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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Reconstructing high-dimensional Hilbert-valued functions via compressed sensing

We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our theoretical framework treats the function approximation problem as a joint sparse recovery problem, where the set of jointly sparse vectors is possibly infinite. To achieve the simultaneous reconstruction of Hilbert-valued functions in both parametric domain and Hilbert space, we propose a novel mixed-norm based `1 regularization method that exploits both energy and sparsity. Our approach requires extensions of concepts such as the restricted isometry and null space properties, allowing us to prove recovery guarantees for sparse Hilbert-valued function reconstruction. We complement the enclosed theory with an algorithm for Hilbert-valued recovery, based on standard forward-backward algorithm, meanwhile establishing its strong convergence in the considered infinite-dimensional setting. Finally, we demonstrate the minimal sample complexity requirements of our approach, relative to other popular methods, with numerical experiments approximating the solutions of high-dimensional parameterized elliptic PDEs.

Dexter, Nick↗
DOE OSTI2020

Electronic structure and thermoelectric properties of CoAsSb with post-DFT approaches

Here, we study the electronic structure and thermoelectric properties of recently synthesized CoAsSb. The calculated bandgap becomes more accurate for increasingly-complex electronic structure methods: generalized gradient approximation, hybrid functionals, selfconsistent linearized quasiparticle GW method (LQSGW), and LQSGW with simplified vertex corrections. By equating the bandgaps of each method from a rigid shift of the bands, we evaluate the contributions made to thermoelectric properties beyond the bandgap. In doing so, we evaluate the efficacy of a commonpractice: a rigid shift applied to less-costly electronic structure methods in order to gain some accuracy of the more-costly methods. We find that while the shift made the Seebeck coefficients much closer to one another than from the original electronic structures, there remain differences in the Goldsmid-Sharp (thermoelectric) bandgap between the methods and from the intended electronic bandgap. Additionally, some lasting differences in temperature dependence remain between the methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Skin and Proximity Effects in Electrodes and Furnace Shells

A review of two-dimensional (2D) analytical models of skin and proximity effects in large industrial furnaces with three electrodes arranged in an equilateral triangle is given. The models cover three different cases: one electrode only, three electrodes where two are approximated by line currents, and induced shell currents where all electrodes are approximated by line currents. The first two models show how the skin and proximity effects depend on electrode material properties and size, and the distance between the electrodes. The third model shows how the strength of the induced shell currents will depend on electrode position and furnace size. These models are compared to numerical studies including distributed electrodes and shell currents. The analytical models are accurate when induced shell currents can be disregarded. However, strong shell currents may have a significant impact on the current distribution within the electrodes. This electrode-shell proximity effect competes with the electrode-electrode proximity effect. Finally, the 2D models have been compared with three-dimensional (3D) case studies of large industrial furnaces. In 3D, the shell currents are significantly smaller than what are predicted by the 2D models, but they are sufficiently strong to cause a significant correction of the electrode current density.

36 MATERIALS SCIENCE↗
DOE OSTI2012

THE TWO STATES OF STAR-FORMING CLOUDS

We examine the effects of self-gravity and magnetic fields on supersonic turbulence in isothermal molecular clouds with high-resolution simulations and adaptive mesh refinement. These simulations use large root grids (512{sup 3}) to capture turbulence and four levels of refinement to follow the collapse to high densities, for an effective resolution of 8192{sup 3}. Three Mach 9 simulations are performed, two super-Alfvenic and one trans-Alfvenic. We find that gravity splits the clouds into two populations, one low-density turbulent state and one high-density collapsing state. The low-density state exhibits properties similar to non-self-gravitating in this regime, and we examine the effects of varied magnetic field strength on statistical properties: the density probability distribution function is approximately lognormal, the velocity power spectral slopes decrease with decreasing mean field strength, the alignment between velocity and magnetic field increases with the field, and the magnetic field probability distribution can be fitted to a stretched exponential. The high-density state is well characterized by self-similar spheres: the density probability distribution is a power law, collapse rate decreases with increasing mean field, density power spectra have positive slopes, P({rho}, k){proportional_to}k, thermal-to-magnetic pressure ratios are roughly unity for all mean field strengths, dynamic-to-magnetic pressure ratios are larger than unity for all mean field strengths, the magnetic field distribution follows a power-law distribution. The high Alfven Mach numbers in collapsing regions explain the recent observations of magnetic influence decreasing with density. We also find that the high-density state is typically found in filaments formed by converging flows, consistent with recent Herschel observations. Possible modifications to existing star formation theories are explored. The overall trans-Alfvenic nature of star-forming clouds is discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Weak values and weak coupling maximizing the output of weak measurements

In a weak measurement, the average output 〈o〉 of a probe that measures an observable A{sup -hat} of a quantum system undergoing both a preparation in a state ρ{sub i} and a postselection in a state E{sub f} is, to a good approximation, a function of the weak value A{sub w}=Tr[E{sub f}A{sup -hat} ρ{sub i}]/Tr[E{sub f}ρ{sub i}], a complex number. For a fixed coupling λ, when the overlap Tr[E{sub f}ρ{sub i}] is very small, A{sub w} diverges, but 〈o〉 stays finite, often tending to zero for symmetry reasons. This paper answers the questions: what is the weak value that maximizes the output for a fixed coupling? What is the coupling that maximizes the output for a fixed weak value? We derive equations for the optimal values of A{sub w} and λ, and provide the solutions. The results are independent of the dimensionality of the system, and they apply to a probe having a Hilbert space of arbitrary dimension. Using the Schrödinger–Robertson uncertainty relation, we demonstrate that, in an important case, the amplification 〈o〉 cannot exceed the initial uncertainty σ{sub o} in the observable o{sup -hat}, we provide an upper limit for the more general case, and a strategy to obtain 〈o〉≫σ{sub o}. - Highlights: •We have provided a general framework to find the extremal values of a weak measurement. •We have derived the location of the extremal values in terms of preparation and postselection. •We have devised a maximization strategy going beyond the limit of the Schrödinger–Robertson relation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Recent Developments in DFTB+, a Software Package for Efficient Atomistic Quantum Mechanical Simulations

DFTB+ is a flexible, open-source software package developed by its community, designed for fast and efficient atomistic quantum mechanical simulations. It employs various methods that approximate density functional theory (DFT), such as density functional-based tight binding (DFTB) and the extended tight binding (xTB) approach allowing simulations of large systems over extended time scales with reasonable accuracy, while being significantly faster than traditional ab initio methods. In recent years, several new extensions of the DFTB method have been developed and implemented in the DFTB+ program package in order to improve the accuracy and generality of the available simulation results. In this paper, we review those enhancements, show several use case examples and discuss the strengths and limitations of its features.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Probabilistic partition of unity networks for high–dimensional regression problems

We explore the probabilistic partition of unity network (PPOU-Net) model in the context of high-dimensional regression problems and propose a general framework focusing on adaptive dimensionality reduction. With the proposed framework, the target function is approximated by a mixture of experts model on a low-dimensional manifold, where each cluster is associated with a fixed-degree polynomial. We present a training strategy that leverages the expectation maximization (EM) algorithm. During the training, we alternate between (i) applying gradient descent to update the DNN coefficients; and (ii) using closed-form formulae derived from the EM algorithm to update the mixture of experts model parameters. Under the probabilistic formulation, step (ii) admits the form of embarrassingly paralleliazable weighted least-squares solves. The PPOU-Nets consistently outperform the baseline fully-connected neural networks of comparable sizes in numerical experiments of various data dimensions. Here, we also explore the proposed model in applications of quantum computing, where the PPOU-Nets act as surrogate models for cost landscapes associated with variational quantum circuits.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Inverse measurement of stiffness by the normalization technique for J-integral fracture toughness

The single specimen normalization technique for J-integral fracture toughness has been successfully employed by several researchers to study the strongly non-linear fracture response of ductile semicrystalline polymers. As part of the normalization technique the load and the plastic component of displacement are normalized. The normalized data is then fit with a normalization function that approximates a power law for small displacements that are dominated by blunting and smoothly transitions to a linear relationship for large displacements that are dominated by stable crack extension. Particularly for very ductile polymers the compliance term used to determine the plastic displacement can dominate the solution and small errors in determining the elastic modulus can lead to large errors in the normalization or even make it ill-posed. This can be further complicated for polymers where the elastic modulus is strong strain rate dependent and simply using a 'quasistatic' modulus from a dogbone measurement may not equate to the dominant strain rate in the compact tension specimen. The current work proposes directly measuring the compliance of the compact tension specimen in the solution of J-integral fracture toughness and then solving for the elastic modulus. By comparison with a range of strain rate data the dominant strain rate can then be determined.

36 MATERIALS SCIENCE↗
DOE OSTI2013

AdS field theory from conformal field theory

We provide necessary and sufficient conditions for a Conformal Field Theory to have a description in terms of a perturbative Effective Field Theory in AdS. The first two conditions are well-known: the existence of a perturbative ‘1/N’ expansion and an approximate Fock space of states generated by a finite number of low-dimension operators. We add a third condition, that the Mellin amplitudes of the CFT correlators must be well- approximated by functions that are bounded by a polynomial at infinity in Mellin space, or in other words, that the Mellin amplitudes have an effective theory-type expansion. We explain the relationship between our conditions and unitarity, and provide an analogy with scattering amplitudes that becomes exact in the flat space limit of AdS. The analysis also yields a simple connection between conformal blocks and AdS diagrams, providing a new calculational tool very much in the spirit of the S-Matrix program. We also begin to explore the potential pathologies associated with higher spin fields in AdS by generalizing Weinberg’s soft theorems to AdS/CFT. The AdS analog of Weinberg’s argument constrains the interactions of conserved currents in CFTs, but there are potential loopholes that are unavailable to theories of massless higher spin particles in flat spacetime.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Improved Architectures and Training Algorithms for Deep Operator Networks

Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under appropriate constraints, they can also be effective in learning the solution operator of partial differential equations (PDEs) in an entirely self-supervised manner. In this work we analyze the training dynamics of deep operator networks (DeepONets) through the lens of Neural Tangent Kernel theory, and reveal a bias that favors the approximation of functions with larger magnitudes. To correct this bias we propose to adaptively re-weight the importance of each training example, and demonstrate how this procedure can effectively balance the magnitude of back-propagated gradients during training via gradient descent. We also propose a novel network architecture that is more resilient to vanishing gradient pathologies. Taken together, our developments provide new insights into the training of DeepONets and consistently improve their predictive accuracy by a factor of 10-50x, demonstrated in the challenging setting of learning PDE solution operators in the absence of paired input-output observations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Initial Fermi orbital descriptors for FLOSIC calculations: The quick-FOD method

Fermi orbital descriptors (FODs) play a key role in Fermi-Löwdin orbital self-interaction correction (FLOSIC) calculations used to remove self-interaction from approximate density functionals. Optimal FODs are obtained by minimizing the self-interaction-corrected total energy, and, in this process, identifying initial sets of FODs becomes crucial. Here we propose, implement and test a novel method for automatically initializing FODs, quick-FOD, based on the minimization of an empirical energy expression that involves a Coulomb-like FOD-electron density attraction, an FOD-FOD short-range repulsion, and an exchange-like FOD-density repulsion. Quick-FOD successfully reproduces FOD arrangements in qualitatively good agreement with Lewis theory and with full-fledged FLOSIC calculations.

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

Gradient-based optimization for regression in the functional tensor-train format

Predictive analysis of complex computational models, such as uncertainty quantification (UQ), must often rely on using an existing database of simulation runs. In this paper we consider the task of performing low-multilinear-rank regression on such a database. Specifically we develop and analyze an efficient gradient computation that enables gradient-based optimization procedures, including stochastic gradient descent and quasi-Newton methods, for learning the parameters of a functional tensor-train (FT). We compare our algorithms with 22 other nonparametric and parametric regression methods on 10 real-world data sets and show that for many physical systems, exploiting low-rank structure facilitates efficient construction of surrogate models. Here, we use a number of synthetic functions to build insight into behavior of our algorithms, including the rank adaptation and group-sparsity regularization procedures that we developed to reduce overfitting. Finally we conclude the paper by building a surrogate of a physical model of a propulsion plant on a naval vessel.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Norm-Conserving Pseudopotentials and Basis Sets to Explore Actinide Chemistry in Complex Environments

We constructed and tested a new set of norm-conserving pseudopotentials, as well as companion Gaussian basis sets, for the actinide series (Ac–Lr) using the Goedecker, Teter and Hutter (GTH) formalism within the generalized gradient approximation (GGA) functional for exchange-correlation of Perdew, Burke and Ernzerhof (PBE). This fills a critical void in the literature for studying the chemistry of 5f–block elements in condensed phase. The accuracy and reliability of the newly parameterized An–GTH pseudopotentials and basis sets, a variety of tests on actinide-containing molecules were carried out and compared to all-electron and available experimental results. The new pseudopotentials include both medium ( [Xe]4f 14 ) and large core ( [Xe]4f 14 5d 10 ) options that successfully reproduced structure and energetics, particularly redox processes. The medium core size set, in particular, reproduced all electron calculations over multiple oxidation states from 0 to VII, whereas the large core set was suitable only for the early series elements and low oxidation states.

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

Pareto Optimization of Oligomer Polarizability and Dipole Moment Using a Genetic Algorithm

High-performance electronic components are highly sought after in order to produce increasingly smaller and cheaper electronic devices. Drawing inspiration from inorganic dielectric materials, in which both polarizability and polarization contribute, organic materials can also maximize both. For a large set of small molecules drawn from PubChem, a Pareto-like front appears between the polarizability and dipole moment, indicating the presence of an apparent trade-off between these two properties. We tested this balance in π-conjugated materials by searching for novel conjugated hexamers with simultaneously large polar- izabilities and dipole moments with potential use for dielectric materials. Using a genetic algorithm (GA) screening technique in conjunction with an approximate density functional tight-binding method for property calculations, we were able to efficiently search chemical space for optimal hexamers. Given the scope of chemical space, using the GA technique saves considerable time and resources by speeding up molecular searches compared to a systematic search. Here, we also explored the underlying structure–function relationships, including sequence and monomer properties, that characterize large polarizability and dipole moment regimes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Adsorption on Fe-MOF-74 for C1–C3 Hydrocarbon Separation

An increase in demand for energy efficient processes for the separation of a mixture of hydrocarbons drives the need for understanding metal–organic frameworks (MOFs) that can provide better noncryogenic alternatives for the fractionation of hydrocarbon mixtures. Here we study the structure and properties of a metal–organic framework, Fe-MOF-74, and its effectiveness to separate C1–C3 hydrocarbon mixtures. The binding of these hydrocarbons to the open metal sites of Fe-MOF-74 has been investigated using a meta-generalized gradient approximation density functional, M06-L, which has previously been validated for systems containing transition metals. For interpretive purposes, charge model 5 (CM5) is used to determine the partial atomic charges on the metal cations and the oxygen atoms of the ligands surrounding these metal centers. Our computations show preferential binding to the metal center of Fe-MOF-74 of unsaturated hydrocarbons over saturated ones in agreement with experimental results, and the calculated binding energies are in semiquantitative agreement with experiment. The results are analyzed in terms of various factors contributing to the binding, including structural distortion, electrostatics, damped dispersion, charge transfer, back bonding, and ligand field effects on the d orbitals. The CM5 charges are not sensitive to small differences in structure.

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

Libration of hydroxyl groups in layered aluminum (oxy)hydroxides and other material analogs: insights from inelastic neutron scattering and theory

We analyzed the hydroxyl librational signatures of five structurally related aluminum (oxy)hydroxides, using inelastic neutron scattering (INS) and plane-wave lattice dynamics simulations. A clear trend across these aluminum-containing phases illustrates the relationship between hydrogen bonding, local atomic structure, and the spectral location and profile of the librational bands. The INS spectra have been compared to previous optical spectroscopy and computational studies, highlighting the complementary nature of the INS technique. Taking into account other structurally or chemically related material analogs, we have identified a correlation between a blueshift (to higher energy) of the upper librational band edge and the geometry of the hydrogen bond interactions, mirroring (with opposite correlation) the well-known redshift in the intramolecular O–H stretching energy with increasing hydrogen bond strength. For hydroxyl groups that do not participate in hydrogen bonding effectively, the bending librations occur at lower energies and hybridize with metal–oxygen lattice modes. Standard density functional theory approximations, including dispersion corrections, struggle to correctly predict vibrational frequencies of motions dominated by H but perform well for metal–oxygen modes, allowing us to make detailed mode assignments in several cases, including a demonstration of how layer-to-layer disorder in boehmite hydrogen bond orientations is reflected in the sharp but minor low energy peaks (at ∼70–80 meV) of the INS spectrum.

Wang, Hsiu-Wen [Oak Ridge National Laboratory (ORN↗