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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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Constraining the Dense Matter Equation of State with Joint Analysis of NICER and LIGO/Virgo Measurements

The Neutron Star Interior Composition Explorer collaboration recently published a joint estimate of the mass and the radius of PSR J0030+0451, derived via X-ray pulse-profile modeling. Raaijmakers et al. explored the implications of this measurement for the dense matter equation of state (EOS) using two parameterizations of the high-density EOS: a piecewise-polytropic model, and a model based on the speed of sound in neutron stars (NSs). In this work we obtain further constraints on the EOS following this approach, but we also include information about the tidal deformability of NSs from the gravitational wave signal of the compact binary merger GW170817. Further, we compare the constraints on the EOS to those set by the recent measurement of a 2.14 Me pulsar, included as a likelihood function approximated by a Gaussian, and find a small increase in information gain. To show the flexibility of our method, we also explore the possibility that GW170817 was a NS–black hole merger, which yields weaker constraints on the EOS.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

nmrfit

Nmrfit reads the output from a nuclear magnetic resonance (NMR) experiment and, through a number of intuitive API calls, produces a least-squares fit of Voigt-function approximations via particle swarm optimization.

Source record↗
DOE OSTI2017

A Fresh Math Perspective Opens New Possibilities for Computational Chemistry

By reformulating the TDDFT problem as a matrix function approximation, making use of a special transformation and taking advantage of the underlying symmetry with respect to a non-Euclidean metric, Yang and his colleagues were able to apply the Lanczos algorithm and a Kernal Polynomial Method (KPM) to approximate the absorption spectrum of several molecules. Both of these algorithms require relatively low-memory compared to non-symmetrical alternatives, which is the key to the computational savings.

Vu, Linda↗
DOE OSTI2013

Determination of Optimal Operating Schemes for a Multi-Reservoir System Under Environmental Constraints

In strati ed reservoirs, both dam tailwater discharge and thermal plant intake water quality and temperature can be highly dependent on structure depth. A two- dimensional laterally-averaged model allows for better prediction of water quality over time at specfi c depths. Because high- fidelity models are typically too computationally expensive for direct inclusion within optimization algorithms, water quality is incorporated using one dimensional models are simple flow requirements. Water quality predictions can be incorporated within the optimization process through using surrogate modeling methods, in this application artificial neural network (ANN) models. ANNs are flexible machine learning tools for function approximation composed of a structure of neurons assembled within a multi-layer architecture. They are capable of handling large amounts of training data and modeling nonlinear dynamic systems, making ANNs a well-suited method for this application. This report illustrates the development of ANN models to emulate the hydrodynamic and water quality modeling capabilities of the high- fidelity, two-dimensional CE-QUAL-W2 (W2) model, as well as a linked riverine reservoir system optimization process which accounts for energy generation, water balance and hydraulics, and compliance point water quality. A process for hourly hydropower generation planning is demonstrated on a pair of reservoirs linked in series. The two reservoirs are U.S. Army Corps of Engineers projects with hydropower capabilities on the Cumberland River near Nashville, Tennessee, USA.

13 HYDRO ENERGY↗
DOE OSTI2021

Computational Math Problems for a Clean Energy Future

Cutting edge computational mathematics are ubiquitous in renewable energy research. Problems in resilient and reliable electric grid operations, infrastructure planning, wind farm yaw control, and more demand sophisticated and scalable computational tools that enable the transition of renewable energy technologies from proof of concept to deployment into our energy system. The mission of the Computational Science Center at NREL is to lead the lab's efforts to solve energy challenges using high-performance computing (HPC), computational science, applied mathematics, scientific data management, visualization, and informatics. In this poster, we provide a short overview of three areas of computational mathematics research at NREL: wind power scenario generation for stochastic grid operations and infrastructure planning, improved rational function approximations for electromagnetic transients codes, and wind farm yaw control using a combination of the Alternating Direction Method of Multipliers (ADMM) and reinforcement learning (RL). Increasing penetrations of renewable energy into power grids motivate the investigation of new approaches to characterizing uncertainty for five-minute economic dispatch problems. Similarly, as the penetration of distributed energy resources on power grids increases, it becomes important to revisit our methods of modelling transient phenomena, i.e. electromagnetic transients programs. Finally, the combination of ADMM and RL for wind farm yaw control presented here can potentially increase the efficiency of the deployed distributed controllers by orders of magnitude.

ADMM↗
DOE OSTI2019

First-principles calculation of correlated electron materials based on Gutzwiller wave function beyond Gutzwiller approximation

We introduce a plan that is under the framework of Gutzwiller wave function but goes beyond the commonly adopted Gutzwiller approximation to improve the accuracy and flexibility in treating the correlation effects. Detailed formalism is described for a dimer which is straightforwardly generalized later to more complicated periodic bulk systems. The accuracy of the approach is shown by evaluating the potential energy curves of spin-singlet N 2 dimer, spin-triplet O 2 dimer, and one-dimensional hydrogen chain. The computational workload of the approach can be easily handled by efficient parallel computing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Robust validation of approximate 1-matrix functionals with few-electron harmonium atoms

A simple comparison between the exact and approximate correlation components U of the electron-electron repulsion energy of several states of few-electron harmonium atoms with varying confinement strengths provides a stringent validation tool for 1-matrix functionals. The robustness of this tool is clearly demonstrated in a survey of 14 known functionals, which reveals their substandard performance within different electron correlation regimes. Unlike spot-testing that employs dissociation curves of diatomic molecules or more extensive benchmarking against experimental atomization energies of molecules comprising some standard set, the present approach not only uncovers the flaws and patent failures of the functionals but, even more importantly, also allows for pinpointing their root causes. Since the approximate values of U are computed at exact 1-densities, the testing requires minimal programming and thus is particularly suitable for rapid screening of new functionals.

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

Gedanken densities and exact constraints in density functional theory

Approximations to the exact density functional for the exchange-correlation energy of a many-electron ground state can be constructed by satisfying constraints that are universal, i.e., valid for all electron densities. Gedanken densities are designed for the purpose of this construction, but need not be realistic. The uniform electron gas is an old gedanken density. Here, we propose a spherical two-electron gedanken density in which the dimensionless density gradient can be an arbitrary positive constant wherever the density is non-zero. The Lieb-Oxford lower bound on the exchange energy can be satisfied within a generalized gradient approximation (GGA) by bounding its enhancement factor or simplest GGA exchange-energy density. This enhancement-factor bound is well known to be sufficient, but our gedanken density shows that it is also necessary. The conventional exact exchange-energy density satisfies no such local bound, but energy densities are not unique, and the simplest GGA exchange-energy density is not an approximation to it. We further derive a strongly and optimally tightened bound on the exchange enhancement factor of a two-electron density, which is satisfied by the local density approximation but is violated by all published GGA's or meta-GGA’s. Finally, some consequences of the non-uniform density-scaling behavior for the asymptotics of the exchange enhancement factor of a GGA or meta-GGA are given.

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

Exploring the limit of accuracy for density functionals based on the generalized gradient approximation: Local, global hybrid, and range-separated hybrid functionals with and without dispersion corrections

The limit of accuracy for semi-empirical generalized gradient approximation (GGA) density functionals is explored by parameterizing a variety of local, global hybrid, and range-separated hybrid functionals. The training methodology employed differs from conventional approaches in 2 main ways: (1) Instead of uniformly truncating the exchange, same-spin correlation, and opposite-spin correlation functional inhomogeneity correction factors, all possible fits up to fourth order are considered, and (2) Instead of selecting the optimal functionals based solely on their training set performance, the fits are validated on an independent test set and ranked based on their overall performance on the training and test sets. The 3 different methods of accounting for exchange are trained both with and without dispersion corrections (DFT-D2 and VV10), resulting in a total of 491 508 candidate functionals. For each of the 9 functional classes considered, the results illustrate the trade-off between improved training set performance and diminished transferability. Since all 491 508 functionals are uniformly trained and tested, this methodology allows the relative strengths of each type of functional to be consistently compared and contrasted. The range-separated hybrid GGA functional paired with the VV10 nonlocal correlation functional emerges as the most accurate form for the present training and test sets, which span thermochemical energy differences, reaction barriers, and intermolecular interactions involving lighter main group elements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Anti-symmetric barron functions and their approximation with sums of determinants

A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The architecture of neural network models for the electron wave function typically comprises an equivariant component followed by a summation of determinants. The recently introduced Generic Antisymmetric (GA) block is designed to enhance the expressivity of such neural wave functions, and it was found that the 2-layer GA block achieved more accurate energies than the corresponding single-determinant FermiNet architecure, suggesting its promise as a way to improve the expressivity of neural wave functions. In this paper we show how the function expressed by the 2-layer GA block can be decomposed into a sum of determinants. We formalize this result by defining the antisymmetric Barron space as a generalized version of the 2-layer GA block and providing an appromation theorem for this function class. This result can be viewed as a negative result showing that the 2-layer GA block is not more expressive than using multiple determinants.

Abrahamsen, Nilin↗
DOE OSTI2020

A step in the direction of resolving the paradox of Perdew–Zunger self-interaction correction. II. Gauge consistency of the energy density at three levels of approximation

The Perdew-Zunger(PZ) self-interaction correction (SIC) was designed to correct the one-electron limit of any approximate density functional for the exchange-correlation (xc) energy, while yielding no correction to the exact functional. Unfortunately, it spoils the slowly-varying-in-space limits of the uncorrected approximate functionals, where those functionals are right by construction. The right limits can be restored by locally scaling down the energy density of the PZ SIC in many-electron regions, but then a spurious correction to the exact functional would be found unless the self-Hartree and exact self-xc terms of the PZ SIC energy density were expressed in the same gauge. Only the local density approximation satisfies the same-gauge condition for the energy density, which explains why the recent local-scaling SIC (LSIC) is found here to work excellently for atoms and molecules only with this basic approximation, and not with the more advanced generalized gradient approximations (GGAs) and meta-GGAs, which lose the Hartree gauge via simplifying integrations by parts. The transformation of energy density that achieves the Hartree gauge for the exact xc functional can also be applied to approximate functionals. Doing so leads to a simple scaled-down self-interaction (sdSIC) correction that is typically much more accurate than PZ SIC in tests for many molecular properties (including equilibrium bond lengths). The present work shows unambiguously that the largest errors of PZ SIC applied to standard functionals at three levels of approximation can be removed by restoring their correct slowlyvarying- density limits. Here, it also confirms the relevance of these limits to atoms and molecules.

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

Nonlinear electronic excitations in crystalline solids using meta-generalized gradient approximation and hybrid functional in time-dependent density functional theory

We develop methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta-generalized gradient approximation was proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional was proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt the predictor-corrector step for a stable time evolution. We have developed a method to evaluate electronic excitation energy without referring to the energy functional which is unknown for the TB-mBJ potential. For the HSE functional, we have developed a method for the operation of the Fock-like term in Fourier space to facilitate efficient use of massive parallel computers equipped with graphic processing units. We compare electronic excitations in silicon and germanium induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: they are close to each other using TB-mBJ and HSE and are much smaller in LDA. At high laser intensities close to the damage threshold, electronic excitation energies do not differ much among the three cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Convergence of multipoint Pade approximants of piecewise analytic functions

The behaviour as n{yields}{infinity} of multipoint Pade approximants to a function which is (piecewise) holomorphic on a union of finitely many continua is investigated. The convergence of multipoint Pade approximants is proved for a function which extends holomorphically from these continua to a union of domains whose boundaries have a certain symmetry property. An analogue of Stahl's theorem is established for two-point Pade approximants to a pair of functions, either of which is a multivalued analytic function with finitely many branch points. Bibliography: 11 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Nonlinear Matrix Approximation with Radial Basis Function Components

We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several modern versions of the gradient descent method, including their scalable stochastic counterparts, are used to solve this problem. We provide extensive empirical evidence of the effectiveness of the RBF decomposition and that of the gradient-based fitting algorithm. While being conceptually motivated by singular value decomposition (SVD), our proposed nonlinear counterpart outperforms SVD by drastically reducing the memory required to approximate a data matrix with the same L2 error for a wide range of matrix types. For example, it leads to 2 to 6 times memory save for Gaussian noise, graph adjacency matrices, and kernel matrices. Moreover, this proximity-based decomposition can offer additional interpretability in applications that involve, e.g., capturing the inner low-dimensional structure of the data, retaining graph connectivity structure, and preserving the acutance of images.

Rebrova, Elizaveta↗
DOE OSTI2017

A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions

In this paper, we present a new algorithm for computing the convolution of two compactly supported functions. The algorithm approximates the functions to be convolved using Fourier extensions and then uses the fast Fourier transform to efficiently compute Fourier extension approximations to the pieces of the result. Finally, the complexity of the algorithm is O(N(log N) 2 ), where N is the number of degrees of freedom used in each of the Fourier extensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A linear surrogate for optimising functions of an orthogonal matrix with applications in wave function theory

The technique of surrogate optimisation is to use a simpler function to approximate a complex function that is time-consuming to evaluate. Here we show that the maximum of a special type of surrogate function f(U)=Tr(AU),UϵO(n) is at A T (AA T ) 1/2 , and that there is one and only one local maximum both in SO(n) and O(n)–SO(n). This function f(U) has been found to be useful in various aspects of electronic structure theory, including proving the Carlson-Keller theorem, and localising orbitals. As one other example, we apply it here to optimise the ground state of molecules using the Generalised Valence Bond wavefunction.

74 ATOMIC AND MOLECULAR PHYSICS↗