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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 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

A demonstration of a whole core neutron transport method in a gas cooled reactor

This paper illustrates a capability of the whole core transport method COMET. Building on previous works which demonstrated the accuracy of the method, this work serves to emphasize the robust capability of the method while also accentuating its efficiency. A set of core configurations is presented based on an operating gas-cooled thermal reactor, Japan's HTTR, and COMET determines the eigenvalue and fission density profile throughout each core configuration. Results for core multiplication factors are compared to MCNP for accuracy and also to compare runtimes. In all cases, the values given by COMET differ by those given by MCNP by less than the uncertainty inherent in the stochastic solution procedure, however, COMET requires runtimes shorter on the order of a few hundred. Figures are provided illustrating the whole core fission density profile, with segments of pins explicitly modeled individually, so that pin-level neutron flux behavior can be seen without any approximation due to simplification strategies such as homogenization. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Sampling frequency thresholds for the quantum advantage of the quantum approximate optimization algorithm

We compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers Gurobi and MQLib to solve the MaxCut problem on 3-regular graphs. We identify the minimum noiseless sampling frequency and depth p required for a quantum device to outperform classical algorithms. There is potential for quantum advantage on hundreds of qubits and moderate depth with a sampling frequency of 10 kHz. We observe, however, that classical heuristic solvers are capable of producing high-quality approximate solutions in linear time complexity. In order to match this quality for large graph sizes N, a quantum device must support depth p > 11. Additionally, multi-shot QAOA is not efficient on large graphs, indicating that QAOA p ≤ 11 does not scale with N. These results limit achieving quantum advantage for QAOA MaxCut on 3-regular graphs. Other problems, such as different graphs, weighted MaxCut, and 3-SAT, may be better suited for achieving quantum advantage on near-term quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Opening band gaps of low-dimensional materials at the meta-GGA level of density functional approximations

The quasiparticle band structure can be properly described by Hedin's GW approximation (GW), at a high computational cost. For band gaps, semilocal density functionals up to the generalized gradient approximation (GGA) level cannot compete with the accuracy of hybrid-based approximations or GW. Meta-GGA density functionals with a strong dependence on the kinetic energy density ingredient can potentially give wider band gaps compared with GGAs. The recent TASK meta-GGA density functional from Aschebrock and Kümmel [ Phys. Rev. Research 1 , 033082 (2019) ], is constructed with an enhanced nonlocality in the generalized Kohn-Sham scheme and therefore harbors great opportunities for band gap prediction. Although this approximation was found to yield excellent band gaps of bulk solids, this accuracy cannot be straightforwardly transferred to low-dimensional materials. Additionally, the reduced screening of these materials results in larger band gaps compared with their bulk counterparts, as an additional barrier to overcome. In this paper we demonstrate how the alteration of this functional affects the band gaps of monolayers and nanoribbons and present accurate band gaps competing with the revised Heyd-Scuseria-Ernzerhof (HSE06) approximation. In order to achieve this goal, we have modified the TASK functional (a) by changing the tight upper bound for one- or two-electron systems ( h X 0 ) from 1.174 to 1.29 and (b) by changing the limit of the interpolation function f X ( α → ∞ ) of the TASK functional that interpolates the exchange enhancement factor F X ( s , α ) from α = 0 to 1. The resulting modified TASK (mTASK) was tested for various materials from three dimensions to two dimensions to one dimension (nanoribbons) and was compared with the results of the higher-level hybrid functional HSE06 or with the G 0 W 0 approximation within many-body perturbation theory. We find that mTASK systematically improves the band gaps and band structures of two-dimensional (2D) and 1D systems, without significantly affecting the accuracy of the original TASK for the bulk 3D materials, when compared with the Perdew-Burke-Ernzerhof (PBE) GGA and the strongly constrained and appropriately normed (SCAN) meta-GGA. We further demonstrate the applicability of mTASK by assessing the band structures of transition metal dichalcogenide nanoribbons with respect to various bending curvatures.

36 MATERIALS SCIENCE↗
DOE OSTI2015

High-fidelity numerical simulation of the dynamic beam equation

A high-fidelity finite difference approximation of the dynamic beam equation is derived. Different types of well-posed boundary conditions are analysed. The boundary closures are based on the summation-by-parts (SBP) framework and the boundary conditions are imposed using a penalty (SAT) technique, to guarantee linear stability. The resulting SBP–SAT approximation leads to fully explicit time integration. The accuracy and stability properties of the newly derived SBP–SAT approximations are demonstrated for both 1-D and 2-D problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Horizon radiation reaction forces

Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton’s constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Certification and the potential energy landscape

Typically, there is no guarantee that a numerical approximation obtained using standard nonlinear equation solvers is indeed an actual solution, meaning that it lies in the quadratic convergence basin. Instead, it may lie only in the linear convergence basin, or even in a chaotic region, and hence not converge to the corresponding stationary point when further optimization is attempted. In some cases, these non-solutions could be misleading. Proving that a numerical approximation will quadratically converge to a stationary point is termed certification. In this report, we provide details of how Smale's α-theory can be used to certify numerically obtained stationary points of a potential energy landscape, providing a mathematical proof that the numerical approximation does indeed correspond to an actual stationary point, independent of the precision employed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Numerical solution of 2D-vector tomography problem using the method of approximate inverse

We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Self-shielding models of MICROX-2 code

The MICROX-2 is a transport theory code that solves for the neutron slowing-down and thermalization equations of a two-region lattice cell. In the previous study, a new fine-group cross section library of the MICROX-2 was generated and tested against reference calculations and measurement data. In this study, existing physics models of the MICROX-2 are reviewed and updated to improve the physics calculation performance of the MICROX-2 code, including the resonance self-shielding model and spatial self-shielding factor. The updated self-shielding models have been verified through a series of benchmark calculations against the Monte Carlo code, using homogeneous and pin cell models selected for this study. The results have shown that the updates of the self-shielding factor calculation model are correct and improve the physics calculation accuracy even though the magnitude of error reduction is relatively small. Compared to the existing models, the updates reduced the prediction error of the infinite multiplication factor by approximately 0.1 % and 0.2% for the homogeneous and pin cell models, respectively, considered in this study. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Predictive modeling of NSTX discharges with the updated multi-mode anomalous transport module

Abstract The objective of this study is twofold: firstly, to demonstrate the consistency between the anomalous transport results produced by updated Multi-Mode Model (MMM) version 9.0.4 and those obtained through gyrokinetic simulations; and secondly, to showcase MMM’s ability to predict electron and ion temperature profiles in low aspect ratio, high beta NSTX discharges. MMM encompasses a range of transport mechanisms driven by electron and ion temperature gradients, trapped electrons, kinetic ballooning, peeling, microtearing, and drift resistive inertial ballooning modes. These modes within MMM are being verified through corresponding gyrokinetic results. The modes that potentially contribute to ion thermal transport are stable in MMM, aligning with both experimental data and findings from linear CGYRO simulations. The isotope effects on these modes are also studied and higher mass is found to be stabilizing, consistent with the experimental trend. The electron thermal power across the flux surface is computed within MMM and compared to experimental measurements and nonlinear CGYRO simulation results. Specifically, the electron temperature gradient modes (ETGM) within MMM account for 2.0 MW of thermal power, consistent with experimental findings. It is noteworthy that the ETGM model requires approximately 5.0 ms of computation time on a standard desktop, while nonlinear CGYRO simulations necessitate 8.0 h on 8 K cores. MMM proves to be highly computationally efficient, a crucial attribute for various applications, including real-time control, tokamak scenario optimization, and uncertainty quantification of experimental data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Improving the efficiency of G 0 W 0 calculations with approximate spectral decompositions of dielectric matrices

Recently, it was shown that the calculation of quasiparticle energies using the G 0 W 0 approximation can be performed without computing explicitly any virtual electronic states, by expanding the Green function and screened Coulomb interaction in terms of the eigenstates of the static dielectric matrix. Avoiding the evaluation of virtual electronic states leads to improved efficiency and ease of convergence of G 0 W 0 calculations. Here, we propose a further improvement of the efficiency of these calculations, based on an approximation of density-density response functions of molecules and solids. The approximation relies on the calculation of a subset of eigenvectors of the dielectric matrix using the kinetic operator instead of the full Hamiltonian, and it does not lead to any substantial loss of accuracy for the quasiparticle energies. The computational savings introduced by this approximation depend on the system, and they become more substantial as the number of electrons increases.

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

Optimization of Simultaneous Measurement for Variational Quantum Eigensolver Applications

Variational quantum eigensolver (VQE) is a promising algorithm suitable for near-term quantum computers. VQE aims to approximate solutions to exponentially-sized optimization problems by executing a polynomial number of quantum sub-problems. However, the number of subproblems scales as N-4 for typical problems of interest-a daunting growth rate that poses a serious limitation for emerging applications such as quantum computational chemistry. We mitigate this issue by exploiting the simultaneous measurability of subproblems corresponding to commuting terms. Our technique transpiles VQE instances into a format optimized for simultaneous measurement, ultimately yielding 8-30x lower cost. Our work also encompasses a synthesis tool for compiling simultaneous measurement circuits with minimal overhead. We demonstrate experimental validation of our techniques by estimating the ground state energy of deuteron with a quantum computer. We also investigate the underlying statistics of simultaneous measurement and devise an adaptive strategy for mitigating harmful covariance terms.

quantum computing↗
DOE OSTI2018

Automated Mapping of a Plane Curvilinear Contour by a Smooth Set of Arcs in Rotary and Deep Extrusion

The use of smooth continuous approximating curves consisting of arcs of circles to solve production problems is considered. A relatively simple and efficient recurrent algorithm is developed for use with Kompas-3D, MS Excel, and other software. The algorithm is based on the property of the bisector of a triangle. An analytical form of the approximating curve is determined. A real-time graphic interactive interface in Kompas-3D software is derived. Some irregular mapping situations are described. Practical results are outlined.

42 ENGINEERING↗
DOE OSTI2013

High order spatial expansion for the method of characteristics applied to 3-D geometries

The method of characteristics is an efficient and flexible technique to solve the neutron transport equation and has been extensively used in two-dimensional calculations because it permits to deal with complex geometries. However, because of a very fast increase in storage requirements and number of floating operations, its direct application to three-dimensional routine transport calculations it is not still possible. In this work we introduce and analyze several modifications aimed to reduce memory requirements and to diminish the computing burden. We explore high-order spatial approximation, the use of intermediary trajectory-dependent flux expansions and the possibility of dynamic trajectory reconstruction from local tracking for typed subdomains. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Extension of PENELOPE to protons: Simulation of nuclear reactions and benchmark with Geant4

Purpose: Describing the implementation of nuclear reactions in the extension of the Monte Carlo code (MC) PENELOPE to protons (PENH) and benchmarking with Geant4.Methods: PENH is based on mixed-simulation mechanics for both elastic and inelastic electromagnetic collisions (EM). The adopted differential cross sections for EM elastic collisions are calculated using the eikonal approximation with the Dirac–Hartree–Fock–Slater atomic potential. Cross sections for EM inelastic collisions are computed within the relativistic Born approximation, using the Sternheimer–Liljequist model of the generalized oscillator strength. Nuclear elastic and inelastic collisions were simulated using explicitly the scattering analysis interactive dialin database for {sup 1}H and ICRU 63 data for {sup 12}C, {sup 14}N, {sup 16}O, {sup 31}P, and {sup 40}Ca. Secondary protons, alphas, and deuterons were all simulated as protons, with the energy adapted to ensure consistent range. Prompt gamma emission can also be simulated upon user request. Simulations were performed in a water phantom with nuclear interactions switched off or on and integral depth–dose distributions were compared. Binary-cascade and precompound models were used for Geant4. Initial energies of 100 and 250 MeV were considered. For cases with no nuclear interactions simulated, additional simulations in a water phantom with tight resolution (1 mm in all directions) were performed with FLUKA. Finally, integral depth–dose distributions for a 250 MeV energy were computed with Geant4 and PENH in a homogeneous phantom with, first, ICRU striated muscle and, second, ICRU compact bone.Results: For simulations with EM collisions only, integral depth–dose distributions were within 1%/1 mm for doses higher than 10% of the Bragg-peak dose. For central-axis depth–dose and lateral profiles in a phantom with tight resolution, there are significant deviations between Geant4 and PENH (up to 60%/1 cm for depth–dose distributions). The agreement is much better with FLUKA, with deviations within 3%/3 mm. When nuclear interactions were turned on, agreement (within 6% before the Bragg-peak) between PENH and Geant4 was consistent with uncertainties on nuclear models and cross sections, whatever the material simulated (water, muscle, or bone).Conclusions: A detailed and flexible description of nuclear reactions has been implemented in the PENH extension of PENELOPE to protons, which utilizes a mixed-simulation scheme for both elastic and inelastic EM collisions, analogous to the well-established algorithm for electrons/positrons. PENH is compatible with all current main programs that use PENELOPE as the MC engine. The nuclear model of PENH is realistic enough to give dose distributions in fair agreement with those computed by Geant4.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2025

Multi-plane moment-of-fluid interface reconstruction in 3D

Moment-of-fluid (MOF) methods for interface reconstruction approximate the region occupied by material in each mesh element only through reference to its geometric moments. Here, we present a 3D MOF method that represents the material (POM) in each cell as the convex intersection of the cell and multiple half-spaces, each selected to minimize the least-squares error between computed moments of the approximated material and provided reference moments. This optimization problem is highly non-linear and non-convex, making the numerical result very sensitive to the initial guess. To create an effective initial guess in each cell, we construct an ellipsoid from 0th–2nd order reference moments such that its shape corresponds with that of the POM. Within this ellipsoid we inscribe a polyhedron, and initialize the minimization problem with the half-spaces defined by each of its faces. The inscribed polyhedron has minimally 4 faces, and using up to 3rd order moments permits optimization over up to 20 unknown values. We therefore define MOF methods that utilize 4, 5, or 6 half-spaces, correspondingly initialized with the faces of a single inscribed tetrahedron, triangular prism, or hexahedron. Stability of the non-linear optimization is further improved with a prepossessing step that normalizes the reference moments according to the axes of the reference ellipsoid. Using this approach, the non-linear least-squares solver reliably converges to a near-global minimum from a single initial guess. We demonstrate accuracy and robustness using single-cell and multi-cell examples over a wide spectrum of geometry. In particular, we demonstrate our ability to exactly reproduce several important and complex features defined by up to four half-spaces, such as corners, filaments, filament tips, and embedded material in the cell.

3D interface reconstruction↗
DOE OSTI2021

Classical symmetries and the Quantum Approximate Optimization Algorithm

Here, we study the relationship between the Quantum Approximate Optimization Algorithm (QAOA) and the underlying symmetries of the objective function to be optimized. Our approach formalizes the connection between quantum symmetry properties of the QAOA dynamics and the group of classical symmetries of the objective function. The connection is general and includes but is not limited to problems defined on graphs. We show a series of results exploring the connection and highlight examples of hard problem classes where a nontrivial symmetry subgroup can be obtained efficiently. In particular, we show how classical objective function symmetries lead to invariant measurement outcome probabilities across states connected by such symmetries, independent of the choice of algorithm parameters or number of layers. To illustrate the power of the developed connection, we apply machine learning techniques toward predicting QAOA performance based on symmetry considerations. We provide numerical evidence that a small set of graph symmetry properties suffices to predict the minimum QAOA depth required to achieve a target approximation ratio on the MaxCut problem, in a practically important setting where QAOA parameter schedules are constrained to be linear and hence easier to optimize.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems

We develop two classes of quasi-classical dynamics that are shown to conserve the initial quantum ensemble when used in combination with the Feynman-Kleinert approximation of the density operator. These dynamics are used to improve the Feynman-Kleinert implementation of the classical Wigner approximation for the evaluation of quantum time correlation functions known as Feynman-Kleinert linearized path-integral. As shown, both classes of dynamics are able to recover the exact classical and high temperature limits of the quantum time correlation function, while a subset is able to recover the exact harmonic limit. A comparison of the approximate quantum time correlation functions obtained from both classes of dynamics is made with the exact results for the challenging model problems of the quartic and double-well potentials. It is found that these dynamics provide a great improvement over the classical Wigner approximation, in which purely classical dynamics are used. In a special case, our first method becomes identical to centroid molecular dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗