CFD) has been widely studied and used in the scientific community and in the industry. Various models were proposed to solve problems in different areas. However, all models deviate from reality. Uncertainty quantification (UQ) process evaluates the overall uncertainties associated with the prediction of quantities of interest. In particular it studies the propagation of input uncertainties to the outputs of the models so that confidence intervals can be provided for the simulation results. In the present work, a non-intrusive quadrature-based uncertainty quantification (QBUQ) approach is proposed. The probability distribution function (PDF) of the system response can be then reconstructed using extended quadrature method of moments (EQMOM) and extended conditional quadrature method of moments (ECQMOM). The report first explains the theory of QBUQ approach, including methods to generate samples for problems with single or multiple uncertain input parameters, low order statistics, and required number of samples. Then methods for univariate PDF reconstruction (EQMOM) and multivariate PDF reconstruction (ECQMOM) are explained. The implementation of QBUQ approach into the open-source CFD code MFIX is discussed next. At last, QBUQ approach is demonstrated in several applications. The method is first applied to two examples: a developing flow in a channel with uncertain viscosity, and an oblique shock problem with uncertain upstream Mach number. The error in the prediction of the moment response is studied as a function of the number of samples, and the accuracy of the moments required to reconstruct the PDF of the system response is discussed. The QBUQ approach is then demonstrated by considering a bubbling fluidized bed as example application. The mean particle size is assumed to be the uncertain input parameter. The system is simulated with a standard two-fluid model with kinetic theory closures for the particulate phase implemented into MFIX. The effect of uncertainty on the disperse-phase volume fraction, on the phase velocities and on the pressure drop inside the fluidized bed are examined, and the reconstructed PDFs are provided for the three quantities studied. Then the approach is applied to a bubbling fluidized bed with two uncertain parameters, particle-particle and particle-wall restitution coefficients. Contour plots of the mean and standard deviation of solid volume fraction, solid phase velocities and gas pressure are provided. The PDFs of the response are reconstructed using EQMOM with appropriate kernel density functions. The simulation results are compared to experimental data provided by the 2013 NETL small-scale challenge problem. Lastly, the proposed procedure is demonstrated by considering a riser of a circulating fluidized bed as an example application. The mean particle size is considered to be the uncertain input parameter. Contour plots of the mean and standard deviation of solid volume fraction, solid phase velocities, and granular temperature are provided. Mean values and confidence intervals of the quantities of interest are compared to the experiment results. The univariate and bivariate PDF reconstructions of the system response are performed using EQMOM and ECQMOM.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

An accurate and asymptotically compatible collocation scheme for nonlocal diffusion problems

Here, in this paper, we develop and analyze a collocation scheme for solving the linear nonlocal diffusion problem with general kernels. To approximate the nonlocal diffusion operator, we take a classic trapezoidal rule based on the linear interpolation as the starting point, and then carefully derive a new improved quadrature rule, which is not only more accurate but also could avoid the evaluations of singular integrals. We then use this rule to construct a collocation scheme for solving the nonlocal diffusion equations, that produces a symmetric positive definite stiffness matrix with Toeplitz structure. The proposed scheme is rigorously shown to be of second order accurate with respect to the mesh size for the nonlocal problem with fixed horizon, and in particular, it can achieve higher order accuracy for the commonly used kernels in the literature. Furthermore, we also prove that the scheme is asymptotically compatible, i.e., the approximate solution of the nonlocal diffusion problem converges to the exact solution of the corresponding local PDE problem when the horizon and the mesh size both go to zero. Finally, numerical experiments are presented to verify the theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Acquisition of STEM Images by Adaptive Compressive Sensing

Compressive Sensing (CS) allows a signal to be sparsely measured first and accurately recovered later in software [1]. In scanning transmission electron microscopy (STEM), it is possible to compress an image spatially by reducing the number of measured pixels, which decreases electron dose and increases sensing speed [2,3,4]. The two requirements for CS to work are: (1) sparsity of basis coefficients and (2) incoherence of the sensing system and the representation system. However, when pixels are missing from the image, it is difficult to have an incoherent sensing matrix. Nevertheless, dictionary learning techniques such as Beta-Process Factor Analysis (BPFA) [5] are able to simultaneously discover a basis and the sparse coefficients in the case of missing pixels. On top of CS, we would like to apply active learning [6,7] to further reduce the proportion of pixels being measured, while maintaining image reconstruction quality. Suppose we initially sample 10% of random pixels. We wish to select the next 1% of pixels that are most useful in recovering the image. Now, we have 11% of pixels, and we want to decide the next 1% of “most informative” pixels. Active learning methods are online and sequential in nature. Our goal is to adaptively discover the best sensing mask during acquisition using feedback about the structures in the image. In the end, we hope to recover a high quality reconstruction with a dose reduction relative to the non-adaptive (random) sensing scheme. In doing this, we try three metrics applied to the partial reconstructions for selecting the new set of pixels: (1) variance, (2) Kullback-Leibler (KL) divergence using a Radial Basis Function (RBF) kernel, and (3) entropy. Figs. 1 and 2 display the comparison of Peak Signal-to-Noise (PSNR) using these three different active learning methods at different percentages of sampled pixels. At 20% level, all the three active learning methods underperform the original CS without active learning. However, they all beat the original CS as more of the “most informative” pixels are sampled. One can also argue that CS equipped with active learning requires less sampled pixels to achieve the same value of PSNR than CS with pixels randomly sampled, since all the three PSNR curves with active learning grow at a faster pace than that without active learning. For this particular STEM image, by observing the reconstructed images and the sensing masks, we find that while the method based on RBF kernel acquires samples more uniformly, the one on entropy samples more areas of significant change, thus less uniformly. The KL-divergence method performs the best in terms of reconstruction error (PSNR) for this example [8].

Xie, Weiyi↗
DOE OSTI2024

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↗
DOE OSTI2016

(Active) Learning on Groups of Data with Information-Theoretic Estimators

A wide range of machine learning problems, including astronomical inference about galaxy clusters, scene classification, parametric statistical inference, and predictions of public opinion, can be well-modeled as learning a function on (samples from) distributions. This project explores problems in learning such functions via kernel methods, particularly for large-scale problems. When learning from large numbers of distributions, the computation of typical methods scales between quadratically and cubically, and so they are not amenable to large datasets. We investigate the approach of approximate embeddings into Euclidean spaces such that inner products in the embedding space approximate kernel values between the source distributions. We first improve the understanding of the workhorse methods of random Fourier features: we show that of the two approaches in common usage, one is strictly superior. We then present a new embedding for a class of information-theoretic distribution distances, and evaluate it and existing embeddings on several real-world applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Multi-objective optimization of peel and shear strengths in ultrasonic metal welding using machine learning-based response surface methodology

Ultrasonic metal welding (UMW) is a solid-state joining technique with varied industrial applications. Despite of its numerous advantages, UMW has a relative narrow operating window and is sensitive to variations in process conditions. As such, it is imperative to quantitatively characterize the influence of welding parameters on the resulting joint quality. The quantification model can be subsequently used to optimize the parameters. Conventional response surface methodology (RSM) usually employs linear or polynomial models, which may not be able to capture the intricate, nonlinear input-output relationships in UMW. Furthermore, some UMW applications call for simultaneous optimization of multiple quality indices such as peel strength, shear strength, electrical conductivity, and thermal conductivity. To address these challenges, this paper develops a machine learning (ML)-based RSM to model the input-output relationships in UMW and jointly optimize two quality indices, namely, peel and shear strengths. The performance of various ML methods including spline regression, Gaussian process regression (GPR), support vector regression (SVR), and conventional polynomial regression models with different orders is compared. A case study using experimental data shows that GPR with radial basis function (RBF) kernel and SVR with RBF kernel achieve the best prediction accuracy. The obtained response surface models are then used to optimize a compound joint strength indicator that is defined as the average of normalized shear and peel strengths. In addition, the case study reveals different patterns in the response surfaces of shear and peel strengths, which has not been systematically studied in the literature. While developed for the UMW application, the method can be extended to other manufacturing processes.

42 ENGINEERING↗
DOE OSTI2018

Discrete Approximations of Determinantal Point Processes on Continuous Spaces: Tree Representations and Tail Triviality

We prove tail triviality of determinantal point processes μ on continuous spaces. Tail triviality has been proved for such processes only on discrete spaces, and hence we have generalized the result to continuous spaces. To do this, we construct tree representations, that is, discrete approximations of determinantal point processes enjoying a determinantal structure. There are many interesting examples of determinantal point processes on continuous spaces such as zero points of the hyperbolic Gaussian analytic function with Bergman kernel, and the thermodynamic limit of eigenvalues of Gaussian random matrices for Sine{sub 2},Airy{sub 2},Bessel{sub 2}, and Ginibre point processes. Our main theorem proves all these point processes are tail trivial.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Gaussian processes for inferring parton distributions

The extraction of parton distribution functions (PDFs) from experimental or lattice QCD data is an ill-posed inverse problem, where regularization strongly impacts both systematic uncertainties and the reliability of the results. We study a framework based on Gaussian Process Regression (GPR) to reconstruct PDFs from lattice QCD matrix elements. Within a Bayesian framework, Gaussian processes serve as flexible priors that encode uncertainties, correlations, and constraints without imposing rigid functional forms. We investigate a wide range of kernel choices, mean functions, and hyperparameter treatments. We quantify information gained from the data using the Kullback-Leibler divergence. Synthetic data tests demonstrate the consistency and robustness of the method. Our study establishes GPR as a systematic and non-parametric approach to PDF reconstruction, offering controlled uncertainty estimates and reduced model bias in lattice QCD analyses.

hadronic spectroscopy↗