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At least 1,045 records · Page 58

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DOE OSTI2025

Simplifying activations with linear approximations in neural networks

A key step in Neural Networks is activation. Among the different types of activation functions, sigmoid, tanh, and others involve the usage of exponents for calculation. From a hardware perspective, exponential implementation implies the usage of Taylor series or repeated methods involving many addition, multiplication, and division steps, and as a result are power-hungry and consume many clock cycles. We implement a piecewise linear approximation of the sigmoid function as a replacement for standard sigmoid activation libraries. This approach provides a practical alternative by leveraging piecewise segmentation, which simplifies hardware implementation and improves computational efficiency. In this paper, we detail piecewise functions that can be implemented using linear approximations and their implications for overall model accuracy and performance gain. Our results show that for the DenseNet, ResNet, and GoogLeNet architectures, the piecewise linear approximation of the sigmoid function provides faster execution times compared to the standard TensorFlow sigmoid implementation while maintaining comparable accuracy. Specifically, for MNIST with DenseNet, accuracy reaches 99.91% (Piecewise) vs. 99.97% (Base) with up to 1.31x speedup in execution time. For CIFAR-10 with DenseNet, accuracy improves to 98.97% (Piecewise) vs. 99.40% (Base) while achieving 1.24x faster execution. Similarly, for CIFAR-100 with DenseNet, the accuracy is 97.93% (Piecewise) vs. 98.39% (Base), with a 1.18x execution time reduction. These results confirm the proposed method’s capability to efficiently process large-scale datasets and computationally demanding tasks, offering a practical means to accelerate deep learning models, including LSTMs, without compromising accuracy.

Activation function↗

DOE OSTI2014

Quark mass functions and pion structure in Minkowski space

We present a study of the dressed quark mass function and the pion structure in Minkowski space using the Covariant Spectator Theory (CST). The quark propagators are dressed with the same kernel that describes the interaction between different quarks. We use an interaction kernel in momentum space that is a relativistic generalization of the linear confining q-qbar potential and a constant potential shift that defines the energy scale. The confining interaction has a Lorentz scalar part that is not chirally invariant by itself but decouples from the equations in the chiral limit and therefore allows the Nambu--Jona-Lasinio (NJL) mechanism to work. We adjust the parameters of our quark mass function calculated in Minkowski-space to agree with LQCD data obtained in Euclidean space. Results of a calculation of the pion electromagnetic form factor in the relativistic impulse approximation using the same mass function are presented and compared with experimental data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Electronic Structure and Linhard Function of Iron-Based Superconductor La{sub 0.5−x}Na{sub 0.5 + x}Fe{sub 2}As{sub 2}

We perform theoretical studies of the iron-based superconductor La{sub 0.5−x}Na{sub 0.5 + x}Fe{sub 2}As{sub 2}. Using density functional calculation with virtual crystal approximation, band structures, density of states, and Fermi surfaces are obtained for different La/Na composition by varying x value. Furthermore, the nesting property is also investigated using the Linhard function. Our main findings are as follows: For undoped (x = 0.0) case, the magnetic and electronic structure share great similarities with extensively studied BaFe{sub 2}As{sub 2}. Upon hole doping (x = 0.3), the Q = (π,π) nesting property are preserved. However, upon electron doping (x = -0.3), the Fermi surfaces undergo a dramastic change into 3D and complex structure. We find this change is attributed to the comprehensive influence of band filling and chemical pressure of La{sup 3+}. We propose the asymmetric change of Fermi surfaces upon doping may in some sense explain the electron-hole asymmetry in phase diagram.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2017

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

Here, a new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm -1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2016

Multiscale Simulation Framework for Coupled Fluid Flow and Mechanical Deformation

Our work in this project is aimed at making fundamental advances in multiscale methods for flow and transport in highly heterogeneous porous media. The main thrust of this research is to develop a systematic multiscale analysis and efficient coarse-scale models that can capture global effects and extend existing multiscale approaches to problems with additional physics and uncertainties. A key emphasis is on problems without an apparent scale separation. Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations. These procedures capture the effects of fine-scale permeability variations through the calculation of specialized coarse-scale basis functions. Most of the multiscale techniques presented to date employ localization approximations in the calculation of these basis functions. For some highly correlated (e.g., channelized) formations, however, global effects are important and these may need to be incorporated into the multiscale basis functions. Other challenging issues facing multiscale simulations are the extension of existing multiscale techniques to problems with additional physics, such as compressibility, capillary effects, etc. In our project, we explore the improvement of multiscale methods through the incorporation of additional (single-phase flow) information and the development of a general multiscale framework for flows in the presence of uncertainties, compressible flow and heterogeneous transport, and geomechanics. We have considered (1) adaptive local-global multiscale methods, (2) multiscale methods for the transport equation, (3) operator-based multiscale methods and solvers, (4) multiscale methods in the presence of uncertainties and applications, (5) multiscale finite element methods for high contrast porous media and their generalizations, and (6) multiscale methods for geomechanics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Multiscale analysis and computation for flows in heterogeneous media

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

The cosmological bootstrap: inflationary correlators from symmetries and singularities

Scattering amplitudes at weak coupling are highly constrained by Lorentz invariance, locality and unitarity, and depend on model details only through coupling constants and the particle content of the theory. For example, four-particle amplitudes are analytic for contact interactions and have simple poles with appropriately positive residues for tree-level exchange. In this paper, we develop an understanding of inflationary correlators which parallels that of flat-space scattering amplitudes. Specifically, we study slow-roll inflation with weak couplings to extra massive particles, for which all correlation functions are controlled by an approximate conformal symmetry on the boundary of the spacetime. After systematically classifying all possible contact terms in de Sitter space, we derive an analytic expression for the four-point function of conformally coupled scalars mediated by the tree-level exchange of massive scalars. Conformal symmetry implies that the correlator satisfies a pair of differential equations with respect to spatial momenta, encoding bulk time evolution in purely boundary terms. The absence of unphysical singularities (and the correct normalization of physical ones) completely fixes this correlator. Moreover, a “spin-raising” operator relates it to the correlators associated with the exchange of particles with spin, while “weight-shifting” operators map it to the four-point function of massless scalars. We explain how these de Sitter four-point functions can be perturbed to obtain inflationary three-point functions. Using our formalism, we reproduce many classic results in the literature, such as the three-point function of slow-roll inflation, and provide a complete classification of all inflationary three- and four-point functions arising from weakly broken conformal symmetry. Remarkably, the inflationary bispectrum associated with the exchange of particles with arbitrary spin is completely characterized by the soft limit of the simplest scalar-exchange four-point function of conformally coupled scalars and a series of contact terms. Finally, we demonstrate that the inflationary correlators contain flat-space scattering amplitudes via a suitable analytic continuation of the external momenta, which can also be directly connected with the signals for particle production seen in the squeezed limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Optimal Portfolio Management in a Modified Constant Elasticity of Variance Model

We investigate the optimal management of a portfolio consisting of a risk asset and a risk-free bond. The asset dynamics is specified by the M-CEV model. Assuming that the investor has a power utility function, we derive an explicit analytical portfolio-management formula that contains confluent hypergeometric functions. The asymptotic form of the proposed portfolio management strategy is obtained, as well as approximate formulas consisting only of elementary functions. We additionally present an application of our results in the context of algorithmic statistical-arbitrage strategies.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Non-Gaussianity in the weak lensing correlation function likelihood – implications for cosmological parameter biases

ABSTRACT We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in 1D marginal distributions of shear two-point correlation functions in simulated weak lensing data. We examine the implications in the context of future surveys, in particular LSST, with derivations of how the non-Gaussianity scales with survey area. We show that there is no significant bias in 1D posteriors of Ωm and σ8 due to the non-Gaussian likelihood distributions of shear correlations functions using the mock data (100 deg2). We also present a systematic approach to constructing approximate multivariate likelihoods with 1D parametric functions by assuming independence or more flexible non-parametric multivariate methods after decorrelating the data points using principal component analysis (PCA). While the use of PCA does not modify the non-Gaussianity of the multivariate likelihood, we find empirically that the 1D marginal sampling distributions of the PCA components exhibit less skewness and kurtosis than the original shear correlation functions. Modelling the likelihood with marginal parametric functions based on the assumption of independence between PCA components thus gives a lower limit for the biases. We further demonstrate that the difference in cosmological parameter constraints between the multivariate Gaussian likelihood model and more complex non-Gaussian likelihood models would be even smaller for an LSST-like survey. In addition, the PCA approach automatically serves as a data compression method, enabling the retention of the majority of the cosmological information while reducing the dimensionality of the data vector by a factor of ∼5.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Effect of XC functionals and dispersion corrections on the DFT‐computed structural and vibrational properties of SrCl 2 –NaCl and ZrF 4 –LiF

Density functional theory (DFT) calculations were performed to examine the impact of exchange–correlation (XC) functionals and van der Waals corrections (specifically the D3 method) on the structural and vibrational properties of the SrCl 2 –NaCl and ZrF 4 –LiF salt systems. Multiple XC functionals, including the local density approximation (LDA), the generalized gradient approximation using the Perdew–Burke–Ernzerhof (PBE) model, and its modified form suitable for solids (PBEsol), the dispersion-corrected PBE-D3 and PBEsol-D3, were considered. Of these functionals, LDA was found to exhibit the highest degree of error, while PBEsol and PBE-D3 displayed the least error. Underestimated lattice parameters compared with experimental values were observed to result in higher force constants, leading to an overprediction of vibrational frequencies. Conversely, an overestimation of lattice parameters was associated with lower vibrational frequencies. The methodology presented in this study yielded results that are in good agreement with experiment, irrespective of the method (finite differences vs. density functional perturbation theory) employed for calculating infrared and Raman spectra. It was further demonstrated that for alkali halides with weak Raman scattering, utilizing a supercell constructed from primitive cells better predicts Raman features than does the use of conventional cells.

Raman↗

DOE OSTI2016

ωB97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation

A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation is presented in this paper. The final 12-parameter functional form is selected from approximately 10 × 10 9 candidate fits that are trained on a training set of 870 data points and tested on a primary test set of 2964 data points. The resulting density functional, ωB97M-V, is further tested for transferability on a secondary test set of 1152 data points. For comparison, ωB97M-V is benchmarked against 11 leading density functionals including M06-2X, ωB97X-D, M08-HX, M11, ωM05-D, ωB97X-V, and MN15. Encouragingly, the overall performance of ωB97M-V on nearly 5000 data points clearly surpasses that of all of the tested density functionals. Finally, in order to facilitate the use of ωB97M-V, its basis set dependence and integration grid sensitivity are thoroughly assessed, and recommendations that take into account both efficiency and accuracy are provided.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

How Well Can the M06 Suite of Functionals Describe the Electron Densities of Ne, Ne 6+ , and Ne 8+ ?

The development of better approximations to the exact exchange-correlation functional is essential to the accuracy of density functionals. A recent study indicated that functionals with few parameters offer more accurate electron densities than recently developed many-parameter functionals for light closed-shell atomic systems. In this study, we calculated electron densities, their gradients, and Laplacians of Ne, Ne 6+ , and Ne 8+ using 19 electronic structure methods, and we compared them to the CCSD reference results. Two basis sets, namely, aug-cc-pωCV5Z and aug-cc-pV5Z, are utilized in the calculations. We found that the choice of basis set has a significant impact on the errors and rankings of some of the selected methods. The errors of electron densities, their gradients, and Laplacians calculated with the aug-cc-pV5Z basis set are substantially reduced, especially for Minnesota density functionals, as compared to the results using the aug-cc-pωCV5Z basis set (a larger basis set utilized in earlier work (Medvedev et al. Science2017, 355, 49–52)). The rankings of the M06 suite of functionals among the 19 methods are greatly improved with the aug-cc-pV5Z basis set. Furthermore, the performances of the HSE06, BMK, MN12-L, and MN12-SX functionals are also improved with the aug-cc-pV5Z basis set. The M06 suite of functionals is capable of providing accurate electron densities, gradients, and Laplacians using the aug-cc-pV5Z basis set, and thus it is suitable for a wide range of applications in chemistry and physics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Comparison of first principles and semi-empirical models of the structural and electronic properties of Ge{sub 1−x}Sn{sub x} alloys

We present and compare three distinct atomistic models—based on first principles and semi-empirical approaches—of the structural and electronic properties of Ge{sub 1−x}Sn{sub x} alloys. Density functional theory calculations incorporating Heyd–Scuseria–Ernzerhof (HSE), local density approximation (LDA) and modified Becke–Johnson (mBJ) exchange-correlation functionals are used to perform structural relaxation and electronic structure calculations for a series of Ge{sub 1−x}Sn{sub x} alloy supercells. Based on HSE calculations, a semi-empirical valence force field (VFF) potential and sp{sup 3}s{sup ∗} tight-binding (TB) Hamiltonian are parametrised. Comparing the HSE, LDA+mBJ and VFF+TB models, and using the HSE results as a benchmark, we demonstrate that: (1) LDA+mBJ calculations provide an accurate first principles description of the electronic structure at reduced computational cost, (2) the VFF potential is sufficiently accurate to circumvent the requirement to perform first principles structural relaxation, and (3) VFF+TB calculations provide a good quantitative description of the alloy electronic structure in the vicinity of the band edges. Our results also emphasise the importance of Sn-induced band mixing in determining the nature of the conduction band structure of Ge{sub 1−x}Sn{sub x} alloys. The theoretical models and benchmark calculations we present inform and enable predictive, computationally efficient and scalable atomistic calculations for disordered alloys and nanostructures. This provides a suitable platform to underpin further theoretical investigations of the properties of this emerging semiconductor alloy.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2014

Prediction of Thermal Conductivity for Irradiated SiC/SiC Composites by Informing Continuum Models with Molecular Dynamics Data

This article proposes a new method to estimate the thermal conductivity of SiC/SiC composites subjected to neutron irradiation. The modeling method bridges different scales from the atomic scale to the scale of a 2D SiC/SiC composite. First, it studies the irradiation-induced point defects in perfect crystalline SiC using molecular dynamics (MD) simulations to compute the defect thermal resistance as a function of vacancy concentration and irradiation dose. The concept of defect thermal resistance is explored explicitly in the MD data using vacancy concentrations and thermal conductivity decrements due to phonon scattering. Point defect-induced swelling for chemical vapor deposited (CVD) SiC as a function of irradiation dose is approximated by scaling the corresponding MD results for perfect crystal β-SiC to experimental data for CVD-SiC at various temperatures. The computed thermal defect resistance, thermal conductivity as a function of grain size, and definition of defect thermal resistance are used to compute the thermal conductivities of CVD-SiC, isothermal chemical vapor infiltrated (ICVI) SiC and nearly-stoichiometric SiC fibers. The computed fiber and ICVI-SiC matrix thermal conductivities are then used as input for an Eshelby-Mori-Tanaka approach to compute the thermal conductivities of 2D SiC/SiC composites subjected to neutron irradiation within the same irradiation doses. Predicted thermal conductivities for an irradiated Tyranno-SA/ICVI-SiC composite are found to be comparable to available experimental data for a similar composite ICVI-processed with these fibers.

SiC/SiC composites, thermal conductivity, fiber/ma↗

DOE OSTI2015

Half-metallic antiferromagnetism in double perovskite BiPbCrCuO{sub 6}

The electronic structure and magnetic properties of BiPbCrCuO{sub 6} double perovskite are investigated based on first-principles density functional calculations with generalized gradient approximation (GGA) and GGA incorporated with Coulomb correlation interaction U (GGA + U). The results suggest the half-metallic (HM) and antiferromagnetic (AFM) properties of BiPbCrCuO{sub 6} double perovskite. The HM-AFM property of the double perovskite is caused by the double-exchange mechanism between neighboring Cr{sup 5+}(t{sub 2g}{sup 1}↓) and Cu{sup 2+}(t{sub 2g}{sup 3}↑t{sub 2g}{sup 3}↓e{sub g}{sup 2}↑e{sub g}↓) via the intermediate O{sup 2−}(2s{sup 2}2p{sup 6}) ion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

QCD factorization with multihadron fragmentation functions

Important aspects of quantum chromodynamics (QCD) factorization theorems are the properties of the objects involved that can be identified as universal. One example is that the definitions of parton densities and fragmentation functions for different types of hadrons differ only in the identity of the nonperturbative states that form the matrix elements, but are otherwise the same. This leads to independence of perturbative calculations on nonperturbative details of external states. It also lends support to interpretations of correlation functions as encapsulations of intrinsic nonperturbative properties. These characteristics have usually been presumed to still hold true in fragmentation functions even when the observed nonperturbative state is a small-mass cluster of n hadrons rather than simply a single isolated hadron. However, the multidifferential aspect of cross sections that rely on these latter types of fragmentation functions complicates the treatment of kinematical approximations in factorization derivations. That has led to recent claims that the operator definitions for fragmentation functions need to be modified from the single hadron case with nonuniversal prefactors. With such concerns as our motivation, we retrace the steps for factorizing the unpolarized semi-inclusive e + e − annihilation cross section and confirm that they do apply without modification to the case of a small-mass multihadron observed in the final state. In particular, we verify that the standard operator definition from single hadron fragmentation, with its usual prefactor, remains equally valid for the small-mass n -hadron case with the same hard parts and evolution kernels, whereas the more recently proposed definitions with nonuniversal prefactors do not. Our results reaffirm the reliability of most past phenomenological applications of dihadron fragmentation functions. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Derivative discontinuity and exchange-correlation potential of meta-GGAs in density-functional theory

We investigate fundamental properties of meta-generalized-gradient approximations (meta-GGAs) to the exchange-correlation energy functional, which have an implicit density dependence via the Kohn-Sham kinetic-energy density. To this purpose, we construct the most simple meta-GGA by expressing the local exchange-correlation energy per particle as a function of a fictitious density, which is obtained by inverting the Thomas-Fermi kinetic-energy functional. This simple functional considerably improves the total energy of atoms as compared to the standard local density approximation. The corresponding exchange-correlation potentials are then determined exactly through a solution of the optimized effective potential equation. These potentials support an additional bound state and exhibit a derivative discontinuity at integer particle numbers. We further demonstrate that through the kinetic-energy density any meta-GGA incorporates a derivative discontinuity. However, we also find that for commonly used meta-GGAs the discontinuity is largely underestimated and in some cases even negative.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Simple Models of Lateral Heterostructures

General analytical expressions for densities of states of a lateral heterostructure, formed by the contact of two square semi-infinite lattices with single-band and two-band spectra, were obtained in the tight-binding approximation by the Green’s function method. The semi-elliptical density of states was used for numerical estimates, and the model of two interacting dimers was proposed to estimate the charge transfer. Application of this approach to description of lateral epitaxial and graphene-like heterostructures is discussed.

77 NANOSCIENCE AND NANOTECHNOLOGY↗