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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Localization in the SCAN meta-generalized gradient approximation functional leading to broken symmetry ground states for graphene and benzene

Density functional theory calculations play a central role in understanding chemical and solid-state systems. Progress depends on density functionals that accurately reproduce both energies, for thermochemistry, and properly describe ground states and other properties that are of interest. The Cr dimer, benzene and graphene are especially important benchmark systems for quantum chemistry and condensed matter physics. The Strongly Constrained and Appropriately Normed (SCAN) functional, which is an advanced meta-generalized gradient approximation functional that significantly improves molecular energies is shown to perform poorly for the Cr dimer. This is connected with its poor performance for itinerant solid-state magnets and is a consequence of over localization of electrons, thus illustrating an analogy between the Cr dimer and itinerant magnets. The Cr dimer is a notoriously difficult system for density functionals. However, we additionally find that SCAN predicts an incorrect symmetry broken ground state for 2D graphene and for the benzene molecule, which is surprising considering that ground states of these are known to be well described even by the simplest local density approximation. We show that SCAN overly favors localized spin polarized states, which is a serious deficiency of this approach. Thus, the challenge of finding density functionals that accurately treat both localized and delocalized electronic systems remains.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Sensitivity of the electronic and magnetic structures of cuprate superconductors to density functional approximations

Abstract We discuss the crystal, electronic, and magnetic structures of La 2− x Sr x CuO 4 (LSCO) for x = 0.0 and x = 0.25 employing 13 density functional approximations, representing the local, semi-local, and hybrid exchange-correlation approximations within the Perdew–Schmidt hierarchy. The meta-generalized gradient approximation (meta-GGA) class of functionals is found to perform well in capturing the key properties of LSCO, a prototypical high-temperature cuprate superconductor. In contrast, the localspin-density approximation, GGA, and the hybrid density functional fail to capture the metal-insulator transition under doping.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Learning nonlinear level sets for dimensionality reduction in function approximation

We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications, where practitioners would replace their computationally intensive physical models (e.g., high-resolution fluid simulators) with fast-to-evaluate predictive machine learning models, so as to accelerate the engineering design processes. There are two major challenges in constructing such predictive models: (a) high-dimensional inputs (e.g., many independent design parameters) and (b) small training data, generated by running extremely time-consuming simulations. Thus, reducing the input dimension is critical to alleviate the over-fitting issue caused by data insufficiency. Existing methods, including sliced inverse regression and active subspace approaches, reduce the input dimension by learning a linear coordinate transformation; our main contribution is to extend the transformation approach to a nonlinear regime. Specifically, we exploit reversible networks (RevNets) to learn nonlinear level sets of a high-dimensional function and parameterize its level sets in low-dimensional spaces. A new loss function was designed to utilize samples of the target functions' gradient to encourage the transformed function to be sensitive to only a few transformed coordinates. The NLL approach is demonstrated by applying it to three 2D functions and two 20D functions for showing the improved approximation accuracy with the use of nonlinear transformation, as well as to an 8D composite material design problem for optimizing the buckling-resistance performance of composite shells of rocket inter-stages.

Zhang, Guannan↗
DOE OSTI2023

Scalable Volume Visualization for Big Scientific Data Modeled by Functional Approximation

Considering the challenges posed by the space and time complexities in handling extensive scientific volumetric data, various data representations have been developed for the analysis of large-scale scientific data. Multivariate functional approximation (MFA) is an innovative data model designed to tackle substantial challenges in scientific data analysis. It computes values and derivatives with high-order accuracy throughout the spatial domain, mitigating artifacts associated with zero- or first-order interpolation. However, the slow query time through MFA makes it less suitable for interactively visualizing a large MFA model. In this work, we develop the first scalable interactive volume visualization pipeline, MFA-DVV, for the MFA model encoded from large-scale datasets. Our method achieves low input latency through distributed architecture, and its performance can be further enhanced by utilizing a compressed MFA model while still maintaining a high-quality rendering result for scientific datasets. We conduct comprehensive experiments to show that MFA-DVV can decrease the input latency and achieve superior visualization results for big scientific data compared with existing approaches.

big scientific dataset↗
NASA NTRS1991

Genetic algorithm based input selection for a neural network function approximator with applications to SSME health monitoring

A genetic algorithm is used to select the inputs to a neural network function approximator. In the application considered, modeling critical parameters of the space shuttle main engine (SSME), the functional relationship between measured parameters is unknown and complex. Furthermore, the number of possible input parameters is quite large. Many approaches have been used for input selection, but they are either subjective or do not consider the complex multivariate relationships between parameters. Due to the optimization and space searching capabilities of genetic algorithms they were employed to systematize the input selection process. The results suggest that the genetic algorithm can generate parameter lists of high quality without the explicit use of problem domain knowledge. Suggestions for improving the performance of the input selection process are also provided.

Peck, Charles C.↗
NASA NTRS1975

Spline function approximation techniques for image geometric distortion representation

Least squares approximation techniques were developed for use in computer aided correction of spatial image distortions for registration of multitemporal remote sensor imagery. Polynomials were first used to define image distortion over the entire two dimensional image space. Spline functions were then investigated to determine if the combination of lower order polynomials could approximate a higher order distortion with less computational difficulty. Algorithms for generating approximating functions were developed and applied to the description of image distortion in aircraft multispectral scanner imagery. Other applications of the techniques were suggested for earth resources data processing areas other than geometric distortion representation.

Anuta, P. E.↗
NASA NTRS1992

Nonlinear functional approximation with networks using adaptive neurons

A novel mathematical framework for the rapid learning of nonlinear mappings and topological transformations is presented. It is based on allowing the neuron's parameters to adapt as a function of learning. This fully recurrent adaptive neuron model (ANM) has been successfully applied to complex nonlinear function approximation problems such as the highly degenerate inverse kinematics problem in robotics.

Tawel, Raoul↗
NASA NTRS2011

Basis Function Approximation of Transonic Aerodynamic Influence Coefficient Matrix

A technique for approximating the modal aerodynamic influence coefficients matrices by using basis functions has been developed and validated. An application of the resulting approximated modal aerodynamic influence coefficients matrix for a flutter analysis in transonic speed regime has been demonstrated. This methodology can be applied to the unsteady subsonic, transonic, and supersonic aerodynamics. The method requires the unsteady aerodynamics in frequency-domain. The flutter solution can be found by the classic methods, such as rational function approximation, k, p-k, p, root-locus et cetera. The unsteady aeroelastic analysis for design optimization using unsteady transonic aerodynamic approximation is being demonstrated using the ZAERO flutter solver (ZONA Technology Incorporated, Scottsdale, Arizona). The technique presented has been shown to offer consistent flutter speed prediction on an aerostructures test wing 2 configuration with negligible loss in precision in transonic speed regime. These results may have practical significance in the analysis of aircraft aeroelastic calculation and could lead to a more efficient design optimization cycle.

Li, Wesley W.↗
NASA NTRS2010

Basis Function Approximation of Transonic Aerodynamic Influence Coefficient Matrix

A technique for approximating the modal aerodynamic influence coefficients [AIC] matrices by using basis functions has been developed and validated. An application of the resulting approximated modal AIC matrix for a flutter analysis in transonic speed regime has been demonstrated. This methodology can be applied to the unsteady subsonic, transonic and supersonic aerodynamics. The method requires the unsteady aerodynamics in frequency-domain. The flutter solution can be found by the classic methods, such as rational function approximation, k, p-k, p, root-locus et cetera. The unsteady aeroelastic analysis for design optimization using unsteady transonic aerodynamic approximation is being demonstrated using the ZAERO(TradeMark) flutter solver (ZONA Technology Incorporated, Scottsdale, Arizona). The technique presented has been shown to offer consistent flutter speed prediction on an aerostructures test wing [ATW] 2 configuration with negligible loss in precision in transonic speed regime. These results may have practical significance in the analysis of aircraft aeroelastic calculation and could lead to a more efficient design optimization cycle

Li, Wesley Waisang↗
DOE OSTI2024

Self‐Consistent Convolutional Density Functional Approximations: Application to Adsorption at Metal Surfaces

The exchange-correlation (XC) functional in density functional theory is used to approximate multi-electron interactions. A plethora of different functionals are available, but nearly all are based on the hierarchy of inputs commonly referred to as “Jacob's ladder.” This paper introduces an approach to construct XC functionals with inputs from convolutions of arbitrary kernels with the electron density, providing a route to move beyond Jacob's ladder. We derive the variational derivative of these functionals, showing consistency with the generalized gradient approximation (GGA), and provide equations for variational derivatives based on multipole features from convolutional kernels. A proof-of-concept functional, PBEq, which generalizes the PBEα framework with mathematical equation being a spatially-resolved function of the monopole of the electron density, is presented and implemented. It allows a single functional to use different GGAs at different spatial points in a system, while obeying PBE constraints. Analysis of the results underlines the importance of error cancellation and the XC potential in data-driven functional design. After testing on small molecules, bulk metals, and surface catalysts, the results indicate that this approach is a promising route to simultaneously optimize multiple properties of interest.

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

Opening band gaps of low-dimensional materials at the meta-GGA level of density functional approximations

The quasiparticle band structure can be properly described by Hedin's GW approximation (GW), at a high computational cost. For band gaps, semilocal density functionals up to the generalized gradient approximation (GGA) level cannot compete with the accuracy of hybrid-based approximations or GW. Meta-GGA density functionals with a strong dependence on the kinetic energy density ingredient can potentially give wider band gaps compared with GGAs. The recent TASK meta-GGA density functional from Aschebrock and Kümmel [ Phys. Rev. Research 1 , 033082 (2019) ], is constructed with an enhanced nonlocality in the generalized Kohn-Sham scheme and therefore harbors great opportunities for band gap prediction. Although this approximation was found to yield excellent band gaps of bulk solids, this accuracy cannot be straightforwardly transferred to low-dimensional materials. Additionally, the reduced screening of these materials results in larger band gaps compared with their bulk counterparts, as an additional barrier to overcome. In this paper we demonstrate how the alteration of this functional affects the band gaps of monolayers and nanoribbons and present accurate band gaps competing with the revised Heyd-Scuseria-Ernzerhof (HSE06) approximation. In order to achieve this goal, we have modified the TASK functional (a) by changing the tight upper bound for one- or two-electron systems ( h X 0 ) from 1.174 to 1.29 and (b) by changing the limit of the interpolation function f X ( α → ∞ ) of the TASK functional that interpolates the exchange enhancement factor F X ( s , α ) from α = 0 to 1. The resulting modified TASK (mTASK) was tested for various materials from three dimensions to two dimensions to one dimension (nanoribbons) and was compared with the results of the higher-level hybrid functional HSE06 or with the G 0 W 0 approximation within many-body perturbation theory. We find that mTASK systematically improves the band gaps and band structures of two-dimensional (2D) and 1D systems, without significantly affecting the accuracy of the original TASK for the bulk 3D materials, when compared with the Perdew-Burke-Ernzerhof (PBE) GGA and the strongly constrained and appropriately normed (SCAN) meta-GGA. We further demonstrate the applicability of mTASK by assessing the band structures of transition metal dichalcogenide nanoribbons with respect to various bending curvatures.

36 MATERIALS SCIENCE↗
NASA NTRS2019

Experimentally-Derived Phase Function Approximations in Support of the Orbital Debris Program Office

The NASA Orbital Debris Program Office (ODPO) has used various optical assets to acquire photometric data of Earth-orbiting objects to define the orbital debris environment. To better characterize and model optical data acquired from ground-based telescopes, the Optical Measurements Center (OMC) at NASA Johnson Space Center emulates illumination conditions seen in space by using equipment and techniques that parallel telescopic observations and source-target-sensor orientations. One of the OMC goals is to improve the size calculation used for optical data by developing an optical-based Size Estimation Model. The current size estimation requires applying a Lambertian phase function, a set albedo value, and range to the observed magnitude. The first step to improving the sampled brightness of laboratory targets is to remove aspect-angle dependencies. Then, the volume of possible object viewing angles is sampled at 21 combinations of azimuth and elevation angles for each solar phase angle. Finally, the acquired images are input into an image processing program that generates approximations for the object’s Bidirectional Reflectance Distribution Function (BRDF) and phase function. The BRDF is a radiometric concept that identifies an object’s material composition by matching a BRDF approximated with photometric data collected by ground-based telescopes with a BRDF generated experimentally from a known object in the laboratory. This paper presents the initial BRDF and phase function approximations for various fragments/targets acquired in the OMC and how the findings will be incorporated into ODPO models. A Lambertian sphere is used as a baseline for initial size estimation calculations and phase function comparisons. Spacecraft materials and fragments from hypervelocity laboratory impact tests are also presented to compare against the current assumed Lambertian phase function used for size estimates. This paper presents the preliminary phase function analysis and plan forward to utilize a laboratory-based phase function to improve the current optical size estimates using BRDF measurements for a large volume of targets composed of various shapes, sizes, and materials.

Hostetler, J.↗
DOE OSTI2019

Semi-local Density Functional Approximations for Bulk, Surface, and Confinement Physics

Due to its balance of accuracy and computational cost, density functional theory has become the method of choice for computing the electronic structure and related properties of materials. However, present-day semi-local approximations to the exchange-correlation energy of density functional theory break down for materials containing d and f electrons. In this report we summarize the results of our research efforts within the LDRD 200202 titled "Making density functional theory work for all materials" in addressing this issue. Our efforts are grouped into two research thrusts. In the first thrust, we develop an exchange-correlation functional (BSC functional) within the subsystem functional formalism. It enables us to capture bulk, surface, and confinement physics with a single, semi-local exchange-correlation functional in density functional theory calculations. We present the analytical properties of the BSC functional and demonstrate that the BSC functional is able to capture confinement physics more accurately than standard semi-local exchange-correlation functionals. The second research thrust focusses on developing a database for transition metal binary compounds. The database consists of materials properties (formation energies, ground-state energies, lattice constants, and elastic constants) of 26 transition metal elements and 89 transition metal alloys. It serves as a reference for benchmarking computational models (such as lower-level modeling methods and exchange-correlation functionals). We expect that our database will significantly impact the materials science community. We conclude with a brief discussion on the future research directions and impact of our results.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Machine learning for accuracy in density functional approximations

Machine learning techniques have found their way into computational chemistry as indispensable tools to accelerate atomistic simulations and materials design. In addition, machine learning approaches hold the potential to boost the predictive power of computationally efficient electronic structure methods, such as density functional theory, to chemical accuracy and to correct for fundamental errors in density functional approaches. In this paper, recent progress in applying machine learning to improve the accuracy of density functional and related approximations is reviewed. Promises and challenges in devising machine learning models transferable between different chemistries and materials classes are discussed with the help of examples applying promising models to systems far outside their training sets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems

Presently the training of neural networks relies on data of comparable accuracy but in real applications only a very small set of high-fidelity data is available while inexpensive lower fidelity data may be plentiful. We propose a new composite neural network (NN) that can be trained based on multi-fidelity data. It is comprised of three NNs, with the first NN trained using the low-fidelity data and coupled to two high-fidelity NNs, one with activation functions and another one without, in order to discover and exploit nonlinear and linear correlations, respectively, between the low-fidelity and the high-fidelity data. We first demonstrate the accuracy of the new multi-fidelity NN for approximating some standard benchmark functions but also a 20-dimensional function that is not easy to approximate with other methods, e.g. Gaussian process regression. Subsequently, we extend the recently developed physics-informed neural networks (PINNs) to be trained with multi-fidelity data sets (MPINNs). MPINNs contain four fully-connected neural networks, where the first one approximates the low-fidelity data, while the second and third construct the correlation between the low- and high-fidelity data and produce the multi-fidelity approximation, which is then used in the last NN that encodes the partial differential equations (PDEs). Specifically, by decomposing the correlation into a linear and nonlinear part, the present model is capable of learning both the linear and complex nonlinear correlations between the low- and high-fidelity data adaptively. By training the MPINNs, we can: (1) obtain the correlation between the low- and high-fidelity data, (2) infer the quantities of interest based on a few scattered data, and (3) identify the unknown parameters in the PDEs. In particular, we employ the MPINNs to learn the hydraulic conductivity field for unsaturated flows as well as the reactive models for reactive transport. The results demonstrate that MPINNs can achieve relatively high accuracy based on a very small set of high-fidelity data. Despite the relatively low dimension and limited number of fidelities (two-fidelity levels) for the benchmark problems in the present study, the proposed model can be readily extended to very high-dimensional regression and classification problems involving multi-fidelity data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

On the Sensitivity to Density-Functional Approximations for CO Binding Energies of Single-Atom Catalysts in Nitrogen-Doped Graphene

Density functional theory (DFT) methods are the working horse in screening new catalytic materials. They are widely used to predict trends in binding energies, which are then used to compare the activity of different materials. Here, the binding strength of CO is an important descriptor to the CO 2 reduction catalytic activity of the single transition metal atoms embedded on nitrogen-doped graphene (TM/NG). In this work, however, we show that CO binding strengths in different TM/NG has very different sensitivity to DFT methods. Specifically, Fe/NG CO binding energy changes dramatically with the percentage of exact exchange in the functional; Co/NG does less so, while Ni/NG nearly has no change. Such varying behaviors is a direct result of different local spin configurations, similar to the performance of DFT methods for metal porphyrin complexes. Therefore, caution should be exercised when using DFT binding energies for quantitative predictions in TM/NG single atom catalysis.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2019

Interaction between water and carbon nanostructures: How good are current density functional approximations?

Due to their current and future technological applications, including realization of water filters and desalination membranes, water adsorption on graphitic sp2-bonded carbon is of overwhelming interest. However, these systems are notoriously challenging to model, even for electronic structure methods such as density functional theory (DFT), because of the crucial role played by London dispersion forces and noncovalent interactions, in general. Recent efforts have established reference quality interactions of several carbon nanostructures interacting with water. Here, we compile a new benchmark set (dubbed WaC18), which includes a single water molecule interacting with a broad range of carbon structures and various bulk (3D) and two-dimensional (2D) ice polymorphs. The performance of 28 approaches, including semilocal exchange-correlation functionals, nonlocal (Fock) exchange contributions, and long-range van der Waals (vdW) treatments, is tested by computing the deviations from the reference interaction energies. The calculated mean absolute deviations on the WaC18 set depend crucially on the DFT approach, ranging from 135 meV for local density approximation (LDA) to 12 meV for PBE0-D4. We find that modern vdW corrections to DFT significantly improve over their precursors. Within the 28 tested approaches, we identify the best performing within the functional classes of generalized gradient approximated (GGA), meta-GGA, vdW-DF, and hybrid DF, which are BLYP-D4, TPSS-D4, rev-vdW-DF2, and PBE0-D4, respectively.

Brandenburg, Jan Gerit (ORCID:0000000292192948)↗