Search NASA⌕ Search

SEARCH · Search NASA

Results for “Function approximation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

The LISE package: solvers for static and time-dependent superfluid local density approximation equations in three dimensions

Nuclear implementation of the density functional theory (DFT) is at present the only microscopic framework applicable to the whole nuclear landscape. The extension of DFT to superfluid systems in the spirit of the Kohn-Sham approach, the superfluid local density approximation (SLDA) and its extension to time-dependent situations, time-dependent superfluid local density ap- proximation (TDSLDA), have been extensively used to describe various static and dynamical problems in nuclear physics, neutron star crust, and cold atom systems. In this paper, we present the codes that solve the static and time-dependent SLDA equations in three-dimensional coordinate space without any symmetry restriction. These codes are fully parallelized with the message passing interface (MPI) library and take advantage of graphic processing units (GPU) for accelerating execution. The dynamic codes have checkpoint/restart capabilities and for initial conditions one can use any generalized Slater determinant type of wave function. The code can describe a large number of physical problems: nuclear fission, collisions of heavy ions, the interaction of quantized vor- tices with nuclei in the nuclear star crust, excitation of superfluid fermion systems by time dependent external fields, quantum shock waves, domain wall generation and propagation, the dynamics of the Anderson-Bogoliubov-Higgs mode, dynamics of fragmented condensates, vortex rings dynamics, generation and dynamics of quantized vortices, their crossing and recombinations and the incipient phases of quantum turbulence.

Jin, Shi↗
DOE OSTI2019

Crystal-momentum-resolved contributions to high-order harmonic generation in solids

We analytically and numerically investigate the emission of high-order harmonic radiation from model solids by intense few-cycle midinfrared laser pulses. In single-active-electron approximation, we expand the active electron's wave function in a basis of adiabatic Houston states and describe the solid's electronic band structure in terms of an adjustable Kronig-Penney model potential. For high-order harmonic generation (HHG) from MgO crystals, we examine spectra from two-band and converged multiband numerical calculations. We discuss the characteristics of intra- and interband contributions to the HHG spectrum for computations including initial crystal momenta either from the Γ point at the center of the first Brioullin zone (BZ) only or from the entire first BZ. For sufficiently high intensities of the driving laser field, we find relevant contributions to HHG from the entire first BZ. Here, based on numerically calculated spectra, we scrutinize the cutoff harmonic orders as a function of the laser peak intensity and find good qualitative agreement with our analytical saddle-point-approximation predictions and published theoretical data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Predicting impurity spectral functions using machine learning

The Anderson Impurity Model (AIM) is a canonical model of quantum many-body physics. Here we investigate whether machine learning models, both neural networks (NN) and kernel ridge regression (KRR), can accurately predict the AIM spectral function in all of its regimes, from empty orbital, to mixed valence, to Kondo. To tackle this question, we construct two large spectral databases containing approximately 410 000 and 600 000 spectral functions of the single-channel impurity problem. We show that the NN models can accurately predict the AIM spectral function in all of its regimes, with pointwise mean absolute errors down to 0.003 in normalized units. We find that the trained NN models outperform models based on KRR and enjoy a speedup on the order of 10 5 over traditional AIM solvers. Finally, the required size of the training set of our model can be significantly reduced using farthest point sampling in the AIM parameter space, which is important for generalizing our method to more complicated multichannel impurity problems of relevance to predicting the properties of real materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Validating first-principles phonon lifetimes via inelastic neutron scattering

Phonon lifetimes are a key component of quasiparticle theories of transport; yet first-principles lifetimes are rarely directly compared with inelastic neutron scattering (INS) results. Existing comparisons show discrepancies even at temperatures where perturbation theory is expected to be reliable. In this paper, we demonstrate that the reciprocal space voxel (q voxel), which is the finite region in reciprocal space required in INS data analysis, must be explicitly accounted for within theory in order to draw a meaningful comparison. Here, we demonstrate accurate predictions of peak widths of the scattering function when accounting for the q voxel in CaF 2 and ThO 2 . Passing this test implies high fidelity of the phonon interactions and the approximations used to compute the Green's function, serving as a critical benchmark of theory and indicating that other material properties should be accurately predicted, which we demonstrate for thermal conductivity.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Prediction of a Dynamically Stable New Half-Metallic Phase for the BaN and BaC Compounds

The structural, magnetic, elastic, mechanical, and thermodynamic properties of BaC and BaN compounds in different phases were studied using first-principle calculations based on spin-polarized density functional theory within the generalized gradient approximation (GGA-PBEsol) and the modified Becke–Johnson approach (mBJ-GGA-PBEsol) for the exchange-correlation energy and potential. The following phases—rock-salt (NaCl), CsCl, zinc blende (ZB), NiAs- and WZ-type hexagonal, tetragonal (P4/nmm), and orthorombic (Pnma) phases of BaC and BaN compounds—were considered. We obtained that Pnma phase has the lowest energy configuration as a function of the volume for both the BaN and BaC compounds. The ferromagnetic phase is energetically favored with respect to the non-magnetic phase in the BaN and BaC compounds, except for the CsCl phase in the BaC compound. Considering the phonon dynamics of BaN and BaC compounds in the Pnma, NaCl, ZB, and WZ phases, we observed that the BaN and BaC compounds in the Pnma, NaCl, and ZB phases are dynamically stable. The calculated elastic properties for the Pnma, NaCl, and ZB phases show that they are elastically stable. The Pnma phase for the BaN and BaC compounds, which is a new phase was found to be dynamically and elastically stable. The BaN and BaC compounds exhibit half-metallic behavior in the Pnma, NaCl, and ZB phases. The half-metallic and magnetic character found in the BaN and BaC compounds are attributed to the presence of spin-polarized 2p orbitals of the nitrogen and carbon atoms, respectively. We found that BaN and BaC compounds are half-metallic ferromagnets with magnetic moment of 1 μ{sub B} and 2 μ{sub B} per formula unit, respectively. Using the GGA-PBEsol (mBJ-GGA-PBEsol) approach, our calculated half-metallic gaps for BaN and BaC compounds are 0.22 eV (0.54 eV) and 0.32 eV (0.44 eV) in the Pnma phase, 0.23 eV (1.32 eV) and 0.35 eV (1.00 eV) in the NaCl phase, and 0.38 eV (1.54 eV) and 0.50 eV (1.57 eV) in the ZB phase, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

A persistent adjoint method with dynamic time-scaling and an application to mass action kinetics

In this article, we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since the derivative of the fixed-point with respect to the parameter can usually not be evaluated exactly, an adjoint dynamical system can be used to estimate gradients. Using this estimation procedure, the optimization algorithm alternates between derivative estimation and an approximate gradient descent step. We analyze a variant of this approach involving dynamic time-scaling, where after each parameter update the adjoint system is iterated until a convergence threshold is passed. Here, we prove that, under certain conditions, the algorithm can find approximate stationary points of the objective function. We demonstrate the approach in the settings of an inverse problem in chemical kinetics, and learning in attractor networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Optimized structure and electronic band gap of monolayer GeSe from quantum Monte Carlo methods

Here, we have used highly accurate quantum Monte Carlo methods to determine the chemical structure and electronic band gaps of monolayer GeSe. Two-dimensional (2D) monolayer GeSe has received a great deal of attention due to its unique thermoelectric, electronic, and optoelectronic properties with a wide range of potential applications. Density functional theory (DFT) methods have usually been applied to obtain optical and structural properties of bulk and 2D GeSe. For the monolayer, DFT typically yields a larger band-gap energy than for bulk GeSe but cannot conclusively determine if the monolayer has a direct or indirect gap. Moreover, the DFT-optimized lattice parameters and atomic coordinates for monolayer GeSe depend strongly on the choice of approximation for the exchange-correlation functional, which makes the ideal structure-and its electronic properties-unclear. In order to obtain accurate lattice parameters and atomic coordinates for the monolayer, we use a surrogate Hessian-based parallel line search within diffusion Monte Carlo to fully optimize the GeSe monolayer structure. The DMC-optimized structure is different from those obtained using DFT, as are calculated band gaps. The potential energy surface has a shallow minimum at the optimal structure. This, combined with the sensitivity of the electronic structure to strain, suggests that the optical properties of monolayer GeSe are highly tunable by strain.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Dynamic mode decomposition for extrapolating nonequilibrium Green's-function dynamics

The Hartree-Fock generalized Kadanoff-Baym ansatz (HF-GKBA) offers an approximate numerical procedure for propagating the two-time nonequilibrium Green's function (NEGF). Here, using the GW self-energy, we compare the HF-GKBA to exact results for a variety of systems with long- and short-range interactions, different two-body interaction strengths, and various nonequilibrium preparations. We find excellent agreement between the HF-GKBA and exact time evolution in models when more realistic long-range exponentially decaying interactions are considered. Furthermore, this agreement persists for long times and for intermediate to strong interaction strengths. In large systems, HF-GKBA becomes prohibitively expensive for long-time evolutions. For this reason, we look at the use of dynamical mode decomposition (DMD) to reconstruct long-time NEGF trajectories from a sample of the initial trajectory. Using no more than 16% of the total time evolution, we reconstruct the total trajectory with high fidelity. Our results show the potential for DMD to be used in conjunction with HF-GKBA to calculate long-time trajectories in large-scale systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Kohn–Sham accuracy from orbital-free density functional theory via Δ-machine learning

Here, we present a Δ-machine learning model for obtaining Kohn–Sham accuracy from orbital-free density functional theory (DFT) calculations. In particular, we employ a machine-learned force field (MLFF) scheme based on the kernel method to capture the difference between Kohn–Sham and orbital-free DFT energies/forces. We implement this model in the context of on-the-fly molecular dynamics simulations and study its accuracy, performance, and sensitivity to parameters for representative systems. We find that the formalism not only improves the accuracy of Thomas–Fermi–von Weizsäcker orbital-free energies and forces by more than two orders of magnitude but is also more accurate than MLFFs based solely on Kohn–Sham DFT while being more efficient and less sensitive to model parameters. We apply the framework to study the structure of molten Al 0.88 Si 0.12 , the results suggesting no aggregation of Si atoms, in agreement with a previous Kohn–Sham study performed at an order of magnitude smaller length and time scales.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Nuclear properties for astrophysical and radioactive-ion-beam applications (II)

We tabulate the ground-state odd-proton and odd-neutron spins and parities, proton and neutron pairing gaps, one- and two-neutron separation energies, quantities related to β-delayed one- and two-neutron emission probabilities, average energy and average number of emitted neutrons, β-decay energy release and half-life with respect to Gamow–Teller decay with a phenomenological treatment of first-forbidden decays, one- and two-proton separation energies, and α-decay energy release and half-life for 9318 nuclei ranging from {sup 16}O to {sup 339}136 and extending from the proton drip line to the neutron drip line. This paper is a new and improved version of Atomic Data And Nuclear Data Tables [66 131 (1997)]. The starting point of our present work is the new study (FRDM(2012)) of nuclear ground-state masses and deformations based on the finite-range droplet model and folded-Yukawa single-particle potential published in a previous issue of Atomic Data And Nuclear Data Tables [109–110, 1 (2016)]. The β-delayed neutron-emission probabilities and Gamow–Teller β-decay rates are obtained from a quasi-particle random-phase approximation with single-particle levels and wave functions at the calculated nuclear ground-state shapes as input quantities. A development since 1997 is we now use a Hauser–Feshbach approach to account for (n, γ) competition and treat first-forbidden decay in a phenomenological approach.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

A new modified BFGS method for unconstrained optimization problems

Using chain rule, we propose a modified secant equation to get a more accurate approximation of the second curvature of the objective function. Then, based on this modified secant equation we present a new BFGS method for solving unconstrained optimization problems. The proposed method makes use of both gradient and function values, and utilizes information from two most recent steps, while the usual secant relation uses only the latest step information. Under appropriate conditions, we show that the proposed method is globally convergent without convexity assumption on the objective function. Comparative numerical results show computational efficiency of the proposed method in the sense of the Dolan–Moré performance profiles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Spectral Analysis of 3-(Adamantan-1-yl)-4-Ethyl-1-[(4-Phenylpiperazin-1-yl) Methyl]-1H-1,2,4-Triazole-5(4H)-Thione

Vibrational IR (3200–650 cm{sup –1}) and Raman spectra (3200–150 cm{sup –1}) of adamantane-containing 3-(adamantan-1-yl)-4-ethyl-1-[(4-phenylpiperazin-1-yl)methyl]-1H-1,2,4-triazole-5(4H)-thione, which is promising for drug design, were examined. The UV/Vis spectrum (450–200 nm) of the compound in EtOH was measured. Full geometry optimization using density functional theory (DFT) in the B3LYP/cc-pVDZ approximation allowed the equilibrium configuration of the molecule to be determined and IR and Raman spectra to be calculated. Based on these, the experimental vibrational IR and Raman spectra were interpreted and the biological activity indices were predicted. The UV/Vis spectrum of the title compound was simulated at the time-dependent DFT/CAM-B3LYP/cc-pVDZ level with and without solvent effects and at the ab initio multi-reference perturbation theory XMCQDPT2 level. The UV/Vis spectrum that was simulated using the multi-reference XMCQDPT2 approximation agreed very successfully with the experimental data, in contrast to the single-reference DFT method. This was probably a consequence of intramolecular charge transfer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Calculation of Young’s Modulus of MoS{sub 2}-Based Single-Wall Nanotubes Using Force-Field and Hybrid Density Functional Theory

A force field is proposed that reproduces with a high accuracy a large number of properties of the bulk crystal MoS{sub 2} phases, monolayers, and nanotubes. The reproduced values are both the experimental results and the results of quantum chemical calculations. The elaborated interaction potential can be useful primarily for investigation of multiwall MoS{sub 2} nanotubes and their thermodynamic properties, especially, since the potential is able to reproduce the frequencies of the crystal phonon spectrum. In this study the proposed potential is applied to simulate the temperature dependence of a number of properties of the armchair and zigzag nanotubes. The calculations have been performed using molecular mechanics method within the framework of quasi harmonic approximation which is carried out through the estimation of the temperature dependence of the Helmholtz free energy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

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

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

36 MATERIALS SCIENCE↗
DOE OSTI2018

Magnetic Properties of La-Doped ZnO(0001)–Zn Polar Surface with and without Vacancies: a First-Principle Study

The effects of La doping with and without vacancies on the magnetism of a ZnO(0001)–Zn polar surface were studied using the generalized gradient approximation + U (GGA + U) method of density functional theory to determine the magnetism source of La-doped ZnO. Results revealed that La doping with O vacancy did not cause ZnO ferromagnetism, but La-doped ZnO with Zn vacancy was ferromagnetic. The net magnetic moment was primarily related to the unpaired electron amount of the O 2p state and slightly modified by orbital and anomalous magnetic moments. The anomalous magnetic moment originated from the radiating magnetism moment via quantum electrodynamics and was confirmed to exist via theoretical calculations of magnetism. Formation energy showed that La doping easily generated Zn vacancies in ZnO, but magnetic quenching occurred when the ratio of La ions to Zn vacancies was 2:1. The unpaired O 2p electrons induced by Zn vacancies were the magnetism source of La-doped ZnO. Moreover, the Curie temperature of La-doped ZnO with Zn vacancy reached room temperature. Results showed that the ZnO(0001)–Zn polar surface can be utilized as the surface of ZnO-based diluted magnetic semiconductors because of its unipolarity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Evaluation of Thermal Scattering Law for U 3 Si 2 Using Temperature-Dependent Phonon Density of States

The thermal scattering law for uranium silicide, a candidate material for high-density nuclear fuel, was evaluated from the temperature-dependent phonon density of states obtained using the quasi-harmonic approximation. For uranium silicide model systems of various volumes near the equilibrium volume, Hellmann-Feynman forces were calculated by performing ab initio lattice dynamics simulations based on density functional theory. Subsequently, the quasi-harmonic approximation was applied by interpolating the results of the harmonic approximation for each volume system. As a sensitivity test, the phonon density of states was calculated for the structures with temperature-dependent volumes at 298 K and 1000 K, obtained by the quasi-harmonic approximation, and the corresponding thermal neutron scattering cross section was evaluated. The temperature-dependent volume and heat capacity of uranium silicide obtained by the quasi-harmonic approximation showed reasonable agreement with experimental data while lattice thermal expansion showed deviation from experimental observations. Thermal scattering cross sections evaluated from 0 K and temperature-dependent phonon density of states exhibited differences of up to 4.1% at 1000 K. This study examines the impact of temperature on the thermal scattering law, employing ab initio lattice dynamics simulations through the quasi-harmonic approximation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2018

Magnetic, Optoelectronic, and Thermodynamic Properties of Sr{sub 2}CrXO{sub 6} (X = La and Y): Half-Metallic and Ferromagnetic Behavior

The effects of spin polarization on the structure, magnetic, and optoelectronic properties of Cr-based series of double perovskites Sr{sub 2}CrXO{sub 6} (X = La and Y) have been studied by using the full-potential linearized augmented plane-wave method (FP-LAPW), based on the density functional theory (DFT) as implemented in the Wien2k code, within the generalized gradient approximation (GGA), GGA + U, and GGA plus Trans-Blaha-modified Becke–Johnson (TB-mBJ) as the exchange correlation. Our results show a similar half-metallic ferromagnetic ground state for both materials. From the electronic properties, it is found that Sr{sub 2}CrYO{sub 6} has a direct band gap at (Γ-Γ) direction and Sr{sub 2}CrLaO{sub 6} has an indirect band gap at (Γ-W) direction. Furthermore, we have computed the optic and thermodynamic properties which are investigated for the first time. Consequently, the magnetic, optoelectronic, and thermodynamic properties show these compounds are promising for high technological applications, namely spintronic materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗