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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Kernel polynomial method for linear spin wave theory

Calculating dynamical spin correlations is essential for matching model magnetic exchange Hamiltonians to momentum-resolved spectroscopic measurements. A major numerical bottleneck is the diagonalization of the dynamical matrix, especially in systems with large magnetic unit cells, such as those with incommensurate magnetic structures or quenched disorder. In this paper, we demonstrate an efficient scheme based on the kernel polynomial method for calculating dynamical correlations of relevance to inelastic neutron scattering experiments. This method reduces the scaling of numerical cost from cubic to linear in the magnetic unit cell size.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Computing the QRPA level density with the finite amplitude method

Here, we describe a new algorithm to calculate the vibrational nuclear level density of an atomic nucleus. Fictitious perturbation operators that probe the response of the system are generated by drawing their matrix elements from some probability distribution function. We use the Finite Amplitude Method to explicitly compute the response for each such sample. With the help of the Kernel Polynomial Method, we build an estimator of the vibrational level density and provide the upper bound of the relative error in the limit of infinitely many random samples. The new algorithm can give accurate estimates of the vibrational level density. Since it is based on drawing multiple samples of perturbation operators, its computational implementation is naturally parallel and scales like the number of available processing units.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Localization dynamics in a centrally coupled system

In systems in which interactions couple a central degree of freedom and a bath, one would expect signatures of the bath's phase to be reflected in the dynamics of the central degree of freedom. This has been recently explored in connection with many-body localized baths coupled with a central qubit or a single-cavity mode - systems with growing experimental relevance in various platforms. Such models also have an interesting connection with Floquet many-body localization via quantizing the external drive, although this has been relatively unexplored. Here we adapt the multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) method, a well-known tree tensor network algorithm, to numerically simulate the dynamics of a central degree of freedom, represented by a d-level system (qudit), coupled to a disordered interacting one-dimensional spin bath. ML-MCTDH allows us to reach ≈10 2 lattice sites, a far larger system size than what is feasible with exact diagonalization or kernel polynomial methods. From the intermediate time dynamics, we find a well-defined thermodynamic limit for the qudit dynamics upon appropriate rescaling of the system-bath coupling. The spin system shows similar scaling collapse in the Edward-Anderson spin-glass order parameter or entanglement entropy at relatively short times. At longer timescales, we see slow growth of the entanglement, which may arise from dephasing mechanisms in the localized system or long-range interactions mediated by the central degree of freedom. Similar signs of localization are shown to appear as well with unscaled system-bath coupling.

1-dimensional spin chains↗
DOE OSTI2024

Absence of quantization in the circular photogalvanic effect in disordered chiral Weyl semimetals

The circularly polarized photogalvanic effect (CPGE) is studied in chiral Weyl semimetals with short-range quenched disorder. Without disorder, the topological properties of chiral Weyl semimetals lead to quantization of the CPGE, which is a second-order optical response. Furthermore, using a combination of diagrammatic perturbation theory in the continuum and exact numerical calculations via the kernel polynomial method on a lattice model, we show that disorder perturbatively destabilizes the quantization of the CPGE.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Semiclassical dynamics of spin density waves

Here, we present a theoretical framework for equilibrium and nonequilibrium dynamical simulation of quantum states with spin-density-wave (SDW) order. Within a semiclassical adiabatic approximation that retains electron degrees of freedom, we demonstrate that the SDW order parameter obeys a generalized Landau-Lifshitz equation. With the aid of an enhanced kernel polynomial method, our linear-scaling quantum Landau-Lifshitz dynamics (QLLD) method enables dynamical SDW simulations with N ≃ 10 5 lattice sites. Our real-space formulation can be used to compute dynamical responses, such as the dynamical structure factor, of complex and even inhomogeneous SDW configurations at zero or finite temperatures. Applying the QLLD to study the relaxation of a noncoplanar topological SDW under the excitation of a short pulse, we further demonstrate the crucial role of spatial correlations and fluctuations in the SDW dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Vacancy-Induced Tunable Kondo Effect in Twisted Bilayer Graphene

In single sheets of graphene, vacancy-induced states have been shown to host an effective spin-1/2 hole that can be Kondo screened at low temperatures. Here, we show how these vacancy-induced impurity states survive in twisted bilayer graphene (TBG), which thus provides a tunable system to probe the critical destruction of the Kondo effect in pseudogap hosts. Ab initio calculations and atomic-scale modeling are used to determine the nature of the vacancy states in the vicinity of the magic angle in TBG, demonstrating that the vacancy can be treated as a quantum impurity. Utilizing this insight, we construct an Anderson impurity model with a TBG host that we solve using the numerical renormalization group combined with the kernel polynomial method. We determine the phase diagram of the model and show how there is a strict dichotomy between vacancies in the AA/BB versus AB/BA tunneling regions. In AB/BA vacancies, the Kondo temperature at the magic angle develops a broad distribution with a tail to vanishing temperatures due to multifractal wave functions at the magic angle. Finally, we argue that scanning tunneling microscopy in the vicinity of the vacancy can act as a probe of both the critical single-particle states and the underlying many-body ground state in magic-angle TBG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws

We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal constitutive laws for stress wave propagation models. The method is an optimization-based technique in which the nonlocal kernel function is approximated via Bernstein polynomials. The kernel, including both its functional form and parameters, is derived so that when used in a nonlocal solver, it generates solutions that closely match high-fidelity data. The optimal kernel therefore acts as a homogenized nonlocal continuum model that accurately reproduces wave motion in a smaller-scale, more detailed model that can include multiple materials. We apply this technique to wave propagation within a heterogeneous bar with a periodic microstructure. Several one-dimensional numerical tests illustrate the accuracy of our algorithm. The optimal kernel is demonstrated to reproduce high-fidelity data for a composite material in applications that are substantially different from the problems used as training data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Tensorized Feature Spaces for Feature Explosion

In this paper 1 1 This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-000R22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan) This research used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-000R22725., we present a novel framework that uses tensor factorization to generate richer feature spaces for pixel classification in hyperspectral images. In particular, we assess the performance of different tensor rank decomposition methods as compared to the traditional kernel-based approaches for the hyperspectral image classification problem. We propose Orion, which takes as input a hyperspectral image tensor and a rank and outputs an enhanced feature space from the factor matrices of the decomposed tensor. Our method is a feature explosion technique that inherently maps low dimensional input space in $\mathbb{R}^{K}$ to high dimensional space in $\mathbb{R}^{R}$ , where $R\gg K$ , say in the order of 1000x, like a kernel. We show how the proposed method exploits the multi-linear structure of hyperspectral three dimensional tensor. We demonstrate the effectiveness of our method with experiments on three publicly available hyperspectral datasets with labeled pixels and compare their classification performance against traditional linear and non-linear supervised learning methods such as SVM with Linear, Polynomial, RBF kernels, and the Multi-Layer Perceptron model. Finally, we explore the relationship between the rank of the tensor decomposition and the classification accuracy using several hyperspectral datasets with ground truth.

Pasricha, Ravdeep Singh↗
DOE OSTI2022

Surface analysis insight note: Differentiation methods applicable to noisy data for determination of sp2‐ versus sp3‐hybridization of carbon allotropes and AES signal strengths

The derivatives of the spectra are commonly used for quantification in Auger Electron Spectroscopy (AES) spectra, while the derivative of the KLL C Auger line has proven to be valuable in obtaining a measure of the relative proportions of sp 2 ‐ and sp 3 ‐hybridization using the D‐parameter in both AES and X‐ray Photoelectron Spectroscopy (XPS). Differentiation of X‐ray Photoelectron Spectroscopy (XPS) and Auger Electron Spectroscopy (AES) spectra by numerical means is presented and illustrated for polymeric, such as PEEK and Nylon, as well as for graphitic materials including highly ordered pyrolytic graphite and graphene oxide. The most commonly available Savitzky–Golay method is explained mathematically and developed through the case of constructing a 5‐point quadratic polynomial convolution kernel suitable for differentiating spectra of adequate signal to noise. The concept of differentiation of spectra where signal to noise is less than adequate is also developed. Two alternative strategies to Savitzky–Golay differentiation are presented, which fit curves to data that allow derivatives to be obtained where Savitzky–Golay would otherwise fail. These alternative methods involve constructing a parametric curve that fits data over the entire energy interval of interest. Derivatives of spectra are then obtained by differentiating these parametric curves directly. A comparison of results for different materials for which specific sp 2 ‐ vs sp 3 ‐hybridized carbon proportions are of interest is used to emphasize the importance of characterizing methods used to differentiate spectra and understanding the characteristics of instrumentation used to measure spectra. The case for using Principal Component Analysis noise reduction with C KLL spectra is made for spectra collected from a heterogeneous graphene oxide sample.

Fairley, Neal↗
DOE OSTI2023

Generalized moving least squares vs. radial basis function finite difference methods for approximating surface derivatives

Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least squares (GMLS) and radial basis function finite differences (RBF-FD) have been shown to be effective for this task as they can give high orders of accuracy at low computational cost, and they can be applied to surfaces defined only by point clouds. However, there have yet to be any studies that perform a direct comparison of these methods for approximating surface differential operators (SDOs). The first purpose of this work is to fill that gap. For this comparison, we focus on an RBF-FD method based on polyharmonic spline kernels and polynomials (PHS+Poly) since they are most closely related to the GMLS method. Additionally, we use a relatively new technique for approximating SDOs with RBF-FD called the tangent plane method since it is simpler than previous techniques and natural to use with PHS+Poly RBF-FD. Further, the second purpose of this work is to relate the tangent plane formulation of SDOs to the local coordinate formulation used in GMLS and to show that they are equivalent when the tangent space to the surface is known exactly. The final purpose is to use ideas from the GMLS SDO formulation to derive a new RBF-FD method for approximating the tangent space for a point cloud surface when it is unknown. For the numerical comparisons of the methods, we examine their convergence rates for approximating the surface gradient, divergence, and Laplacian as the point clouds are refined for various parameter choices. We also compare their efficiency in terms of accuracy per computational cost, both when including and excluding setup costs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A 3D Ginibre Point Field

We introduce a family of three-dimensional random point fields using the concept of the quaternion determinant. The kernel of each field is an n-dimensional orthogonal projection on a linear space of quaternionic polynomials. We find explicit formulas for the basis of the orthogonal quaternion polynomials and for the kernel of the projection. For number of particles n→∞, we calculate the scaling limits of the point field in the bulk and at the center of coordinates. We compare our construction with the previously introduced Fermi-sphere point field process.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Affine Approximation of Parametrized Kernels and Model Order Reduction for Nonlocal and Fractional Laplace Models

In this work, we consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by the fractional power $s\in(0,1)$, are studied. Furthermore, in order to provide an efficient and reliable approximation of the solution for different values of the parameters, we develop the reduced basis method as a parametric model order reduction approach. Major difficulties arise since the kernels are not affine in the parameters, singular, and discontinuous. Moreover, the spatial regularity of the solutions depends on the varying fractional power $s$. To address this, we derive regularity and differentiability results with respect to $\delta$ and $s$, which are of independent interest for other applications such as optimization and parameter identification. We then use these results to construct affine approximations of the kernels by local polynomials. Finally, we certify the method by providing reliable a posteriori error estimators, which account for all approximation errors, and support the theoretical findings by numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Active learning of reactive Bayesian force fields applied to heterogeneous catalysis dynamics of H/Pt

Abstract Atomistic modeling of chemically reactive systems has so far relied on either expensive ab initio methods or bond-order force fields requiring arduous parametrization. Here, we describe a Bayesian active learning framework for autonomous “on-the-fly” training of fast and accurate reactive many-body force fields during molecular dynamics simulations. At each time-step, predictive uncertainties of a sparse Gaussian process are evaluated to automatically determine whether additional ab initio training data are needed. We introduce a general method for mapping trained kernel models onto equivalent polynomial models whose prediction cost is much lower and independent of the training set size. As a demonstration, we perform direct two-phase simulations of heterogeneous H 2 turnover on the Pt(111) catalyst surface at chemical accuracy. The model trains itself in three days and performs at twice the speed of a ReaxFF model, while maintaining much higher fidelity to DFT and excellent agreement with experiment.

42 ENGINEERING↗
DOE OSTI2018

Quantum Optimization and Approximation Algorithms

Shor's groundbreaking quantum algorithm for integer factoring provides an exponential speedup over the best-known classical algorithms. In the 20 years since Shor's algorithm was conceived, only a handful of fundamental quantum algorithmic kernels, generally providing modest polynomial speedups over classical algorithms, have been invented. To better understand the potential advantage quantum resources provide over their classical counterparts, one may consider other resources than execution time of algorithms. Quantum Approximation Algorithms direct the power of quantum computing towards optimization problems where quantum resources provide higher-quality solutions instead of faster execution times. We provide a new rigorous analysis of the recent Quantum Approximate Optimization Algorithm, demonstrating that it provably outperforms the best known classical approximation algorithm for special hard cases of the fundamental Maximum Cut graph-partitioning problem. We also develop new types of classical approximation algorithms for finding near-optimal low-energy states of physical systems arising in condensed matter by extending seminal discrete optimization techniques. Our interdisciplinary work seeks to unearth new connections between discrete optimization and quantum information science.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Testing the LSST Difference Image Analysis Pipeline Using Synthetic Source Injection Analysis

Abstract We evaluate the performance of the Legacy Survey of Space and Time Science Pipelines Difference Image Analysis (DIA) on simulated images. By adding synthetic sources to galaxies on images, we trace the recovery of injected synthetic sources to evaluate the pipeline on images from the Dark Energy Science Collaboration Data Challenge 2. The pipeline performs well, with efficiency and flux accuracy consistent with the signal-to-noise ratio of the input images. We explore different spatial degrees of freedom for the Alard–Lupton polynomial-Gaussian image subtraction kernel and analyze for trade-offs in efficiency versus artifact rate. Increasing the kernel spatial degrees of freedom reduces the artifact rate without loss of efficiency. The flux measurements with different kernel spatial degrees of freedom are consistent. We also here provide a set of DIA flags that substantially filter out artifacts from the DIA source table. We explore the morphology and possible origins of the observed remaining subtraction artifacts and suggest that given the complexity of these artifact origins, a convolution kernel with a set of flexible bases with spatial variation may be needed to yield further improvements.

Liu, S. (ORCID:0000000244612143)↗
DOE OSTI2024

Galaxy bispectrum in the spherical Fourier-Bessel basis

The bispectrum, the three-point correlation in Fourier space, is a crucial statistic for studying many effects targeted by the next-generation galaxy surveys, such as primordial non-Gaussianity (PNG) and general relativistic (GR) effects on large scales. In this work we develop a formalism for the bispectrum in the spherical Fourier-Bessel (SFB) basis—a natural basis for computing correlation functions on the curved sky, as it diagonalizes the Laplacian operator in spherical coordinates. Working in the SFB basis allows for line-of-sight effects such as redshift space distortions and GR to be accounted for exactly, i.e., without having to resort to perturbative expansions to go beyond the plane-parallel approximation. Only analytic results for the SFB bispectrum exist in the literature given the intensive computations needed. We numerically calculate the SFB bispectrum for the first time, enabled by a few techniques: We implement a template decomposition of the redshift-space kernel Z 2 into Legendre polynomials, and separately treat the PNG and velocity-divergence terms. We derive an identity to integrate a product of three spherical harmonics connected by a Dirac delta function as a simple sum and use it to investigate the limit of a homogeneous and isotropic Universe. Furthermore, we present a formalism for convolving the signal with separable window functions and use a toy spherically symmetric window to demonstrate the computation and give insights into the properties of the observed bispectrum signal. While our implementation remains computationally challenging, it is a step toward a feasible full extraction of information on large scales via a SFB bispectrum analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

The effective number of parameters in kernel density estimation

We devise a new formula for measuring the effective degrees of freedom (EDoF) in kernel density estimation (KDE). Starting from the orthogonal polynomial sequence (OPS) expansion for the ratio of the empirical to the oracle density, we show how convolution with the kernel leads to a new OPS with respect to which one may express the resulting KDE. The expansion coefficients of the two OPS systems can then be related via a kernel sensitivity matrix, which leads to a natural oracle definition of EDoF through the trace operator. Asymptotic properties of the (empirical) plug-in EDoF are worked out through influence functions, and connections with other empirical EDoFs are established. Minimization of Kullback-Leibler divergence is investigated as an alternative to integrated squared error based bandwidth selection rules, yielding a new normal scale rule. The methodology, which arises from a proper oracle formulation and is not restricted to convolution kernels, suggests the possibility of a new bandwidth selection rule based on an information criterion such as AIC.

bandwidth selection↗
DOE OSTI2018

Superconvergence results of Legendre spectral projection methods for Volterra integral equations of second kind

In this paper, Legendre spectral projection methods are applied for the Volterra integral equations of second kind with a smooth kernel. We prove that the approximate solutions of the Legendre Galerkin and Legendre collocation methods converge to the exact solution with the order O(n{sup −r}) in L{sup 2}-norm and order O(n{sup −r+(1/2)}) in infinity norm, and the iterated Legendre Galerkin solution converges with the order O(n{sup −2r}) in both L{sup 2}-norm and infinity norm, whereas the iterated Legendre collocation solution converges with the order O(n{sup −r}) in both L{sup 2}-norm and infinity norm, n being the highest degree of Legendre polynomials employed in the approximation and r being the smoothness of the kernels. We have also considered multi-Galerkin method and its iterated version, and prove that the iterated multi-Galerkin solution converges with the order O(n{sup −3r}) in both infinity and L{sup 2} norm. Numerical examples are given to illustrate the theoretical results.

97 MATHEMATICS AND COMPUTING↗