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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

The Good, the Bad, and the Ugly: Pseudopotential Inconsistency Errors in Molecular Applications of Density Functional Theory

The pseudopotential (PP) approximation is one of the most common techniques in computational chemistry. Despite its long history, the development of custom PPs has not tracked with the explosion of different density functional approximations (DFAs). As a result, the use of PPs with exchange/correlation models for which they were not developed is widespread, although this practice is known to be theoretically unsound. The extent of PP inconsistency errors (PPIEs) associated with this practice has not been systematically explored across the types of energy differences commonly evaluated in chemical applications. Here, we evaluate PPIEs for a number of PPs and DFAs across 196 chemically relevant systems of both transition-metal and main-group elements, as represented by the W4-11, TMC34, and S22 data sets. Near the complete basis set limit, these PPs are found to cleanly approach all-electron (AE) results for noncovalent interactions but introduce root-mean-squared errors (RMSEs) upwards of 15 kcal mol –1 into predictions of covalent bond energies for a number of popular DFAs. We achieve significant improvements through the use of empirical atom- and DFA-specific PP corrections, indicating considerable systematicity of the PPIEs. The results of this work have implications for chemical modeling in both molecular contexts and for DFA design, which we discuss.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Communication: A new class of non-empirical explicit density functionals on the third rung of Jacob’s ladder

We construct an orbital-free non-empirical meta-generalized gradient approximation (GGA) functional, which depends explicitly on density through the density overlap regions indicator [P. de Silva and C. Corminboeuf, J. Chem. Theory Comput. 10, 3745 (2014)]. The functional does not depend on either the kinetic energy density or the density Laplacian; therefore, it opens a new class of meta-GGA functionals. By construction, our meta-GGA yields exact exchange and correlation energy for the hydrogen atom and recovers the second order gradient expansion for exchange in the slowly varying limit. We show that for molecular systems, overall performance is better than non-empirical GGAs. For atomization energies, performance is on par with revTPSS, without any dependence on Kohn-Sham orbitals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2005

Adaptive Filtering Using Recurrent Neural Networks

A method for adaptive (or, optionally, nonadaptive) filtering has been developed for estimating the states of complex process systems (e.g., chemical plants, factories, or manufacturing processes at some level of abstraction) from time series of measurements of system inputs and outputs. The method is based partly on the fundamental principles of the Kalman filter and partly on the use of recurrent neural networks. The standard Kalman filter involves an assumption of linearity of the mathematical model used to describe a process system. The extended Kalman filter accommodates a nonlinear process model but still requires linearization about the state estimate. Both the standard and extended Kalman filters involve the often unrealistic assumption that process and measurement noise are zero-mean, Gaussian, and white. In contrast, the present method does not involve any assumptions of linearity of process models or of the nature of process noise; on the contrary, few (if any) assumptions are made about process models, noise models, or the parameters of such models. In this regard, the method can be characterized as one of nonlinear, nonparametric filtering. The method exploits the unique ability of neural networks to approximate nonlinear functions. In a given case, the process model is limited mainly by limitations of the approximation ability of the neural networks chosen for that case. Moreover, despite the lack of assumptions regarding process noise, the method yields minimum- variance filters. In that they do not require statistical models of noise, the neural- network-based state filters of this method are comparable to conventional nonlinear least-squares estimators.

Parlos, Alexander G.↗
DOE OSTI2022

Machine learning for impurity charge-state transition levels in semiconductors from elemental properties using multi-fidelity datasets

Quantifying charge-state transition energy levels of impurities in semiconductors is critical to understanding and engineering their optoelectronic properties for applications ranging from solar photovoltaics to infrared lasers. While these transition levels can be measured and calculated accurately, such efforts are time-consuming and more rapid prediction methods would be beneficial. Here, we significantly reduce the time typically required to predict impurity transition levels using multi-fidelity datasets and a machine learning approach employing features based on elemental properties and impurity positions. We use transition levels obtained from low-fidelity (i.e., local-density approximation or generalized gradient approximation) density functional theory (DFT) calculations, corrected using a recently proposed modified band alignment scheme, which well-approximates transition levels from high-fidelity DFT (i.e., hybrid HSE06). Further, the model fit to the large multi-fidelity database shows improved accuracy compared to the models trained on the more limited high-fidelity values. Crucially, in our approach, when using the multi-fidelity data, high-fidelity values are not required for model training, significantly reducing the computational cost required for training the model. Our machine learning model of transition levels has a root mean squared (mean absolute) error of 0.36 (0.27) eV vs high-fidelity hybrid functional values when averaged over 14 semiconductor systems from the II–VI and III–V families. As a guide for use on other systems, we assessed the model on simulated data to show the expected accuracy level as a function of bandgap for new materials of interest. Finally, we use the model to predict a complete space of impurity charge-state transition levels in all zinc blende III–V and II–VI systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Ab initio study of the structural, electronic and optical properties of ZnTe compound

Structural, electronic and optical properties of ZnTe compound were calculated using Density Functional Theory (DFT) based on the pseudopotentials and planewaves (PP-PW) method as implemented in the ABINIT computer code, where the exchange–correlation functional is approximated using the local density approximation (LDA) and the generalized gradient approximation (GGA). The obtained results from either LDA or GGa calculation for lattice parameter, energy band gap and optical parameters, such as the fundamental absorption edge, the peaks observed in the imaginary part of the dielectric function, the macroscopic dielectric constants and the optical dielectric constant, are compared with the available theoretical results and experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Hyperspherical Sparse Approximation Techniques for High-Dimensional Discontinuity Detection

This work proposes a hyperspherical sparse approximation framework for detecting jump discontinuities in functions in high-dimensional spaces. The need for a novel approach results from the theoretical and computational inefficiencies of well-known approaches, such as adaptive sparse grids, for discontinuity detection. Our approach constructs the hyperspherical coordinate representation of the discontinuity surface of a function. Then sparse approximations of the transformed function are built in the hyperspherical coordinate system, with values at each point estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the new technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. Several approaches are used to approximate the transformed discontinuity surface in the hyperspherical system, including adaptive sparse grid and radial basis function interpolation, discrete least squares projection, and compressed sensing approximation. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. In conclusion, rigorous complexity analyses of the new methods are provided, as are several numerical examples that illustrate the effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment

Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions, and near degeneracy static correlations. In this work, we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function f (r{sub 12}) depending on the interelectronic distance r{sub 12}. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems, we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation, we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function ansatz correctly incorporates the long range Van der Waals interactions. We further show that the approximate wave function gives an excellent binding curve and is able to describe static correlations. We show that in order to do this the correlation function f (r{sub 12}) needs to diverge for large r{sub 12} at large internuclear distances while for shorter bond distances it increases as a function of r{sub 12} to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nev- ertheless, the majority of these studies examine how well deep neural networks can model functions with uniform regularities. In this paper, we explore a different angle: how deep neural networks can adapt to varying degrees of smoothness in functions and nonuni- form data distributions across different locations and scales. More precisely, we focus on a broad class of functions defined by nonlinear tree-based approximation methods. This class encompasses a range of function types, such as functions with uniform regularities and discontinuous functions. We develop nonparametric approximation and estimation theories for this class using deep ReLU networks. Our results show that deep neural networks are adaptive to the nonuniform smoothness of functions and nonuniform data distributions at different locations and scales. We apply our results to several function classes, and derive the corresponding approximation and generalization errors. The validity of our results is demonstrated through numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On estimating the curvature attributes and strain invariants of deformed surface through radial basis functions

Numerical methods in approximation of derivatives on regular or irregular gridded and scattered data points are of significance in the study of numerous problems in engineering and geoscience. A mathematically accurate and stable method is assessed to compute the differential quantities, while being flexible and easy to implement. Strain-invariant parameters in deformation analysis and curvature attributes in geometrical analysis of approximated surfaces are independent quantities which could be derived numerically through radial basis functions (RBFs) for scattered data points. Approximation of a function or its derivatives through RBFs is highly correlated to its shape parameter which depends on the number and distribution of the particles on the support domain. A procedure to find the optimal shape parameter for RBFs in the influence domain of each nodal point together with the presentation of a manner of calculating the curvature attributes and strain parameters through Gaussian RBFs is proposed here. Results indicate a significant improvement in the approximation accuracy of strain parameters and curvature attributes, while this approximation is more stable when RBFs with optimal shape parameter are implemented rather than the traditional moving least squares.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2007

Space Shuttle Debris Impact Tool Assessment Using the Modern Design of Experiments

Complex computer codes are used to estimate thermal and structural reentry loads on the Shuttle Orbiter induced by ice and foam debris impact during ascent. Such debris can create cavities in the Shuttle Thermal Protection System. The sizes and shapes of these cavities are approximated to accommodate a code limitation that requires simple "shoebox" geometries to describe the cavities -- rectangular areas and planar walls that are at constant angles with respect to vertical. These approximations induce uncertainty in the code results. The Modern Design of Experiments (MDOE) has recently been applied to develop a series of resource-minimal computational experiments designed to generate low-order polynomial graduating functions to approximate the more complex underlying codes. These polynomial functions were then used to propagate cavity geometry errors to estimate the uncertainty they induce in the reentry load calculations performed by the underlying code. This paper describes a methodological study focused on evaluating the application of MDOE to future operational codes in a rapid and low-cost way to assess the effects of cavity geometry uncertainty.

DeLoach, Richard↗
DOE OSTI2024

Chapter 7: Learning Stable Local Volt/Var Controllers in Distribution Grids

This chapter describes a framework to synthesize provably stable local Volt/Var controllers for distributed energy resources (DERs) in power distribution grids (DGs). The goal is to control the reactive power injections of DERs to improve the system performance as quantified by a generic optimal reactive power flow (ORPF) problem. To achieve this, we jointly design for each DER the control function, which prescribes the reactive power update rule, and the equilibrium function, which approximates the ORPF solutions from local measurements of voltages and powers. We provide conditions on the equilibrium functions and the control parameters ensuring the stability of the closed-loop system. In particular, we discuss the trade-offs between each set of conditions accounting for practical considerations, like fully exploiting the DERs' generation capabilities and reducing the optimality gap. These conditions are then translated into learning constraints on the neural networks' parameters that are enforced in the training phase. We validate our framework with numerical simulations on the IEEE 37-bus network and through a comparison with an optimized version of standard piece wise linear control rules.

closed-loop asymptotic stability↗
NASA NTRS1990

Causal compensated perturbations in cosmology

A theoretical framework is developed to calculate linear perturbations in the gravitational and matter fields which arise causally in response to the presence of stiff matter sources in a FRW cosmology. It is shown that, in order to satisfy energy and momentum conservation, the gravitational fields of the source must be compensated by perturbations in the matter and gravitational fields, and the role of such compensation in containing the initial inhomogeneities in their subsequent evolution is discussed. A complete formal solution is derived in terms of Green functions for the perturbations produced by an arbitrary source in a flat universe containing cold dark matter. Approximate Green function solutions are derived for the late-time density perturbations and late-time gravitational waves in a universe containing a radiation fluid. A cosmological energy-momentum pseudotensor is defined to clarify the nature of energy and momentum conservation in the expanding universe.

Veeraraghavan, Shoba↗
DOE OSTI2019

First-principles study of the infrared spectrum in liquid water from a systematically improved description of H-bond network

An accurate ab initio theory of the H-bond structure of liquid water requires a high-level exchange correlation approximation from density functional theory. Based on the liquid structures modeled by ab initio molecular dynamics by using maximally localized Wannier functions as a basis, we study the infrared spectrum of water within the canonical ensemble. In particular, we employ both the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) and the state-of-the-art meta-GGA level approximation provided by the strongly constrained and appropriately normed (SCAN) functional. In this work, we demonstrate that the SCAN functional improves not only the water structure but also the theoretical infrared spectrum of water. Our analyses show that the improvement in the stretching and bending bands can be mainly attributed to better descriptions of directional H bonding and the covalency at the inter- and intramolecular levels, respectively. On the other hand, better agreements in libration and hindered translation bands are due to the improved dynamics of the H-bond network enabled by a less structured liquid in the experimental direction. The spectrum predicted by SCAN shows much better agreement with experimental data than the conventionally widely adopted PBE functional at the GGA level.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

Optimization of the Jastrow factor using the random-phase approximation and a similarity-transformed Hamiltonian: Application to band-structure calculation for some semiconductors and insulators

Based on the random-phase approximation and the transcorrelated (TC) method, we optimize the Jastrow factor together with one-electron orbitals in the Slater determinant in the correlated wave function with a new scheme for periodic systems. The TC method is one of the promising wave function theories for first-principles electronic structure calculation, where the many-body wave function is approximated as a product of a Slater determinant and a Jastrow factor, and the Hamiltonian is similarity-transformed by the Jastrow factor. Using this similarity-transformed Hamiltonian, we can optimize the one-electron orbitals without evaluating 3N-dimensional integrations for the N-electron system. In contrast, optimization of the Jastrow factor within the framework of the TC method is computationally much more expensive and has not been performed for solid-state calculations before. In this study, we also benefit from the similarity-transformation in optimizing the Jastrow factor. Our optimization scheme is tested in applications to some solids from narrow-gap semiconductors to wide-gap insulators, and it is verified that the band gap of a wide-gap insulator and the lattice constants of some solids are improved by this optimization with reasonable computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

First-principle study of quantum confinement effect on small sized silicon quantum dots using density-functional theory

Density functional theory (DFT), as a first-principle approach has successfully been implemented to study nanoscale material. Here, DFT by numerical basis-set was used to study the quantum confinement effect as well as electronic properties of silicon quantum dots (Si-QDs) in ground state condition. Selection of quantum dot models were studied intensively before choosing the right structure for simulation. Next, the computational result were used to examine and deduce the electronic properties and its density of state (DOS) for 14 spherical Si-QDs ranging in size up to ∼ 2 nm in diameter. The energy gap was also deduced from the HOMO-LUMO results. The atomistic model of each silicon QDs was constructed by repeating its crystal unit cell of face-centered cubic (FCC) structure, and reconstructed until the spherical shape obtained. The core structure shows tetrahedral (T{sub d}) symmetry structure. It was found that the model need to be passivated, and hence it was noticed that the confinement effect was more pronounced. The model was optimized using Quasi-Newton method for each size of Si-QDs to get relaxed structure before it was simulated. In this model the exchange-correlation potential (V{sub xc}) of the electrons was treated by Local Density Approximation (LDA) functional and Perdew-Zunger (PZ) functional.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Incorporating Electronic Information into Machine Learning Potential Energy Surfaces via Approaching the Ground-State Electronic Energy as a Function of Atom-Based Electronic Populations

Machine learning (ML) approximations to density functional theory (DFT) potential energy surfaces (PESs) are showing great promise for reducing the computational cost of accurate molecular simulations, but at present, they are not applicable to varying electronic states, and in particular, they are not well suited for molecular systems in which the local electronic structure is sensitive to the medium to long-range electronic environment. With this issue as the focal point, we present a new machine learning approach called "BpopNN" for obtaining efficient approximations to DFT PESs. Conceptually, the methodology is based on approaching the true DFT energy as a function of electron populations on atoms; in practice, this is realized with available density functionals and constrained DFT (CDFT). Additionally, the new approach creates approximations to this function with neural networks. These approximations thereby incorporate electronic information naturally into a ML approach, and optimizing the model energy with respect to populations allows the electronic terms to self-consistently adapt to the environment, as in DFT. We confirm the effectiveness of this approach with a variety of calculations on LinHn clusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1993

Actuator and aerodynamic modeling for high-angle-of-attack aeroservoelasticity

Accurate prediction of airframe/actuation coupling is required by the imposing demands of modern flight control systems. In particular, for agility enhancement at high angle of attack and low dynamic pressure, structural integration characteristics such as hinge moments, effective actuator stiffness, and airframe/control surface damping can have a significant effect on stability predictions. Actuator responses are customarily represented with low-order transfer functions matched to actuator test data, and control surface stiffness is often modeled as a linear spring. The inclusion of the physical properties of actuation and its installation on the airframe is therefore addressed using detailed actuator models which consider the physical, electrical, and mechanical elements of actuation. The aeroservoelastic analysis procedure is described in which the actuators are modeled as detailed high-order transfer functions and as approximate low-order transfer functions. The impacts of unsteady aerodynamic modeling on aeroservoelastic stability are also investigated by varying the order of approximation, or number of aerodynamic lag states, in the analysis. Test data from a thrust-vectoring configuration of an F/A-l8 aircraft are compared to predictions to determine the effects on accuracy as a function of modeling complexity.

Brenner, Martin J.↗
DOE OSTI2018

Exploring non-adiabatic approximations to the exchange–correlation functional of TDDFT

A decomposition of the exact exchange–correlation potential of time-dependent density functional theory into an interaction component and a kinetic component offers a new starting point for non-adiabatic approximations. The components are expressed in terms of the exchange–correlation hole and the difference between the one-body density matrix of the interacting and Kohn–Sham systems, which must be approximated in terms of quantities accessible from the Kohn–Sham evolution. We explore several preliminary approximations, evaluate their fulfillment of known exact conditions, and test their performance on simple model systems for which available exact solutions indicate the significance of going beyond the adiabatic approximation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗