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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Algorithm 1049: The Delaunay Density Diagnostic

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the density of inputs is sufficient to identify the relevant variations in outputs—i.e., the “geometric scale” of the function—despite the fact that sampling density is closely tied to the success or failure of an approximation method. In this article, we introduce a general purpose, computational approach to detecting the geometric scale of real-valued functions over a fixed domain using a deterministic interpolation technique from computational geometry. The algorithm is intended to work on scalar data in moderate dimensions (2–10). Our algorithm is based on the observation that a sequence of piecewise linear interpolants will converge to a continuous function at a quadratic rate (in L 2 norm) if and only if the data are sampled densely enough to distinguish the feature from noise (assuming sufficiently regular sampling). We present numerical experiments demonstrating how our method can identify feature scale, estimate uncertainty in feature scale, and assess the sampling density for fixed (i.e., static) datasets of input–output pairs. Finally, we include analytical results in support of our numerical findings and have released lightweight code that can be adapted for use in a variety of data science settings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Thermodynamics of Anharmonic Systems: Uncoupled Mode Approximations for Molecules

The partition functions, heat capacities, entropies, and enthalpies of selected molecules were calculated using uncoupled mode (UM) approximations, where the full-dimensional potential energy surface for internal motions was modeled as a sum of independent one-dimensional potentials for each mode. The computational cost of such approaches scales the same with molecular size as standard harmonic oscillator vibrational analysis using harmonic frequencies (HO hf ). To compute thermodynamic properties, a computational protocol for obtaining the energy levels of each mode was established. The accuracy of the UM approximation depends strongly on how the one-dimensional potentials of each modes are defined. If the potentials are determined by the energy as a function of displacement along each normal mode (UM-N), the accuracies of the calculated thermodynamic properties are not significantly improved versus the HO hf model. Significant improvements can be achieved by constructing potentials for internal rotations and vibrations using the energy surfaces along the torsional coordinates and the remaining vibrational normal modes, respectively (UM-VT). For hydrogen peroxide and its isotopologs at 300 K, UM-VT captures more than 70% of the partition functions on average. By con trast, the HO hf model and UM-N can capture no more than 50%. For a selected test set of C2 to C8 linear and branched alkanes and species with different moieties, the enthalpies calculated using the HO hf model, UM-N, and UM-VT are all quite accurate comparing with reference values though the RMS errors of the HO model and UM-N are slightly higher than UM-VT. However, the accuracies in entropy calculations differ significantly between these three models. For the same test set, the RMS error of the standard entropies calculated by UM-VT is 2.18 cal mol -1 K -1 at 1000 K. By contrast, the RMS error obtained using the HO model and UM-N are 6.42 and 5.73 cal mol -1 K -1 , respectively. For a test set composed of nine alkanes ranging from C5 to C8, the heat capacities calculated with the UM-VT model agree with the experimental values to within a RMS error of 0.78 cal mol -1 K -1 , which is less than one-third of the RMS error of the HO hf (2.69 cal mol -1 K -1) and UM-N (2.41 cal mol -1 K -1) models.

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

On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks

Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cases where the target functions to be approximated exhibit high-frequency or multi-scale features. Here in this work we investigate this limitation through the lens of Neural Tangent Kernel (NTK) theory and elucidate how PINNs are biased towards learning functions along the dominant eigen-directions of their limiting NTK. Using this observation, we construct novel architectures that employ spatio-temporal and multi-scale random Fourier features, and justify how such coordinate embedding layers can lead to robust and accurate PINN models. Numerical examples are presented for several challenging cases where conventional PINN models fail, including wave propagation and reaction–diffusion dynamics, illustrating how the proposed methods can be used to effectively tackle both forward and inverse problems involving partial differential equations with multi-scale behavior.

42 ENGINEERING↗
DOE OSTI2020

Gauges, loops, and polynomials for partition functions of graphical models

Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and optimization applications. The problem is #P-hard that is of an exponential complexity with respect to the number of variables. Here, aimed at approximating the partition function, we consider multi-graph models where binary variables and multivariable factors are associated with edges and nodes, respectively, of an undirected multi-graph. We suggest a new methodology for analysis and computations that combines the Gauge function technique from Chertkov and Chernyak with the technique developed in Anari and Oveis Gharan 2017 arXiv:1702.02937; Gurvits 2011 arXiv:1106.2844; Straszak and Vishnoi 2017 55th Annual Allerton Conf. on Communication, Control, and Computing, based on the recent progress in the field of real stable polynomials. We show that the Gauge function, representing a single-out term in a finite sum expression for the partition function which achieves extremum at the so-called belief-propagation gauge, has a natural polynomial representation in terms of gauges/variables associated with edges of the multi-graph. Moreover, Gauge function can be used to recover the partition function through a sequence of transformations allowing appealing algebraic and graphical interpretations. Algebraically, one step in the sequence consists of the application of a differential operator over gauges associated with an edge. Graphically, the sequence is interpreted as a repetitive elimination/contraction of edges resulting in multi-graph models on decreasing in size (number of edges) graphs with the same partition function as in the original multi-graph model. Even though the complexity of computing factors in the sequence of the derived multi-graph models and respective Gauge functions grow exponentially with the number of eliminated edges, polynomials associated with the new factors remain bi-stable if the original factors have this property. Moreover, we show that BP estimations in the sequence do not decrease, each low-bounding the partition function.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Smooth indentation of orthotropic beams

An approximate Green's function for surface displacements in an orthotropic beam is derived as the superposition of the half-plane solution for displacements and the beam theory deflections. The Green's function is used to formulate the integral equation for the problem of smooth contact between a rigid-cylinder and a simply supported orthotropic beam. The integral equation is solved using a least-squares approximation procedure. The contact stress distribution is presented for three materials with different degrees of orthotropy. Numerical results are given for contact force-contact length and contact force-indentation relations. The effects of curvature of the deflected beam, shear deformation and length-to-thickness ratio of the beam on the contact behavior are discussed.

Sankar, B. V.↗
DOE OSTI2018

Construction and Investigation of the Third-Order Approximation to the Solution of the Heat-Conduction Equation for Thin Shallow Shells by Using Legendre Polynomials in the Case of Stationary Heat Exchange

By using the N th order approximation of temperature function and its first derivative by Legendre polynomials, we construct the solution of problem of heat conduction for a thin-walled shallow isotropic shell and deduce the system of resolving equations for the N th approximation. For the first and third approximations, we solve this problem for the case of concentrated heat sources. In the third approximation, we also construct the plots of the dependences of temperature on the distance to the heat source and on the curvature of the shell under the conditions of symmetric or asymmetric stationary heat exchange.

42 ENGINEERING↗
DOE OSTI2022

Augmented Adam-Gibbs model for glass melt viscosity and configuration entropy as functions of temperature and composition

As the temperature of glass melt increases, its structure approaches the state of a simple liquid while the configuration entropy approaches a maximum value. We describe this gradual change using a power law function of inverse temperature. The Adam-Gibbs model for glass viscosity as a function of temperature and glass composition augmented in this way is greatly simplified when applied to common glass families occupying moderate composition regions, such as float glass or nuclear waste glasses, on which properties can be approximated as linear functions of composition. The parsimonious model thus obtained is preferable for use in optimizing glass formulation and mathematical modeling of glass melting and forming. For multicomponent glasses with N viscosity-affecting components, the augmented Adam-Gibbs model requires 2N + 3 adjustable parameters. The model efficacy is demonstrated by fitting the model to a viscosity-temperature-composition dataset for low-activity nuclear waste glasses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2002

Effect of 6 degrees head-down tilt on cardiopulmonary function: comparison with microgravity

BACKGROUND: Head-down tilt (HDT) of 6 degrees is a commonly used model of weightlessness, but there are few comparisons with actual microgravity. HYPOTHESIS: Our study was designed to prove that the changes in cardiopulmonary function seen in HDT would be similar to those seen in microgravity. METHODS: We compared measurements of cardiovascular and pulmonary function from three separate spaceflights of 14 to 17 d duration, with data collected during a 17-d period of HDT. RESULTS: HDT proved a good model of the cardiovascular response to microgravity, resulting in increases in cardiac output and stroke volume of a similar magnitude to those seen in microgravity, with a concomitant reduction in heart rate. By contrast, HDT was a poor model of the effects of microgravity on pulmonary ventilation and gas exchange. CONCLUSION: Pulmonary function in HDT approximated the changes seen in the 1-G supine posture, while in microgravity this was much closer to that seen in the 1-G upright position. The differences probably reflect the fact that changes in cardiovascular function result primarily from fluid shifts within the entire body, whereas changes in pulmonary ventilation are primarily a result of mechanical influences on the lung and chest and abdominal wall.

NASA Discipline Cardiopulmonary↗
NASA NTRS2004

Miniature Robotic Spacecraft for Inspecting Other Spacecraft

A report discusses the Miniature Autonomous Extravehicular Robotic Camera (Mini AERCam)-- a compact robotic spacecraft intended to be released from a larger spacecraft for exterior visual inspection of the larger spacecraft. The Mini AERCam is a successor to the AERCam Sprint -- a prior miniature robotic inspection spacecraft that was demonstrated in a space-shuttle flight experiment in 1997. The prototype of the Mini AERCam is a demonstration unit having approximately the form and function of a flight system. The Mini AERCam is approximately spherical with a diameter of about 7.5 in. (.19 cm) and a weight of about 10 lb (.4.5 kg), yet it has significant additional capabilities, relative to the 14-in. (36-cm), 35-lb (16-kg) AERCam Sprint. The Mini AERCam includes miniaturized avionics, instrumentation, communications, navigation, imaging, power, and propulsion subsystems, including two digital video cameras and a high-resolution still camera. The Mini AERCam is designed for either remote piloting or supervised autonomous operations, including station keeping and point-to-point maneuvering. The prototype has been tested on an air-bearing table and in a hardware-in-the-loop orbital simulation of the dynamics of maneuvering in proximity to the International Space Station.

Fredrickson, Steven↗
DOE OSTI2019

Bootstrap-based confidence interval estimation for thermal security region of bulk power grid

Thermal security region (TSR) is a powerful tool for monitoring and controlling the thermal security of bulk power grid with high penetration of renewable energy. One of the major challenges of TSR in practical application is to obtain the exact analytical expression of the TSR boundary (TSRB) because TSRB is a nonlinear hypersurface described by an implicit function. For this reason, the TSRB is usually approximated by hyperplane instead of getting the exact analytical expression. Traditionally, the coefficients of the hyperplane are estimated with a set of original TSRB points using least square estimation (LSE). However, LSE is a point estimation method, which is incapable of evaluating the quality of the estimation. In addition, the accuracy and computational efficiency of the hyperplane approximation are influenced by the number of TSRB points significantly. Here, a bootstrap based confidence interval estimation is proposed to estimate not only the coefficients of TSRB approximation hyperplane, but also the standard deviations and confidence intervals of the coefficients for evaluating the quality and reliability of the approximation results. First, empirical distribution functions (EDFs) of the coefficients of TSRB approximation hyperplane are approximated from a set of original TSRB points by using residual resampling bootstrap method. Then, the EDFs of the coefficients are employed to estimate the coefficients of the approximation hyperplane. Meanwhile, the standard deviations and confidence intervals of the estimated coefficients of the hyperplanes are also calculated for evaluating the quality and reliability of the approximation. The proposed approach is tested on the China Southern Power Grid (CSG). Results of simulations validate the accuracy and efficiency of the proposed approach in approximating the TSRB.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2015

Calculation of the spectrum of quasiparticle electron excitations in organic molecular semiconductors

A quasiparticle electronic spectrum belongs to the characteristics of nanoobjects that are most important for applications. The following methods of calculating the electronic spectrum are analyzed: the Kohn-Sham equations of the density functional theory (DFT), the hybrid functional method, the GW approximation, and the Lehmann approximation used in the spectral representation of one-electron Green’s function. The results of these approaches are compared with the data of photoemission measurements of benzene, PTCDA, and phthalocyanine (CuPc, H{sub 2}Pc, FePc, PtPc) molecules, which are typical representatives of organic molecular semiconductors (OMS). This comparison demonstrates that the Kohn-Sham equations of DFT incorrectly reproduce the electronic spectrum of OMS. The hybrid functional method correctly describes the spectrum of the valence and conduction bands; however, the HOMO-LUMO gap width is significantly underestimated. The correct gap width is obtained in both the GW approximation and the Lehmann approach, and the total energy in this approach can be calculated in the local density approximation of DFT.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Revisiting Competing Paths in Electrochemical CO 2 Reduction on Copper via Embedded Correlated Wavefunction Theory

We re-evaluate two key steps in the mechanism of CO 2 reduction on copper at a higher level of theory capable of correcting inherent errors in density functional theory (DFT) approximations, namely, embedded correlated wavefunction (ECW) theory. Here, we consider the CO reduction step on Cu(111), which is critical to understanding reaction selectivity. Here, we optimize embedding potentials at the periodic plane-wave DFT level using density functional embedding theory (DFET). All possible adsorption sites (adsites) for each adsorbate then are screened with ECW theory at the catalytically active site to refine the local electronic structure. Unsurprisingly, DFT and ECW theory predict different adsite preferences, largely because of DFT’s inability to properly situate the CO 2π* level. Differing preferred adsites suggest that different reaction pathways could emerge from DFT versus ECW theory. Starting from these preferred ECW theory adsites, we then obtain reaction pathways at the plane-wave DFT level using the climbing-image nudged elastic band method to determine minimum energy paths. Thereafter, we perform ECW calculations at the catalytically active site to correct the energetics at each interpolated structure (image) along the reaction pathways. Via this approach, we confirm that the first step in CO reduction via hydrogen transfer on Cu(111) is to form hydroxymethylidyne (*COH) instead of formyl (*CHO). Although the prediction to preferentially form *COH is consistent with that of DFT, the two theories predict quite different structural and mechanistic behaviors, suggesting that verification is needed for other parts of the mechanism of CO 2 reduction, which is the subject of ongoing work.

30 DIRECT ENERGY CONVERSION↗
NASA NTRS1986

Reflection and emission models for deserts derived from Nimbus-7 ERB scanner measurements

Broadband shortwave and longwave radiance measurements obtained from the Nimbus-7 Earth Radiation Budget scanner were used to develop reflectance and emittance models for the Sahara-Arabian, Gibson, and Saudi Deserts. The models were established by fitting the satellite measurements to analytic functions. For the shortwave, the model function is based on an approximate solution to the radiative transfer equation. The bidirectional-reflectance function was obtained from a single-scattering approximation with a Rayleigh-like phase function. The directional-reflectance model followed from integration of the bidirectional model and is a function of the sum and product of cosine solar and viewing zenith angles, thus satisfying reciprocity between these angles. The emittance model was based on a simple power-law of cosine viewing zenith angle.

Staylor, W. F.↗
DOE OSTI2022

Influence of the complete basis set approximation, tight weighted-core, and diffuse functions on the DLPNO-CCSD(T1) atomization energies of neutral H,C,O-compounds

The impact of complete basis set extrapolation schemes (CBS), diffuse functions, and tight weighted core functions on enthalpies of formation predicted via the DLPNO-CCSD(T1) reduced Feller Peterson-Dixon approach has been examined for neutral H,C,O-compounds. All tested three-point (TZ/QZ/5Z) extrapolation schemes result in mean unsigned deviation (MUD) below 2 kJ mol -1 relative to the experiment. Here, the two-point QZ/5Z and TZ/QZ CBS 1/$l^3_{max}$ extrapolation schemes are inferior to their inverse power counterpart (1/($l_{max}$ + 1/2) 4 ) by 1.3 and 4.3 kJ mol -1 . The CBS extrapolated frozen core atomization energies are insensitive (within 1 kJ mol -1 ) to augmentation of the basis set with tight weighted core functions. The core-valence correlation effects converge already at triple-ζ, although double- ζ/triple- ζ CBS extrapolation performs better and is recommended. The effect of diffuse function augmentation converges slowly, and cannot be reproduced with double- ζ or triple- ζ calculations as these are plagued with basis set superposition and incompleteness errors.

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

Blanco DECam Bulge Survey (BDBS) II: project performance, data analysis, and early science results

ABSTRACT The Blanco DECam Bulge Survey (BDBS) imaged more than 200 sq deg of the Southern Galactic bulge using the ugrizY filters of the Dark Energy Camera, and produced point spread function photometry of approximately 250 million unique sources. In this paper, we present details regarding the construction and collation of survey catalogues, and also discuss the adopted calibration and dereddening procedures. Early science results are presented with a particular emphasis on the bulge metallicity distribution function and globular clusters. A key result is the strong correlation (σ ∼ 0.2 dex) between (u − i)o and [Fe/H] for bulge red clump giants. We utilized this relation to find that interior bulge fields may be well described by simple closed box enrichment models, but fields exterior to b ∼ −6° seem to require a secondary metal-poor component. Applying scaled versions of the closed box model to the outer bulge fields is shown to significantly reduce the strengths of any additional metal-poor components when compared to Gaussian mixture models. Additional results include: a confirmation that the u band splits the subgiant branch in M22 as a function of metallicity, the detection of possible extratidal stars along the orbits of M 22 and FSR 1758, and additional evidence that NGC 6569 may have a small but discrete He spread, as evidenced by red clump luminosity variations in the reddest bands. We do not confirm previous claims that FSR 1758 is part of a larger extended structure.

Johnson, Christian I.↗