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Results for “Approximate Computing”

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 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Computational flow modeling of triply periodic minimal surfaces as feed channel spacers in ultra-high pressure reverse osmosis applications

Triply periodic minimal surfaces (TPMS) are a special class of mathematical surfaces characterized by a high surface area-to-volume ratio. They have generated considerable interest in fields such as acoustics, heat transfer, and membrane-based filtration processes. This study evaluates the performance of four different TPMS designs—Schoen Gyroid, Schoen Crossed Layers of Parallels (CLP), Schoen Transverse Crossed Layers of Parallels (tCLP), and Schwarz-Primitive—when used as feed channel spacers under ultra-high pressure reverse osmosis (UHPRO) conditions, at approximately 200 bar. Our experimentally validated computational fluid dynamics model reveal different flow patterns within the feed channels for each of the four TPMS designs, leading to varying hydrodynamic and permeation properties. Under the simulated UHPRO conditions, the Gyroid and tCLP designs yield up to a 23% increase in average permeate velocity and a 14% reduction in average membrane-surface concentration relative to a non-woven spacer of the same porosity. Furthermore, the enhanced performance comes with an increased feed channel pressure drop, although it only constitutes less than 4% of the operating pressure when extrapolated for a meter-long membrane module. Additionally, the study analyzes the effects of varying inlet velocity and spacer porosity on membrane performance. Overall, this research provides valuable insights into the potential use of TPMS spacers in UHPRO applications.

36 MATERIALS SCIENCE↗
DOE OSTI2015

galpy: A python LIBRARY FOR GALACTIC DYNAMICS

I describe the design, implementation, and usage of galpy, a python package for galactic-dynamics calculations. At its core, galpy consists of a general framework for representing galactic potentials both in python and in C (for accelerated computations); galpy functions, objects, and methods can generally take arbitrary combinations of these as arguments. Numerical orbit integration is supported with a variety of Runge-Kutta-type and symplectic integrators. For planar orbits, integration of the phase-space volume is also possible. galpy supports the calculation of action-angle coordinates and orbital frequencies for a given phase-space point for general spherical potentials, using state-of-the-art numerical approximations for axisymmetric potentials, and making use of a recent general approximation for any static potential. A number of different distribution functions (DFs) are also included in the current release; currently, these consist of two-dimensional axisymmetric and non-axisymmetric disk DFs, a three-dimensional disk DF, and a DF framework for tidal streams. I provide several examples to illustrate the use of the code. I present a simple model for the Milky Way's gravitational potential consistent with the latest observations. I also numerically calculate the Oort functions for different tracer populations of stars and compare them to a new analytical approximation. Additionally, I characterize the response of a kinematically warm disk to an elliptical m = 2 perturbation in detail. Overall, galpy consists of about 54,000 lines, including 23,000 lines of code in the module, 11,000 lines of test code, and about 20,000 lines of documentation. The test suite covers 99.6% of the code. galpy is available at http://github.com/jobovy/galpy with extensive documentation available at http://galpy.readthedocs.org/en/latest.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Solving numerically nonlinear systems of balance laws by multivariate sigmoidal functions approximation

A numerical method for solving systems of nonlinear one-dimensional balance laws, based on multivariate sigmoidal functions approximation, is developed. Constructive approximation theorems are first established in both, uniform and L{sup p} norms. A priori as well as a posteriori error estimates are derived for the numerical solutions, when various kinds of sigmoidal functions, such as unit step, logistic and Gompertz functions, are chosen. The residual of the numerical method is also estimated. Numerical examples are given to test the performance of the algorithm, a comparison with the Godunov method is made concerning accuracy and computational cost. Finally, the numerical stability of the method is analyzed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Efficient Ensemble-Based Stochastic Gradient Methods for Optimization Under Geological Uncertainty

Ensemble-based stochastic gradient methods, such as the ensemble optimization (EnOpt) method, the simplex gradient (SG) method, and the stochastic simplex approximate gradient (StoSAG) method, approximate the gradient of an objective function using an ensemble of perturbed control vectors. These methods are increasingly used in solving reservoir optimization problems because they are not only easy to parallelize and couple with any simulator but also computationally more efficient than the conventional finite-difference method for gradient calculations. In this work, we show that EnOpt may fail to achieve sufficient improvement of the objective function when the differences between the objective function values of perturbed control variables and their ensemble mean are large. On the basis of the comparison of EnOpt and SG, we propose a hybrid gradient of EnOpt and SG to save on the computational cost of SG. We also suggest practical ways to reduce the computational cost of EnOpt and StoSAG by approximating the objective function values of unperturbed control variables using the values of perturbed ones. We first demonstrate the performance of our improved ensemble schemes using a benchmark problem. Results show that the proposed gradients saved about 30–50% of the computational cost of the same optimization by using EnOpt, SG, and StoSAG. As a real application, we consider pressure management in carbon storage reservoirs, for which brine extraction wells need to be optimally placed to reduce reservoir pressure buildup while maximizing the net present value. Results show that our improved schemes reduce the computational cost significantly.

58 GEOSCIENCES↗
DOE OSTI2024

Plasmonic surface lattice resonances in nanoparticle arrays

This work reviews the literature and provides a detailed computational analysis of the optical properties of one- and two-dimensional arrays of silver and gold nanoparticles, with emphasis on surface lattice resonances (SLRs) that arise when localized plasmon resonances (LSPRs) in the nanoparticles couple to diffraction resonances that are determined by the interparticle spacing to give polariton modes in which the two types of excitations are coherently coupled. The computations are based on the coupled dipole approximation, which provides a nearly quantitative description of the extinction spectra for arrays of this type where the particles are well separated and not too large. The computations are used to determine many characteristics of SLRs associated with the lower polariton mode that is mostly photonic in nature, and we also study the upper polariton that is dominated by the LSPR response, as well as Rayleigh anomalies (RAs) that correspond to purely diffractive excitation. The calculations explore the sensitivity of these excitations to the directions of the incident wave and polarization vectors relative to the array axis, the effect of array spacing and number of particles in the array, and the effect of nanoparticle radius and background refractive indices. Details of the physical mechanisms involved in determining blue- and/or redshifts as structural parameters are varied is provided, with SLR’s being sensitive to far-field coupling, while LSPR’s can also be sensitive to near- and intermediatefield interactions that in some cases are similar to effects found in dye molecule aggregates.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2014

Joint discrete universality of Hurwitz zeta functions

We obtain a joint discrete universality theorem for Hurwitz zeta functions. Here the parameters of zeta functions and the step of shifts of these functions approximating a given family of analytic functions are connected by some condition of linear independence. Nesterenko's theorem gives an example satisfying this condition. The universality theorem is applied to estimate the number of zeros of a linear combination of Hurwitz zeta functions. Bibliography: 20 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Bayesian model updating with finite element vs surrogate models: Application to a miter gate structural system

Bayesian finite element (FE) model updating using direct model evaluations of large-scale high-fidelity FE models is extremely computationally expensive. Surrogate models can be used as fast emulators of FE models to accelerate the model calibration process. The physics/mechanics-based FE models are still the underpinning behind the surrogate models. Here, this paper evaluates the loss in accuracy and the gain in computational time while performing Bayesian model updating by using surrogate model evaluations compared to using direct FE model evaluations. This evaluation is crucial before entirely relying on surrogate models in model updating for structural health monitoring (SHM) and damage prognosis (DP) purposes. This paper also demonstrates Bayesian updating and surrogate model construction of large-scale high-fidelity FE models of infrastructure systems. In this regard, the miter gate structural system is considered as the testbed structure. Three predominant damage modes (loss of contact between gate and wall, loss of thickness due to corrosion, and loss of tension in the diagonal rods) are considered for model updating purposes. Bayesian model updating is performed using direct FE evaluations by leveraging parallel computing. Two types of surrogates, namely polynomial chaos expansion (PCE) and Gaussian process regression (GPR), are developed for the miter gate. Model updating is performed again using the trained surrogate models, and the updating results are compared with their counterparts obtained using the direct FE evaluation results. The posterior distribution of the FE model parameters obtained using the trained surrogates are sufficiently accurate with respect to the posterior obtained utilizing the direct FE evaluations. In addition, an approximate 4-fold decrease in the computational time was observed when using surrogate model evaluations instead of direct FE evaluations for model updating.

42 ENGINEERING↗
DOE OSTI2020

Advanced Multilevel Monte Carlo Methods

This article reviews the application of some advanced Monte Carlo techniques in the context of multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations, which can be biassed in some sense, for instance, by using the discretization of an associated probability law. The MLMC approach works with a hierarchy of biassed approximations, which become progressively more accurate and more expensive. Additionally, using a telescoping representation of the most accurate approximation, the method is able to reduce the computational cost for a given level of error versus i.i.d. sampling from this latter approximation. All of these ideas originated for cases where exact sampling from couples in the hierarchy is possible. This article considers the case where such exact sampling is not currently possible. We consider some Markov chain Monte Carlo and sequential Monte Carlo methods, which have been introduced in the literature, and we describe different strategies that facilitate the application of MLMC within these methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Tunneling splittings in formic acid dimer: An adiabatic approximation to the Herring formula

Small symmetric molecules and low-dimensional model Hamiltonians are excellent systems for benchmarking theories to compute tunneling splittings. In this work, we investigate a three dimensional model Hamiltonian coupled to a harmonic bath that describes concerted proton transfer in the formic acid dimer. The three modes include the symmetric proton stretch, the symmetric dimer rock, and the dimer stretch. These modes provide a paradigm for the symmetric and anti-symmetric coupled tunneling pathways, these being recognized in the literature as two of the more important classes of coupling. The effects of selective vibrational excitation and coupling to a bath on the tunneling splittings are presented. The splittings for highly excited states are computed using a novel method that makes an adiabatic approximation to the Herring estimate. Results, which are in excellent agreement with the exact splittings, are compared with those obtained using the Makri-Miller approach. This latter method has been shown to provide quality results for tunneling splittings including highly excited vibrational states.

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

Analytical Voltage Sensitivity Analysis for Unbalanced Power Distribution System

Large scale integration of distributed energy resources and electric vehicles in a transactive energy environment present new challenges in terms of voltage stability and fluctuations in a power distribution system. The impact of different level of DER/EV penetration on the voltages across the network is typically quantified through voltage sensitivity analyses. Existing methods of voltage sensitivity analysis are computationally expensive and prior efforts to develop analytical approximation lacks generality and have not been effectively validated. The objective of this work is to provide a new analytical method of voltage sensitivity analysis that has low computational cost and also allows for stochastic analysis of voltage change. This paper first derives an analytical approximation of change in voltage at a particular bus due to change in power consumption at other bus in a radial three phase unbalanced power distribution system. Then, the proposed method is shown to be valid for different load configurations, which demonstrates its generality. The results from our analytical approach is validated via classical load flow simulation of the test system based on IEEE 37 bus network. The proposed method is shown to have good accuracy, and computation complexity is of order O(1), compared to O(n3) in classical sensitivity analysis approaches.

Munikoti, Sai↗
DOE OSTI2022

The Impulse Approximation Scattering Function and Its Use in Monte Carlo Photon Transport Simulations

The viability of using the impulse approximation scattering function in Monte Carlo photon transport simulations is explored. This scattering function can be constructed from the double differential incoherent scattering cross section developed by Ribberfors and Berggren. A commonly used method for modeling photon Doppler broadening, which is referred to as the hybrid Doppler broadening method, can also be derived from this cross section. A new photon Doppler broadening method, called the consistent Doppler broadening method, is derived and discussed. This method eliminates some of the commonly employed approximations in the hybrid Doppler broadening method, in part, by using the impulse approximation scattering function. Integrated incoherent cross sections generated using the impulse approximation scattering function and the widely used Waller-Hartree scattering function are in good agreement above 20 keV. Below 20 keV, differences as high as 70% are observed, which differs from the roughly 5% differences observed by Ribberfors for some of the materials. Integral and spectral quantities for two problems are also generated using the Monte Carlo photon transport capabilities of the Framework for REsearch in Nuclear ScIence and Engineering (FRENSIE). Due to the small, relative result differences observed when using the impulse approximation scattering function, it is considered a viable alternative to the Waller-Hartree scattering function. In addition, some small, but expected, differences in spectral fluxes at low energies can be avoided by adopting the consistent Doppler broadening method.

42 ENGINEERING↗
DOE OSTI2019

Efficiently embedding QUBO problems on adiabatic quantum computers

Adiabatic quantum computers like the D-Wave 2000Q can approximately solve the QUBO problem, which is an NP-hard problem, and have been shown to outperform classical computers on several instances. Solving the QUBO problem literally means solving virtually any NP-hard problem like the traveling salesman problem, airline scheduling problem, protein folding problem, genotype imputation problem, thereby enabling significant scientific progress, and potentially saving millions/billions of dollars in logistics, airlines, healthcare and many other industries. Yet, before QUBO problems are solved on quantum computers, they must be embedded (or compiled) onto the hardware of quantum computers, which in itself is a very hard problem. Here, we propose an efficient embedding algorithm, that lets us embed QUBO problems fast, uses less qubits and gets the objective function value close to the global minimum value. We then compare the performance of our embedding algorithm to that of D-Wave’s embedding algorithm, which is the current state of the art, and show that our embedding algorithm convincingly outperforms D-Wave’s embedding algorithm. Our embedding approach works with perfect Chimera graphs, i.e., Chimera graphs with no missing qubits.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Multilevel summation methods for efficient evaluation of long-range pairwise interactions in atomistic and coarse-grained molecular simulation.

The availability of efficient algorithms for long-range pairwise interactions is central to the success of numerous applications, ranging in scale from atomic-level modeling of materials to astrophysics. This report focuses on the implementation and analysis of the multilevel summation method for approximating long-range pairwise interactions. The computational cost of the multilevel summation method is proportional to the number of particles, N, which is an improvement over FFTbased methods who s cost is asymptotically proportional to N logN. In addition to approximating electrostatic forces, the multilevel summation method can be use to efficiently approximate convolutions with long-range kernels. As an application, we apply the multilevel summation method to a discretized integral equation formulation of the regularized generalized Poisson equation. Numerical results are presented using an implementation of the multilevel summation method in the LAMMPS software package. Preliminary results show that the computational cost of the method scales as expected, but there is still a need for further optimization.

Bond, Stephen D.↗
DOE OSTI2014

High angular momentum states of lithium atom, studied with symmetry-projected explicitly correlated Gaussian lobe functions

Method of construction of wave functions approximating eigenfunctions of the L{sup ^2} operator is proposed for high angular momentum states of few-electron atoms. Basis functions are explicitly correlated Gaussian lobes, projected onto irreducible representations of finite point groups. Variational calculations have been carried out for the lowest states of lithium atom, with quantum number L in the range from 1 to 8. Nonrelativistic energies accurate to several dozens of nanohartree have been obtained. For 2{sup 2}P, 3{sup 2}D, and 4{sup 2}F states they agree well with the reference results. Transition frequencies have been computed and compared with available experimental data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Numerical Method for Fractional Advection-Diffusion Equation with Heredity

We propose a method of construction of difference schemes for fractional partial differential equations with delay in time. For the fractional equation with two-sided diffusion, fractional transfer in time, and a functional aftereffect, we construct an implicit difference scheme. We use the shifted Grünwald–Letnikov formulas for the approximation of fractional derivatives with respect to spatial variables and the L1-algorithm for the approximation of fractional derivatives in time. Also we use piecewise constant interpolation and extrapolation by extending the discrete prehistory of the model in time. The algorithm is a fractional analog of a purely implicit method; on each time step, it is reduced to the solution of linear algebraic systems. We prove the stability of the method and find its order of convergence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Benchmarking of calculation schemes in APOLLO2 and COBAYA3 for WER lattices

This paper presents solutions of the NURISP WER lattice benchmark using APOLLO2, TRIPOLI4 and COBAYA3 pin-by-pin. The main objective is to validate MOC based calculation schemes for pin-by-pin cross-section generation with APOLLO2 against TRIPOLI4 reference results. A specific objective is to test the APOLLO2 generated cross-sections and interface discontinuity factors in COBAYA3 pin-by-pin calculations with unstructured mesh. The VVER-1000 core consists of large hexagonal assemblies with 2 mm inter-assembly water gaps which require the use of unstructured meshes in the pin-by-pin core simulators. The considered 2D benchmark problems include 19-pin clusters, fuel assemblies and 7-assembly clusters. APOLLO2 calculation schemes with the step characteristic method (MOC) and the higher-order Linear Surface MOC have been tested. The comparison of APOLLO2 vs. TRIPOLI4 results shows a very close agreement. The 3D lattice solver in COBAYA3 uses transport corrected multi-group diffusion approximation with interface discontinuity factors of Generalized Equivalence Theory (GET) or Black Box Homogenization (BBH) type. The COBAYA3 pin-by-pin results in 2, 4 and 8 energy groups are close to the reference solutions when using side-dependent interface discontinuity factors. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Solving the $k$-Sparse Eigenvalue Problem with Reinforcement Learning

We examine the possibility of using a reinforcement learning (RL) algorithm to solve large-scale eigenvalue problems in which the desired the eigenvector can be approximated by a sparse vector with at most k nonzero elements, where k is relatively small compare to the dimension of the matrix to be partially diagonalized. Here, this type of problem arises in applications in which the desired eigenvector exhibits localization properties and in large-scale eigenvalue computations in which the amount of computational resource is limited. When the positions of these nonzero elements can be determined, we can obtain the k-sparse approximation to the original problem by computing eigenvalues of a k × k submatrix extracted from k rows and columns of the original matrix. We review a previously developed greedy algorithm for incrementally probing the positions of the nonzero elements in a k-sparse approximate eigenvector and show that the greedy algorithm can be improved by using an RL method to refine the selection of k rows and columns of the original matrix. We describe how to represent states, actions, rewards and policies in an RL algorithm designed to solve the k-sparse eigenvalue problem and demonstrate the effectiveness of the RL algorithm on two examples originating from quantum many-body physics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Structure and osmotic pressure of ionic microgel dispersions

We investigate structural and thermodynamic properties of aqueous dispersions of ionic microgels—soft colloidal gel particles that exhibit unusual phase behavior. Starting from a coarse-grained model of microgel macroions as charged spheres that are permeable to microions, we perform simulations and theoretical calculations using two complementary implementations of Poisson-Boltzmann (PB) theory. Within a one-component model, based on a linear-screening approximation for effective electrostatic pair interactions, we perform molecular dynamics simulations to compute macroion-macroion radial distribution functions, static structure factors, and macroion contributions to the osmotic pressure. For the same model, using a variational approximation for the free energy, we compute both macroion and microion contributions to the osmotic pressure. Within a spherical cell model, which neglects macroion correlations, we solve the nonlinear PB equation to compute microion distributions and osmotic pressures. By comparing the one-component and cell model implementations of PB theory, we demonstrate that the linear-screening approximation is valid for moderately charged microgels. By further comparing cell model predictions with simulation data for osmotic pressure, we chart the cell model’s limits in predicting osmotic pressures of salty dispersions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗