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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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS2020

Neural Network Repair of Lossy Compression Artifacts in the Sept 2015 – March 2016 Duration of the MMS/FPI Dataset

During the Sept 2015 –March 2016 duration (sometimes referred to as Phase 1A) of the Magnetospheric Multiscale Mission (MMS), the Dual Electron Spectrometers (DES) were configured to generously utilize lossy compression. While this maximized the number of velocity distribution functions downlinked, it cameat the expense of lost information content for a fractionof the frames. Following this period of lossy compression, the DES was re-configured in a way that allowed for 95% of the framesto arrive to the ground without loss. Using this high-quality set offrameson-orbit observations, we compressed and decompressed the frameson the ground to create a side-by-side record of the compression effect. This record was used to drive an optimization method that (a) derived basis functions capable of approximating the lossless sample space and with non-negative coefficients and (b) fitted a function which maps the lossy framesto basis weights that recreate the framewithout compression artifacts. This methodis introduced and evaluated in this paper.Data users should expect a higher level of confidence in the absolute scale of density/temperature measurements andnotice less sinusoidal bias in the velocity X and Y components(GSE).

Magnetosphere, Neural Networks, Image Processing, ↗
NASA NTRS1984

Chemical application of diffusion quantum Monte Carlo

The diffusion quantum Monte Carlo (QMC) method gives a stochastic solution to the Schroedinger equation. This approach is receiving increasing attention in chemical applications as a result of its high accuracy. However, reducing statistical uncertainty remains a priority because chemical effects are often obtained as small differences of large numbers. As an example, the single-triplet splitting of the energy of the methylene molecule CH sub 2 is given. The QMC algorithm was implemented on the CYBER 205, first as a direct transcription of the algorithm running on the VAX 11/780, and second by explicitly writing vector code for all loops longer than a crossover length C. The speed of the codes relative to one another as a function of C, and relative to the VAX, are discussed. The computational time dependence obtained versus the number of basis functions is discussed and this is compared with that obtained from traditional quantum chemistry codes and that obtained from traditional computer architectures.

Reynolds, P. J.↗
NASA NTRS1990

Theoretical investigation of gas-surface interactions

A Dirac-Hartree-Fock code was developed for polyatomic molecules. The program uses integrals over symmetry-adapted real spherical harmonic Gaussian basis functions generated by a modification of the MOLECULE integrals program. A single Gaussian function is used for the nuclear charge distribution, to ensure proper boundary conditions at the nuclei. The Gaussian primitive functions are chosen to satisfy the kinetic balance condition. However, contracted functions which do not necessarily satisfy this condition may be used. The Fock matrix is constructed in the scalar basis and transformed to a jj-coupled 2-spinor basis before diagonalization. The program was tested against numerical results for atoms with a Gaussian nucleus and diatomic molecules with point nuclei. The energies converge on the numerical values as the basis set size is increased. Full use of molecular symmetry (restricted to D sub 2h and subgroups) is yet to be implemented.

Dyall, Kenneth G.↗
DOE OSTI2021

Atomic forces from Dirac-Kohn-Sham equations: Implementation in flexible (APW+lo/LAPW)+LO basis set

The atomic forces formulation based on the Dirac-Kohn-Sham equation and the flexible (APW+lo/LAPW)+LO basis set is presented here. The formulation was implemented in the code FlapwMBPT and allows a user to easily switch between different basis functions of the augmentation type (APW or LAPW) and between different kind of local orbitals. Similar to the work (Phys.Rev.B 91 (2015) 035105), the implementation takes into account small discontinuities of the wave functions, density, and potential at the muffin-tin sphere boundaries. Applications to the materials with strong relativistic effects, such as $\alpha$-Uranium, PuCoGa$_{5}$, and FePt, demonstrate robustness of the method. The comparison of the calculated forces with the ones obtained by numerical differentiation of free energy shows close agreement with deviations about 0.1% or less.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Downfolding from ab initio to interacting model Hamiltonians: comprehensive analysis and benchmarking of the DFT+cRPA approach

Abstract Model Hamiltonians are regularly derived from first principles to describe correlated matter. However, the standard methods for this contain a number of largely unexplored approximations. For a strongly correlated impurity model system, here we carefully compare a standard downfolding technique with the best possible ground-truth estimates for charge-neutral excited-state energies and wave functions using state-of-the-art first-principles many-body wave function approaches. To this end, we use the vanadocene molecule and analyze all downfolding aspects, including the Hamiltonian form, target basis, double-counting correction, and Coulomb interaction screening models. We find that the choice of target-space basis functions emerges as a key factor for the quality of the downfolded results, while orbital-dependent double-counting corrections diminish the quality. Background screening of the Coulomb interaction matrix elements primarily affects crystal-field excitations. Our benchmark uncovers the relative importance of each downfolding step and offers insights into the potential accuracy of minimal downfolded model Hamiltonians.

Chemistry↗
DOE OSTI2022

Analytic Gaussian covariance matrices for galaxy N-point correlation functions

Here, we derive analytic covariance matrices for the N-point correlation functions (NPCFs) of galaxies in the Gaussian limit. Our results are given for arbitrary N and projected onto the isotropic basis functions given by spherical harmonics and Wigner 3j symbols. A numerical implementation of the 4PCF covariance is compared to the sample covariance obtained from a set of lognormal simulations, Quijote dark matter halo catalogues, and MultiDark-Patchy galaxy mocks, with the latter including realistic survey geometry. The analytic formalism gives reasonable predictions for the covariances estimated from mock simulations with a periodic-box geometry. Furthermore, fitting for an effective volume and number density by maximizing a likelihood based on Kullback-Leibler divergence is shown to partially compensate for the effects of a nonuniform window function. Our result is recently shown to facilitate NPCF analysis on a realistic survey data.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1991

Total recall in distributive associative memories

Iterative error correction of asymptotically large associative memories is equivalent to a one-step learning rule. This rule is the inverse of the activation function of the memory. Spectral representations of nonlinear activation functions are used to obtain the inverse in closed form for Sparse Distributed Memory, Selected-Coordinate Design, and Radial Basis Functions.

Danforth, Douglas G.↗
NASA NTRS2000

Robust Inversion and Data Compression in Control Allocation

We present an off-line computational method for control allocation design. The control allocation function delta = F(z)tau = delta (sub 0) (z) mapping commanded body-frame torques to actuator commands is implicitly specified by trim condition delta (sub 0) (z) and by a robust pseudo-inverse problem double vertical line I - G(z) F(z) double vertical line less than epsilon (z) where G(z) is a system Jacobian evaluated at operating point z, z circumflex is an estimate of z, and epsilon (z) less than 1 is a specified error tolerance. The allocation function F(z) = sigma (sub i) psi (z) F (sub i) is computed using a heuristic technique for selecting wavelet basis functions psi and a constrained least-squares criterion for selecting the allocation matrices F (sub i). The method is applied to entry trajectory control allocation for a reusable launch vehicle (X-33).

Hodel, A. Scottedward↗
DOE OSTI2022

Implementation of real‐time TDDFT for periodic systems in the open‐source PySCF software package

Abstract We present a new implementation of real‐time time‐dependent density functional theory (RT‐TDDFT) for calculating excited‐state dynamics of periodic systems in the open‐source Python‐based PySCF software package. Our implementation uses Gaussian basis functions in a velocity gauge formalism and can be applied to periodic surfaces, condensed‐phase, and molecular systems. As representative benchmark applications, we present optical absorption calculations of various molecular and bulk systems and a real‐time simulation of field‐induced dynamics of a (ZnO) 4 molecular cluster on a periodic graphene sheet. We present representative calculations on optical response of solids to infinitesimal external fields as well as real‐time charge‐transfer dynamics induced by strong pulsed laser fields. Due to the widespread use of the Python language, our RT‐TDDFT implementation can be easily modified and provides a new capability in the PySCF code for real‐time excited‐state calculations of chemical and material systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Solution of the Schrödinger equation for quasi-one-dimensional materials using helical waves

We formulate and implement a spectral method for solving the Schrödinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials such as nanotubes (of arbitrary chirality), nanowires, nanoribbons, chiral nanoassemblies, nanosprings and nanocoils, in an accurate, efficient and systematic manner. Our work is motivated by the observation that one of the most successful methods for carrying out electronic structure calculations of bulk/crystalline systems — the plane-wave method — is a spectral method based on eigenfunction expansion. Our scheme avoids computationally onerous approximations involving periodic supercells often employed in conventional plane-wave calculations of quasi-one-dimensional materials, and also overcomes several limitations of other discretization strategies, e.g., those based on finite differences and atomic orbitals. The basis functions in our method — called helical waves (or twisted waves) — are eigenfunctions of the Laplacian with symmetry adapted boundary conditions, and are expressible in terms of plane waves and Bessel functions in helical coordinates. We describe the setup of fast transforms to carry out discretization of the governing equations using our basis set, and the use of matrix-free iterative diagonalization to obtain the electronic eigenstates. Miscellaneous computational details, including the choice of eigensolvers, use of a preconditioning scheme, evaluation of oscillatory radial integrals and the imposition of a kinetic energy cutoff are discussed. We have implemented these strategies into a computational package called HelicES (Helical Electronic Structure). We demonstrate the utility of our method in carrying out systematic electronic structure calculations of various quasi-one-dimensional materials through numerous examples involving nanotubes, nanoribbons and nanowires. We also explore the convergence properties of our method, and assess its accuracy and computational efficiency by comparison against reference finite difference, transfer matrix method and plane-wave results. We anticipate that our method will find applications in computational nanomechanics and multiscale modeling, for carrying out transport calculations of interest to the field of semiconductor devices, and for the discovery of novel chiral phases of matter that are of relevance to the burgeoning quantum hardware industry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Multiscale simulations for multi-continuum Richards equations

In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation (for pressure head), and these equations are coupled to one another by transfer terms. On its own, Richards equation is already a nonlinear partial differential equation, and it is exceedingly difficult to solve numerically due to the extra nonlinear dependencies involving the soil water. To deal with multiple scales, our strategy is that starting from a microscopic scale, we upscale the coupled system of dual-continuum Richards equations via homogenization by the two-scale asymptotic expansion, to obtain a homogenized system, at an intermediate scale (level). Based on a hierarchical approach, the homogenization’s effective coefficients are computed through solving the arising cell problems. Furthermore, to tackle the nonlinearity, after time discretization, we use Picard iteration procedure for linearization of the homogenized Richards equations. At each Picard iteration, some degree of multiscale still remains from the intermediate level, so we utilize the generalized multiscale finite element method (GMsFEM) combining with a multi-continuum approach, to upscale the homogenized system to a macroscopic (coarse-grid) level. This scheme involves building uncoupled and coupled multiscale basis functions, which are used not only to construct coarse-grid solution approximation with high accuracy but also (with the coupled multiscale basis) to capture the interactions among continua. These prospects and convergence are demonstrated by several numerical results for the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Sparse adaptive basis set methods for solution of the time dependent Schrodinger equation

Scalable numerical solutions to the time dependent Schrodinger equation remain an outstanding goal in theoretical chemistry. Here we present a method which utilises recent breakthroughs in signal processing to consistently adapt a dictionary of basis functions to the dynamics of the system. Further, we show that for two low-dimensional model problems the size of the basis set does not grow quickly with time and appears only weakly dependent on dimensionality. The generality of this finding remains to be seen. The method primarily uses energies and gradients of the potential, opening the possibility for its use in on-the-fly ab initio quantum wavepacket dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Discontinuous Galerkin discretization for quantum simulation of chemistry

All-electron electronic structure methods based on the linear combination of atomic orbitals method with Gaussian basis set discretization offer a well established, compact representation that forms much of the foundation of modern correlated quantum chemistry calculations—on both classical and quantum computers. Despite their ability to describe essential physics with relatively few basis functions, these representations can suffer from a quartic growth of the number of integrals. Recent results have shown that, for some quantum and classical algorithms, moving to representations with diagonal two-body operators can result in dramatically lower asymptotic costs, even if the number of functions required increases significantly. We introduce a way to interpolate between the two regimes in a systematic and controllable manner, such that the number of functions is minimized while maintaining a block-diagonal structure of the two-body operator and desirable properties of an original, primitive basis. Techniques are analyzed for leveraging the structure of this new representation on quantum computers. Empirical results for hydrogen chains suggest a scaling improvement from O(N 4.5 ) in molecular orbital representations to O(N 2.6 ) in our representation for quantum evolution in a fault-tolerant setting, and exhibit a constant factor crossover at 15 to 20 atoms. Moreover, we test these methods using modern density matrix renormalization group methods classically, and achieve excellent accuracy with respect to the complete basis set limit with a speedup of 1–2 orders of magnitude with respect to using the primitive or Gaussian basis sets alone. These results suggest our representation provides significant cost reductions while maintaining accuracy relative to molecular orbital or strictly diagonal approaches for modest-sized systems in both classical and quantum computation for correlated systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1984

An urnful of blinding functions

There is a fundamental connection between the mathematical theory of discrete probability distributions and the parametric curves and surfaces of computer-aided geometric design. It is no accident that the blending functions of Bezier curves and surfaces have an obvious probabilistic interpretation, nor is it a coincidence that the normalized uniform B-spline basis functions also model a simple stochastic process. The link between probability and geometry, and how to exploit simple probabilistic arguments to derive many of the classical geometric properties of the parametric curves and surfaces currently in vogue in computer-aided geometric design is discussed. This probabilistic approach is also used to introduce many new types of curves and surfaces, and it is demonstrated how probability theory can be used to simplify, unify, and generalize many well-known results.

Goldman, R. N.↗
DOE OSTI2025

Deep Learning without Global Optimization by Random Fourier Neural Networks

Here we introduce a new training algorithm for deep neural networks that utilize random complex exponential activation functions. Our approach employs a Markov chain Monte Carlo sampling procedure to iteratively train network layers, avoiding global and gradient-based optimization while maintaining error control. It consistently attains the theoretical approximation rate for residual networks with complex exponential activation functions, determined by network complexity. Additionally, it enables efficient learning of multiscale and high-frequency features, producing interpretable parameter distributions. Despite using sinusoidal basis functions, we do not observe Gibbs phenomena in approximating discontinuous target functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Isogeometric Bézier dual mortaring: The Kirchhoff–Love shell problem

Here in this paper we develop an isogeometric Bézier dual mortar method for coupling multi-patch Kirchhoff–Love shell structures. The proposed approach weakly enforces the continuity of the solution at patch interfaces through a dual mortar method and can be applied to both conforming and non-conforming discretizations. As the employed dual basis functions have local supports and satisfy the biorthogonality property, the resulting stiffness matrix is sparse. In addition, the coupling accuracy is optimal because the dual basis possesses the polynomial reproduction property. We also formulate the continuity constraints through the Rodrigues’ rotation operator which gives a unified framework for coupling patches that are intersected with G 1 continuity as well as patches that meet at a kink. Several linear and nonlinear examples demonstrated the performance and robustness of the proposed coupling techniques.

42 ENGINEERING↗
DOE OSTI2025

Resolving local structural motifs across the phase evolution of zinc titanates with computational x-ray absorption spectroscopy

Resolving the local structure motifs that characterize phase evolution as a function of composition is a key challenge in structure characterization of complex materials. Here, in this study, we combine first-principles simulations and x-ray absorption near-edge structures (XANES) analysis to gain insights into the structure evolution revealed by measurements across a combinatorial zinc titanate thin film, which was grown with smoothly varying composition over a wide range of the Ti:Zn ratio. Specifically, we propose a cluster blind-signal-separation (cBSS) method for XANES spectral analysis based on a library of the structures and spectra of representative local motifs. In addition to motifs from zinc titanate crystals, two types of Ti-defect models constructed in this study are key to the understanding of the structure characteristics in the Zn-rich region. The cBSS method makes use of both spectral clustering of the simulated site-XANES spectra library and the BSS procedure to construct high-fidelity spectral basis functions from an experimental spectral sequence. The method provides a rigorous measure of the spectral sensitivity and basis completeness. The results of the XANES analysis are corroborated with other experimental modalities, including x-ray diffraction and spectroscopic ellipsometry, to validate the cBSS method. The calculated motif weights resulting from fitting the XANES spectra with the cBSS basis probe the atomic structure characteristics of both crystalline and amorphous phases as a function of the Ti/Zn composition. The insights of the local structure motif evolution are pivotal to the understanding of the nonmonotonic trend in the optical gap, which may lead to potential applications through tuning the optical properties of zinc titanate. The workflow of the XANES spectral analysis developed in this work can be generalized to construct the structure-property relationship in a broad material space.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Comparing machine learning and interpolation methods for loop-level calculations

The need to approximate functions is ubiquitous in science, either due to empirical constraints or high computational cost of accessing the function. In high-energy physics, the precise computation of the scattering cross-section of a process requires the evaluation of computationally intensive integrals. A wide variety of methods in machine learning have been used to tackle this problem, but often the motivation of using one method over another is lacking. Comparing these methods is typically highly dependent on the problem at hand, so we specify to the case where we can evaluate the function a large number of times, after which quick and accurate evaluation can take place. We consider four interpolation and three machine learning techniques and compare their performance on three toy functions, the four-point scalar Passarino-Veltman D_0 D 0 function, and the two-loop self-energy master integral M. We find that in low dimensions (d = 3), traditional interpolation techniques like the Radial Basis Function perform very well, but in higher dimensions (d=5, 6, 9) we find that multi-layer perceptrons (a.k.a neural networks) do not suffer as much from the curse of dimensionality and provide the fastest and most accurate predictions.

97 MATHEMATICS AND COMPUTING↗