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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Asynchronous Iterative Solvers for Extreme-Scale Computing

The Asynchronous Iterative Solvers for Extreme-Scale Computing (AsyncIS) project aims to explore more efficient numerical algorithms by decreasing their overhead. AsyncIS does this by replacing the outer Krylov subspace solver with an asynchronous optimized Schwarz method, thereby removing the global synchronization and bulk synchronous operations typically used in numerical codes. AsyncIS—a U.S. Department of Energy (DOE)-funded collaboration between Georgia Tech, the University of Tennessee, Knoxville, Temple University, and Sandia National Laboratories—also focuses on the development and optimization of asynchronous preconditioners (i.e., preconditioners that are generated and/or applied in an asynchronous fashion). The novel preconditioning algorithms that provide fine-grained parallelism enable preconditioned Krylov solvers to run efficiently on large-scale distributed systems and manycore accelerators like GPUs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Grassmannian Diffusion Maps--Based Dimension Reduction and Classification for High-Dimensional Data

This work introduces the Grassmannian diffusion maps (GDMaps), a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the Grassmann manifold. Here, the method is designed for applications, such as image recognition and data-based classification of constrained high-dimensional data where each data point itself is a high-dimensional object (i.e., a large matrix) that can be compactly represented in a lower-dimensional subspace. The GDMaps is composed of two stages. The first is a pointwise linear dimensionality reduction wherein each high-dimensional object is mapped onto the Grassmann manifold representing the low-dimensional subspace on which it resides. The second stage is a multipoint nonlinear kernel-based dimension reduction using diffusion maps to identify the subspace structure of the points on the Grassmann manifold. To this end, an appropriate Grassmannian kernel is used to construct the transition matrix of a random walk on a graph connecting points on the Grassmann manifold. Spectral analysis of the transition matrix yields low-dimensional Grassmannian diffusion coordinates embedding the data into a low-dimensional reproducing kernel Hilbert space. Further, a novel data classification/recognition technique is developed based on the construction of an overcomplete dictionary of reduced dimension whose atoms are given by the Grassmannian diffusion coordinates. Three examples are considered. First, a "toy" example shows that the GDMaps can identify an appropriate parametrization of structured points on the unit sphere. The second example demonstrates the ability of the GDMaps to revealing the intrinsic subspace structure of high-dimensional random field data. In the last ex- ample, a face recognition problem is solved considering face images subject to varying illumination conditions, changes in face expressions, and occurrence of occlusions. The technique presented high recognition rates (i.e., 95% in the best case) using a fraction of the data required by conventional methods.

42 ENGINEERING↗
DOE OSTI2023

Optimization of the generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double- β decay: Ridge regression for nuclei with axial deformation

The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. The computational complexity of the GCM increases rapidly with the number of collective coordinates. It imposes a strong restriction on the applicability of the method. In this work, we propose a subspace-reduction algorithm that employs optimal statistical ML models as surrogates for exact quantum-number projection calculations for norm and Hamiltonian kernels. The model space of the original GCM is reduced to a subspace relevant for nuclear low energy spectra and the NME of ground state to ground state 0νββ decay based on the orthogonality condition (OC) and the energy-transition-orthogonality procedure (ENTROP), respectively. For simplicity, the polynomial ridge regression (RR) algorithm is used to learn the norm and Hamiltonian kernels of axially deformed configurations. The efficiency and accuracy of this algorithm are illustrated for 76 Ge and 76 Se by comparing results obtained using the optimal RR models to direct GCM calculations. The low-lying energy spectra of 76 Ge and 76 Se, as well as the 0νββ-decay NME between their ground states, are computed. Furthermore, the results show that the performance of the GCM+OC/ENTROP+RR is more robust than that of the GCM+RR alone, and the former can reproduce the results of the original GCM calculation accurately with a significantly reduced computational cost.

59 ≤ A ≤ 89↗
DOE OSTI2020

Reduced scaling extended multi-state CASPT2 (XMS-CASPT2) using supporting subspaces and tensor hyper-contraction

We present a reduced scaling formulation of the extended multi-state CASPT2 (XMS-CASPT2) method, which is based on our recently developed state-specific CASPT2 (SS-CASPT2) formulation using supporting subspaces and tensor hyper-contraction. By using these two techniques, the off-diagonal elements of the effective Hamiltonian can be computed with only O(N 3 ) operations and O(N 2 ) memory, where N is the number of basis functions. Furthermore, this limits the overall computational scaling to O(N 4 ) operations and O(N 2 ) memory. Thus, excited states can now be obtained at the same reduced (relative to previous algorithms) scaling we achieved for SS-CASPT2.

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

Convergence of Eigenvector Continuation

Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to selected training values of the control parameters. The method has proven to be very efficient and accurate for interpolating and extrapolating eigenvectors. However, almost nothing is known about how the method converges, and its rapid convergence properties have remained mysterious. In this Letter, we present the first study of the convergence of eigenvector continuation. In order to perform the mathematical analysis, we introduce a new variant of eigenvector continuation that we call vector continuation. We first prove that eigenvector continuation and vector continuation have identical convergence properties and then analyze the convergence of vector continuation. Our analysis shows that, in general, eigenvector continuation converges more rapidly than perturbation theory. The faster convergence is achieved by eliminating a phenomenon that we call differential folding, the interference between nonorthogonal vectors appearing at different orders in perturbation theory. From our analysis we can predict how eigenvector continuation converges both inside and outside the radius of convergence of perturbation theory. Further, while eigenvector continuation is a nonperturbative method, we show that its rate of convergence can be deduced from power series expansions of the eigenvectors. Our results also yield new insights into the nature of divergences in perturbation theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Bosonic field digitization for quantum computers

Quantum simulation of quantum field theory is a flagship application of quantum computers that promises to deliver capabilities beyond classical computing. The realization of quantum advantage will require methods that can accurately predict error scaling as a function of the resolution and parameters of the model and that can be implemented efficiently on quantum hardware. In this paper, we address the representation of lattice bosonic fields in a discretized field amplitude basis, develop methods to predict error scaling, and present efficient qubit implementation strategies. A low-energy subspace of the bosonic Hilbert space, defined by a boson occupation number cutoff, can be represented with exponentially good accuracy by a low-energy subspace of a finite-size Hilbert space. The finite representation construction and the associated errors are directly related to the accuracy of the Nyquist-Shannon sampling and the finite Fourier transforms of the boson number states in the field and the conjugate-field bases. We analyze the relation between the boson mass, the discretization parameters used for wave function sampling, and the finite representation size. Numerical simulations of small size Φ 4 problems demonstrate that the boson mass optimizing the sampling of the ground state wave function is a good approximation to the optimal boson mass yielding the minimum low-energy subspace size. However, we find that accurate sampling of general wave functions does not necessarily result in accurate representation. Finally, we develop methods for validating and adjusting the discretization parameters to achieve more accurate simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Spatial noise correlations in a Si/SiGe two-qubit device from Bell state coherences

Here, we study spatial noise correlations in a Si/SiGe two-qubit device with integrated micromagnets. Our method relies on the concept of decoherence-free subspaces, whereby we measure the coherence time for two different Bell states, designed to be sensitive only to either correlated or anticorrelated noise, respectively. From these measurements we find weak correlations in low-frequency noise acting on the two qubits, while no correlations could be detected in high-frequency noise. We expect nuclear spin noise to have an uncorrelated nature. A theoretical model and numerical simulations give further insight into the additive effect of multiple independent (anti)correlated noise sources with an asymmetric effect on the two qubits as can result from charge noise. Such a scenario in combination with nuclear spins is plausible given the data and the known decoherence mechanisms. This work is highly relevant for the design of optimized quantum error correction codes for spin qubits in quantum dot arrays, as well as for optimizing the design of future quantum dot arrays.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Applications to Materials for Catalysis and Electrochemistry

Modeling complex materials using high-fidelity, ab initio methods at low cost is a fundamental goal for quantum chemical software packages. The GW approximation and random phase approximation (RPA) provide a unified description of both electronic structure and total energies using the same physics in a many-body perturbative approach that can be more accurate than generalized-gradient density functional theory (DFT) methods. However, GW/RPA implementations have historically been limited to either specific materials classes or application toward small chemical systems. Here, the static subspace approximation allows for reduced cost full-frequency GW/RPA calculations and has previously been benchmarked thoroughly for GW calculations. Here, we describe our approach to including partial occupations of electronic orbitals in full-frequency GW and RPA calculations for the study of electrocatalysts. We benchmarked RPA total energy calculations using the subspace approximation across a diverse test suite of materials for a variety of computational parameters. The benchmarking quantifies the impact of different extrapolation procedures for representing the static polarizability at infinite screened cutoff, and shows that using screened cutoffs above 20-25 Ryd result in diminishing accuracy returns for predicting RPA total energies. Additionally, for moderately sized electrocatalytic models, 2-3 times fewer computational resources are used to compute RPA total energies by representing the static polarizability with 20-30% of the static subspace basis, with an error of approximately 0.01 eV or better in RPA adsorption energy calculations. Finally, we show that for these electrochemical models RPA can shift DFT adsorption energy shifts by up to 0.5 eV and that GW can frequently shift DFT eigenvalues of surface and adsorbate states by approximately 0.5-1 eV.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Analysis of diagonal G and subspace W approximations within fully self-consistent GW calculations for bulk semiconducting systems

Fully self-consistent GW (sc-GW) methods are now available to evaluate quasiparticle and spectral properties of various molecular and bulk systems. However, such techniques based on the full matrix of G and W are computationally demanding. Additionally, the routinely used single-shot GW approximation (G 0 W 0 ) has an undesirable dependency on the choice of initial exchange-correlation functional. In the literature, many so-called self-consistent GW methods are based on diagonal approximation of G and low-ranking approximation of W. It is thus worth checking how good such approximations are in comparison with the full matrix method. In this work, we consider AlAs, AlP, GaP, and ZnS as the prototype systems to perform sc-GW calculations by expressing the full G matrix using a plane-wave basis set. We compared our sc-GW results with the diagonal G and subspace W approximated sc-GW results (sc-GW-diagG and sc-GW-subW methods). In the sc-GW-diagG method, interacting G is expanded in the eigenvectors of noninteracting G such that only diagonal elements are retained, whereas the number of eigenmodes is truncated in sc-GW-subW calculations. A systematic analysis of the results obtained from the above techniques is presented. The differences in the quasiparticle band gap between the approximated and the full matrix sc-GW approaches are mostly less than 1.7%, which validates such widely adopted approximations, and also shows how such low-ranking approximation can be used to include higher-order terms such as the vertex correction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Quantum simulation of boson-related Hamiltonians: techniques, effective Hamiltonian construction, and error analysis

Elementary quantum mechanics proposes that a closed physical system consistently evolves in a reversible manner. However, control and readout necessitate the coupling of the quantum system to the external environment, subjecting it to relaxation and decoherence. Consequently, system-environment interactions are indispensable for simulating physically significant theories. A broad spectrum of physical systems in condensed-matter and high-energy physics, vibrational spectroscopy, and circuit and cavity QED necessitates the incorporation of bosonic degrees of freedom, such as phonons, photons, and gluons, into optimized fermion algorithms for near-future quantum simulations. In particular, when a quantum system is surrounded by an external environment, its basic physics can usually be simplified to a spin or fermionic system interacting with bosonic modes. Nevertheless, troublesome factors such as the magnitude of the bosonic degrees of freedom typically complicate the direct quantum simulation of these interacting models, necessitating the consideration of a comprehensive plan. This strategy should specifically include a suitable fermion/boson-to-qubit mapping scheme to encode sufficiently large yet manageable bosonic modes, and a method for truncating and/or downfolding the Hamiltonian to the defined subspace for performing an approximate but highly accurate simulation, guided by rigorous error analysis. In this pedagogical tutorial review, we aim to provide such an exhaustive strategy, focusing on encoding and simulating certain bosonic-related model Hamiltonians, inclusive of their static properties and time evolutions. Specifically, we emphasize two aspects: (1) the discussion of recently developed quantum algorithms for these interacting models and the construction of effective Hamiltonians, and (2) a detailed analysis regarding a tightened error bound for truncating the bosonic modes for a class of fermion-boson interacting Hamiltonians.

bosonic Hamiltonian↗
DOE OSTI2021

Efficacy of the Method of Four Coefficients to Determine Charge-Carrier Scattering

The investigation of the electronic properties of semiconductors from transport measurements (i.e., resistivity, Hall, and Seebeck coefficient measurements) is challenging due to the averaging of charge-carrier dynamics inherent in such measurements. Here, we investigate the incorporation of a fourth measurement of electronic transport, the Nernst coefficient, into the analysis, termed the method of four coefficients. This approach yields the Fermi level, effective mass, scattering exponent, and relaxation time prefactor. We begin with a review of the underlying mathematics and investigate the mapping between the four-dimensional material property and transport coefficient spaces. We then investigate how the traditional single-parabolic band method yields a single, potentially incorrect point on the solution subspace. This uncertainty can be resolved through Nernst coefficient measurements and we map the span of the ensuing subspace. We conclude with an investigation of how sensitive the analysis of transport coefficients is to experimental error for different sample types.

charge carriers↗
DOE OSTI2022

Ferroelectric HfO 2 and the importance of strain

Ferroelectric oxides based on HfO 2 show tremendous promise for the next generation of memory and logic devices. The ferroelectric polymorph is one of several that can be derived from the high symmetry cubic fluorite structure of HfO 2 . A single grain of HfO 2 may consist of a coherent mixture of multiple orientational and translational variants of different polymorphs. Here, we use symmetry-adapted strain-order parameters to elucidate the relationship between the different HfO 2 polymorphs and their symmetrically equivalent variants. We use first-principles electronic structure methods to identify minimum energy pathways and map them in subspaces of the symmetry-adapted strain order parameters. We next investigate the atomic structure of domain boundaries that separate coexisting variants of ferroelectric HfO 2 . Further, we rely on Gibbsian excess quantities and a precise specification of mechanical boundary conditions to describe the thermodynamic properties of domain boundaries. Our first-principles calculations show that the O and Hf shuffle arrangement within a domain boundary is closely related to the intermediate shuffle patterns of the homogeneous pathways between ferroelectric variants. Furthermore, the preferred structure within a boundary is very sensitive to local strain constraints imposed by the adjacent ferroelectric variants, leading to highly anisotropic domain boundary energies.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Towards dynamical low-rank approximation for neutrino kinetic equations. Part I: Analysis of an idealized relaxation model

Dynamical low-rank approximation (DLRA) is an emerging tool for reducing computational costs and provides memory savings when solving high-dimensional problems. Here, in this work, we propose and analyze a semi-implicit dynamical low-rank discontinuous Galerkin (DLR-DG) method for the space homogeneous kinetic equation with a relaxation operator, modeling the emission and absorption of particles by a background medium. Both DLRA and the discontinuous Galerkin (DG) scheme can be formulated as Galerkin equations. To ensure their consistency, a weighted DLRA is introduced so that the resulting DLR-DG solution is a solution to the fully discrete DG scheme in a subspace of the standard DG solution space. Similar to the standard DG method, we show that the proposed DLR-DG method is well-posed. We also identify conditions such that the DLR-DG solution converges to the equilibrium. Numerical results are presented to demonstrate the theoretical findings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Accurate and efficient description of interacting carriers in quantum nanostructures by selected configuration interaction and perturbation theory

In this paper, we present a method to accurately and efficiently calculate many-body states of interacting carriers in quantum nanostructures based on a combination of iterative selection of configurations and perturbation theory. This method enables investigations of large excitonic complexes and multielectron systems with near full configuration interaction accuracy, even though only a small subspace of the full many-body Hilbert space is sampled, thus saving orders of magnitudes in computational resources. Important advantages of this method are that the convergence is controlled by a single parameter, the threshold, and that ground and excited states can be treated on an equal footing. On the example of InAsP nanowire quantum dots described using a million-atom tight-binding approach, we demonstrate the extreme efficiency of the method by numerical studies of large excitonic complexes filling up to the fourth electronic shell. We find that the method generally converges fast as a function of the threshold, profiting from a significant acceleration due to the perturbative corrections. The role of the choice of single-particle basis states is discussed. It is found that the algorithm converges faster in the Hartree-Fock basis only for highly charged systems, where Coulomb repulsion dominates. Finally, based on the observation that second-order perturbative energy corrections only depend on off-diagonal elements of the many-body Hamiltonian, we present a way to accurately calculate many-body states that requires only a relatively small number of Coulomb matrix elements.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A unified exploration of the chronology of the Galaxy

The Milky Way has distinct structural stellar components linked to its formation and subsequent evolution, but disentangling them is non-trivial. With the recent availability of high-quality data for a large numbers of stars in the Milky Way, it is a natural next step for research in the evolution of the Galaxy to perform automated explorations with unsupervised methods of the structures hidden in the combination of large-scale spectroscopic, astrometric, and asteroseismic data sets. We determine precise stellar properties for 21 076 red giants, mainly spanning 2–15 kpc in Galactocentric radii, making it the largest sample of red giants with measured asteroseismic ages available to date. We explore the nature of different stellar structures in the Galactic disc by using Gaussian mixture models as an unsupervised clustering method to find substructure in the combined chemical, kinematic, and age subspace. The best-fitting mixture model yields four distinct physical Galactic components in the stellar disc: the thin disc, the kinematically heated thin disc, the thick disc, and the stellar halo. We find hints of an age asymmetry between the Northern and Southern hemisphere, and we measure the vertical and radial age gradient of the Galactic disc using the asteroseismic ages extended to further distances than previous studies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Automated Design-for-Reliability of a Power Electronics Module

The design of a power electronics module is a multiphysics problem and involves electrical, thermal, and reliability targets and constraints. Although the electrical and thermal design consider multiple aspects such as materials, geometry, and energy losses, reliability design is often limited to the selection of the attachment materials and electrical interconnect types. In this paper, we incorporate reliability metrics in the design phase by investigating the impact of package geometry on the thermomechanical behavior of the die-attachment material. To this end, we conducted thermal and power cycling simulations of a commercial six-pack power module with silicon carbide devices to compute junction temperature and strain energy density per cycle, respectively. We performed multiple simulations with different geometric dimensions and established a correlation between input features and output variables using subspace-based dimension reduction. The machine learning-based dimension reduction method serves as a surrogate model, which can be employed to identify the optimal module design from a thermal and reliability standpoint.

design-for-reliability↗
DOE OSTI2023

A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering

The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state dimension. To alleviate the effects of these errors EnKF relies on model-specific heuristics such as covariance localization, which takes advantage of the spatial locality of correlations among the model variables. This work proposes an approach to alleviate sampling errors that utilizes a locally averaged-in-time dynamics of the model, described in terms of a climatological covariance of the dynamical system. We use this covariance as the target matrix in covariance shrinkage methods, and develop a stochastic covariance shrinkage approach where synthetic ensemble members are drawn to enrich both the ensemble subspace and the ensemble transformation. We additionally provide for a way in which this methodology can be localized similar to the state-of-the-art LETKF method, and that for a certain model setup, our methodology significantly outperforms it.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Accelerating self-consistent field iterations in Kohn-Sham density functional theory using a low-rank approximation of the dielectric matrix

We present an efficient preconditioning technique for accelerating the fixed-point iteration in real-space Kohn-Sham density functional theory (DFT) calculations. The preconditioner uses a low-rank approximation of the dielectric matrix (LRDM) based on Gâteaux derivatives of the residual of fixed-point iteration along appropriately chosen direction functions. We develop a computationally efficient method to evaluate these Gâteaux derivatives in conjunction with the Chebyshev filtered subspace iteration procedure, an approach widely used in large-scale Kohn-Sham DFT calculations. Further, we propose a variant of LRDM preconditioner based on adaptive accumulation of low-rank approximations from previous self-consistent field iterations, and also extend the LRDM preconditioner to spin-polarized Kohn-Sham DFT calculations. We demonstrate the robustness and efficiency of the LRDM preconditioner against other widely used preconditioners on a range of benchmark systems with sizes ranging from ~100 to 1100 atoms (~500–20,000 electrons). The benchmark systems include various combinations of metal-insulating-semiconducting heterogeneous material systems, nanoparticles with localized d orbitals near the Fermi energy, nanofilm with metal dopants, and magnetic systems. In all benchmark systems, the LRDM preconditioner converges robustly within 20–30 iterations. In contrast, other widely used preconditioners show slow convergence in many cases, as well as divergence of the fixed-point iteration in some cases. Lastly, we demonstrate the computational efficiency afforded by the LRDM method, with up to 3.4-fold reduction in computational cost for the total ground-state calculation compared to other preconditioners.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗