SEARCH · Engineering Papers

Results for “Approximation methods”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

All sources NASA NTRS DOE OSTI

DOE OSTI2023

Accelerating full-waveform inversion using source stacking: synthetic experiments at the global scale in a realistic 3-D earth model

SUMMARY The spectral element method is currently the method of choice for computing accurate synthetic seismic wavefields in realistic 3-D earth models at the global scale. However, it requires significantly more computational time, compared to normal mode-based approximate methods. Source stacking, whereby multiple earthquake sources are aligned on their origin time and simultaneously triggered, can reduce the computational costs by several orders of magnitude. We present the results of synthetic tests performed on a realistic radially anisotropic 3-D model, slightly modified from model SEMUCB-WM1 with three component synthetic waveform ‘data’ for a duration of 10 000 s, and filtered at periods longer than 60 s, for a set of 273 events and 515 stations. We consider two definitions of the misfit function, one based on the stacked records at individual stations and another based on station-pair cross-correlations of the stacked records. The inverse step is performed using a Gauss–Newton approach where the gradient and Hessian are computed using normal mode perturbation theory. We investigate the retrieval of radially anisotropic long wavelength structure in the upper mantle in the depth range 100–800 km, after fixing the crust and uppermost mantle structure constrained by fundamental mode Love and Rayleigh wave dispersion data. The results show good performance using both definitions of the misfit function, even in the presence of realistic noise, with degraded amplitudes of lateral variations in the anisotropic parameter ξ. Interestingly, we show that we can retrieve the long wavelength structure in the upper mantle, when considering one or the other of three portions of the cross-correlation time series, corresponding to where we expect the energy from surface wave overtone, fundamental mode or a mixture of the two to be dominant, respectively. We also considered the issue of missing data, by randomly removing a successively larger proportion of the available synthetic data. We replace the missing data by synthetics computed in the current 3-D model using normal mode perturbation theory. The inversion results degrade with the proportion of missing data, especially for ξ, and we find that a data availability of 45 per cent or more leads to acceptable results. We also present a strategy for grouping events and stations to minimize the number of missing data in each group. This leads to an increased number of computations but can be significantly more efficient than conventional single-event-at-a-time inversion. We apply the grouping strategy to a real picking scenario, and show promising resolution capability despite the use of fewer waveforms and uneven ray path distribution. Source stacking approach can be used to rapidly obtain a starting 3-D model for more conventional full-waveform inversion at higher resolution, and to investigate assumptions made in the inversion, such as trade-offs between isotropic, anisotropic or anelastic structure, different model parametrizations or how crustal structure is accounted for.

Geochemistry & Geophysics↗

DOE OSTI2022

Optimal Power Dispatch of DGs in Radial and Mesh AC Grids: A Hybrid Solution Methodology between the Salps Swarm Algorithm and Successive Approximation Power Flow Method

In this paper, we address the problem of the optimal power dispatch of Distributed Generators (DGs) in Alternating Current (AC) networks, better known as the Optimal Power Flow (OPF) problem. We used, as the objective function, the minimization of power losses (P loss ) associated with energy transport, which are subject to the set of constraints that compose AC networks in an environment of distributed generation. To validate the effectiveness of the proposed methodology in solving the OPF problem in any network topology, we employed one 10-node mesh test system and three radial text systems: 10, 33, and 69 nodes. In each test system, DGs were allowed to inject 20%, 40%, and 60% of the power supplied by the slack generator in the base case. To solve the OPF problem, we used a master–slave methodology that integrates the optimization method Salps Swarm Algorithm (SSA) and the load flow technique based on the Successive Approximation (SA) method. Moreover, for comparison purposes, we employed some of the algorithms reported in the specialized literature to solve the OPF problem (the continuous genetic algorithm, the particle swarm optimization algorithm, the black hole algorithm, the antlion optimization algorithm, and the Multi-Verse Optimizer algorithm), which were selected because of their excellent results in solving such problems. The results obtained by the proposed solution methodology demonstrate its superiority and convergence capacity in terms of minimization of P loss in both radial and mesh systems. It provided the best reduction in minimum P loss in short processing times and showed excellent repeatability in each test system and scenario under analysis.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2026

Score-based deterministic density sampling

We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density π given only its score ∇ log π. Our method approximates the Wasserstein gradient flow on KL($f_t$∥π) by learning the time-varying score ∇ log $f_t$ on the fly using score matching. While having the same marginal distribution as Langevin dynamics, our method produces smooth deterministic trajectories, resulting in monotone noise-free convergence. We prove that our method dissipates relative entropy at the same rate as the exact gradient flow, provided sufficient training. Numerical experiments validate our theoretical findings: our method converges at the optimal rate, has smooth trajectories, and is often more sample efficient than its stochastic counterpart. Experiments on high-dimensional image data show that our method produces high-quality generations in as few as 15 steps and exhibits natural exploratory behavior. The memory and runtime scale linearly in the sample size.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Non-orthogonal spin-adaptation of coupled cluster methods: A new implementation of methods including quadruple excitations

The theory of non-orthogonal spin-adaptation for closed-shell molecular systems is applied to coupled cluster methods with quadruple excitations (CCSDTQ). Calculations at this level of detail are of critical importance in describing the properties of molecular systems to an accuracy which can meet or exceed modern experimental techniques. Such calculations are of significant (and growing) importance in such fields as thermodynamics, kinetics, and atomic and molecular spectroscopies. With respect to the implementation of CCSDTQ and related methods, we show that there are significant advantages to non-orthogonal spin-adaption with respect to simplification and factorization of the working equations and to creating an efficient implementation. The resulting algorithm is implemented in the CFOUR program suite for CCSDT, CCSDTQ, and various approximate methods (CCSD(T), CC3, CCSDT-n, and CCSDT(Q))

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

An efficient approach for solving Klein–Gordon equation arising in quantum field theory using wavelets

A new approach for the solution of Klein–Gordon equation using Legendre wavelet-based approximation method is presented. The properties of Legendre wavelets are used to reduce the problem to the solution of system of algebraic equations. Usually 2{sup (k−1)}M{sup 2} connection coefficients are required to solve the Klein–Gordon equation by Legendre wavelets method as mentioned in the literature. But, our proposed method based on Legendre wavelets and algebraic polynomials require only 2{sup (k−1)}M connection coefficients instead of 2{sup (k−1)}M{sup 2} . Also the convergence analysis and error estimation for the proposed function approximation through the truncated series have been discussed and approved with the exact solution. Illustrative examples are discussed to demonstrate the validity and applicability of the technique with lesser computational effort.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Numerical modelling of emission of a two-level atom near a metal nanoparticle with account for tunnelling of an electron from an atom into a particle

We report the results of numerical modelling of emission of a two-level atom near a metal nanoparticle under resonant interaction of light with plasmon modes of the particle. Calculations have been performed for different polarisations of light by a dipole approximation method and a complex multipole method. Depending on the distance between a particle and an atom, the contribution of the nonradiative process of electron tunnelling from a two-level atom into a particle, which is calculated using the quasi-classical approximation, has been taken into account and assessed. We have studied spherical gold and silver particles of different diameters (10 – 100 nm). The rates of electron tunnelling and of spontaneous decay of the excited atomic state are found. The results can be used to develop nanoscale plasmonic emitters, lasers and photodetectors. (nanooptics)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Communication: HK propagator uniformized along a one-dimensional manifold in weakly anharmonic systems

A simplification of the Heller-Herman-Kluk-Kay (HK) propagator is presented that does not suffer from the need for an increasing number of trajectories with dimensions of the system under study. This is accomplished by replacing HK’s uniformizing integral over all of phase space by a one-dimensional curve that is appropriately selected to lie along the fastest growing manifold of a defining trajectory. It is shown that this modification leads to eigenspectra of quantum states in weakly anharmonic systems that can outperform the comparatively computationally cheap thawed Gaussian approximation method and frequently approach the accuracy of spectra obtained with the full HK propagator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Wide ranging equation of state with Tartarus: A hybrid Green’s function/orbital based average atom code

Average atom models are widely used to make equation of state tables and for calculating other properties of materials over a wide range of conditions, from zero temperature isolated atom to fully ionized free electron gases. The numerical challenge of making these density functional theory based models work for any temperature, density or nuclear species is formidable. Here we present in detail a hybrid Green’s function/orbital based approach that has proved to be stable and accurate for wide ranging conditions. Algorithmic strategies are discussed. In particular the decomposition of the electron density into numerically advantageous parts is presented and a robust and rapid self consistent field method based on a quasi-Newton algorithm is given. Example application to the equation of state of lutetium (Z = 71) is explored in detail, including the effect of relativity, finite temperature exchange and correlation, and a comparison to a less approximate method. Furthermore, the hybrid scheme is found to be numerically stable and accurate for lutetium over at least 6 orders of magnitude in density and 5 orders of magnitude in temperature.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2018

An improved target velocity sampling algorithm for free gas elastic scattering

We present an improved algorithm for sampling the target velocity when simulating elastic scattering in a Monte Carlo neutron transport code that correctly accounts for the energy dependence of the scattering cross section. The algorithm samples the relative velocity directly, thereby avoiding a potentially inefficient rejection step based on the ratio of cross sections. Here, we have shown that this algorithm requires only one rejection step, whereas other methods of similar accuracy require two rejection steps. The method was verified against stochastic and deterministic reference results for upscattering percentages in 238 U. Simulations of a light water reactor pin cell problem demonstrate that using this algorithm results in a 3% or less penalty in performance when compared with an approximate method that is used in most production Monte Carlo codes

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Efficient hybrid explicit-implicit learning for multiscale problems

Splitting method is a powerful method to handle application problems by splitting physics, scales, domain, and so on. Many splitting algorithms have been designed for efficient temporal discretization. Here, in this paper, our goal is to use temporal splitting concepts in designing machine learning algorithms and, at the same time, help splitting algorithms by incorporating data and speeding them up. We propose a machine learning assisted splitting scheme which improves the efficiency of the scheme meanwhile preserves the accuracy. We consider a recently introduced multiscale splitting algorithms, where the multiscale problem is solved on a coarse grid. To approximate the dynamics, only a few degrees of freedom are solved implicitly, while others explicitly. This splitting concept allows identifying degrees of freedom that need implicit treatment. In this paper, we use this splitting concept in machine learning and propose several strategies. First, the implicit part of the solution can be learned as it is more difficult to solve, while the explicit part can be computed. This provides a speed-up and data incorporation for splitting approaches. Secondly, one can design a hybrid neural network architecture because handling explicit parts requires much fewer communications among neurons and can be done efficiently. Thirdly, one can solve the coarse grid component via PDEs or other approximation methods and construct simpler neural networks for the explicit part of the solutions. We discuss these options and implement one of them by interpreting it as a machine translation task. This interpretation of the splitting scheme successfully enables us using the Transformer since it can perform model reduction for multiple time series and learn the connection between them. We also find that the splitting scheme is a great platform to predict the coarse solution with insufficient information of the target model: the target problem is partially given and we need to solve it through a known problem which approximates the target. Our machine learning model can incorporate and encode the given information from two different problems and then solve the target problems. We conduct four numerical examples and the results show that our method is stable and accurate.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Exploring the sensitivity of charge-exchange ( p , n ) reactions to the neutron density distribution

The determination of the nuclear neutron properties suffers from uncontrolled uncertainties, which have attracted considerable attention recently, such as in the context of the PREX experiment. Our aim is to analyze the sensitivity of charge-exchange (p,n) reactions to the neutron density distribution ρ n and constrain the neutron characteristics in the nuclear structure models. Method: By combing the folding and the mean-field models, the nucleon-nucleus (N,A) potential can be obtained from the nuclear density distribution. Further, the (p,p) and (p,n) cross sections for 48 Ca and 208 Pb are calculated following the distorted-wave Born approximation method. As a result, compared with the (p,p) cross section, the effects of ρ n variation on the (p,n) cross section are significant, which is due to the impact of isovector properties. Based on the global folding model analyses of data, it is found that 48 Ca and 208 Pb have relatively large neutron skin thickness ΔR np . Results illustrate that the charge-exchange (p,n) reaction is a sensitive probe of ρ n . The results in this paper can offer useful guides for future experiments of neutron characteristics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2019

Critical Temperature of the Three-Vertex Potts Model on a Kagome Lattice

The Potts model on a Kagome lattice is considered. The Monte Carlo method is used to obtain the temperature dependences of the thermodynamic parameters: heat capacity C, order parameter m, and susceptibility χ. The calculations were performed for systems with periodic boundary conditions. Systems with linear dimensions L × L = N, L = 20–90, were considered. Based on the fourth-order Binder cumulant method, the critical temperature (T{sub c}) was calculated for the three-vertex Potts model on a Kagome lattice. It is shown that the obtained value of T{sub c}, within the statistical error, is in good agreement with the results obtained by the transfer matrix and polynomial approximation methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Comparing Outdoor to Indoor Performance for Bifacial Modules Affected by Polarization-Type Potential-Induced Degradation

Bifacial photovoltaic (PV) modules have the advantage of using light reflected off of the ground to contribute to power production. Predicting the energy gain is challenging and requires complex models to do so accurately. Often, module degradation over time is neglected in models for the sake of simplicity or is underestimated. Comparing outdoor and indoor current–voltage (I–V) performance for bifacial modules is more challenging than for monofacial modules, as there are additional variables to consider such as rear albedo non-uniformity, cell mismatch, and their effects on temperature. This challenge is compounded when heterogeneous degradation modes occur, such as polarization-type potential-induced degradation (PID-p). To examine the effects of PID-p on I–V predictions using an empirical data-driven approach, 16 bifacial PERC modules are installed outdoors on racks with different albedo conditions. A subset is exposed to high-voltage biases of −1500 V or +1500 V. Outdoor data are traced at irradiance ranges of 150–250 W/m 2 , 500–600 W/m 2 , and 900–1000 W/m 2 . These curves are corrected using control module temperature, wire resistivity, and module resistance measured indoors. We examine several methods to transform indoor I–V curves to accurately, and more simply than existing methods, approximate outdoor performance for bifacial modules without and with varying levels of PID-p degradation. This way, bifacial performance modeling can be more accessible and informed by fielded, degraded modules. Distributions of percent errors between indoor and outdoor performance parameters and Mean Absolute Percent Errors (MAPEs) are used to assess method quality. Results including low-irradiance data (150–250 W/m 2 ) are discussed but are filtered for quantifying method quality as these data introduce substantial errors. The method with the most optimal tradeoff between low MAPE and analysis simplicity involves measuring the front side of a module indoors at an irradiance equal to plane-of-array irradiance plus the product of module bifaciality and albedo irradiance. This method gives MAPE values of 1–6.5% for non-degraded and 1.6–5.9% for PID-p degraded module performance.

14 SOLAR ENERGY↗

DOE OSTI2014

Analytical estimation of emission zone mean position and width in organic light-emitting diodes from emission pattern image-source interference fringes

We present an analytical method for evaluating the first and second moments of the effective exciton spatial distribution in organic light-emitting diodes (OLED) from measured emission patterns. Specifically, the suggested algorithm estimates the emission zone mean position and width, respectively, from two distinct features of the pattern produced by interference between the emission sources and their images (induced by the reflective cathode): the angles in which interference extrema are observed, and the prominence of interference fringes. The relations between these parameters are derived rigorously for a general OLED structure, indicating that extrema angles are related to the mean position of the radiating excitons via Bragg's condition, and the spatial broadening is related to the attenuation of the image-source interference prominence due to an averaging effect. The method is applied successfully both on simulated emission patterns and on experimental data, exhibiting a very good agreement with the results obtained by numerical techniques. We investigate the method performance in detail, showing that it is capable of producing accurate estimations for a wide range of source-cathode separation distances, provided that the measured spectral interval is large enough; guidelines for achieving reliable evaluations are deduced from these results as well. As opposed to numerical fitting tools employed to perform similar tasks to date, our approximate method explicitly utilizes physical intuition and requires far less computational effort (no fitting is involved). Hence, applications that do not require highly resolved estimations, e.g., preliminary design and production-line verification, can benefit substantially from the analytical algorithm, when applicable. This introduces a novel set of efficient tools for OLED engineering, highly important in the view of the crucial role the exciton distribution plays in determining the device performance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Approximate Green’s Function Coupled Cluster A Method Employing Effective Dimension Reduction

The Green’s function coupled cluster (GFCC) method, originally proposed in the early 1990s, is a powerful many-body tool for computing and analyzing the electronic structures of molecular structures and periodic systems, especially when electrons are strongly correlated. However, in order for the GFCC method to become an approach that can be routinely used in the electronic structure calculations, more robust linear algebraic techniques and approximations need to be employed to reduce its extremely high computational overhead. In our recent studies, we showed that the GFCC equation can be numerically solved by seeking solutions of multiple linear systems in the frequency regime of interest, which can be easily distributed in a massively parallel environment, and broaden the avenue for more state-of-the-art numerical linear algebraic tools associated with multiple linear systems to be kicked in to this field. In the present pursuit of this practice, we show a successful application of model order reduction (MOR) techniques in the GFCC framework. Briefly speaking, for a frequency regime of interest that requires a high resolution of spectral function, instead of solving GFCC linear equation in the original dimension for every single frequency point, an easily-solvable linear system model with reduced dimension can be built upon projecting the original GFCC linear system into a subspace, from which the interpolation and extrapolation can give a reasonable approximation to the results of the original GFCC linear equations. Here, we show that the subspace can be properly constructed in an iterative manner from the auxiliary vectors of the GFCC linear equations at some select frequencies inside the frequency regime. During the iterations, the quality of the subspace, as well as the linear system model, can be systematically improved. The approach is tested in this work in terms of the efficiency and accuracy of computing spectral functions for some typical molecular systems including carbon monoxide, 1,3-butadiene, benzene, and adenine molecules. As a byproduct, the high quality linear system model is also found to be able to provide high quality initial guess for the existing linear solver to improve the convergence performance.

Peng, Bo↗

DOE OSTI2016

SCALE Code System

The SCALE Code System is a widely-used modeling and simulation suite for nuclear safety analysis and design that is developed, maintained, tested, and managed by the Reactor and Nuclear Systems Division (RNSD) of Oak Ridge National Laboratory (ORNL). SCALE provides a comprehensive, verified and validated, user-friendly tool set for criticality safety, reactor and lattice physics, radiation shielding, spent fuel and radioactive source term characterization, and sensitivity and uncertainty analysis. Since 1980, regulators, licensees, and research institutions around the world have used SCALE for safety analysis and design. SCALE provides an integrated framework with dozens of computational modules including three deterministic and three Monte Carlo radiation transport solvers that are selected based on the desired solution strategy. SCALE includes current nuclear data libraries and problem-dependent processing tools for continuous-energy (CE) and multigroup (MG) neutronics and coupled neutron-gamma calculations, as well as activation, depletion, and decay calculations. SCALE includes unique capabilities for automated variance reduction for shielding calculations, as well as sensitivity and uncertainty analysis. SCALE’s graphical user interfaces assist with accurate system modeling, visualization of nuclear data, and convenient access to desired results.SCALE 6.2 provides many new capabilities and significant improvements of existing features.New capabilities include:• ENDF/B-VII.1 nuclear data libraries CE and MG with enhanced group structures,• Neutron covariance data based on ENDF/B-VII.1 and supplemented with ORNL data,• Covariance data for fission product yields and decay constants,• Stochastic uncertainty and correlation quantification for any SCALE sequence with Sampler,• Parallel calculations with KENO,• Problem-dependent temperature corrections for CE calculations,• CE shielding and criticality accident alarm system analysis with MAVRIC,• CE depletion with TRITON (T5-DEPL/T6-DEPL),• CE sensitivity/uncertainty analysis with TSUNAMI-3D,• Simplified and efficient LWR lattice physics with Polaris,• Large scale detailed spent fuel characterization with ORIGAMI and ORIGAMI Automator,• Advanced fission source convergence acceleration capabilities with Sourcerer,• Nuclear data library generation with AMPX, and• Integrated user interface with Fulcrum.Enhanced capabilities include:• Accurate and efficient CE Monte Carlo methods for eigenvalue and fixed source calculations,• Improved MG resonance self-shielding methodologies and data,• Resonance self-shielding with modernized and efficient XSProc integrated into most sequences,• Accelerated calculations with TRITON/NEWT (generally 4x faster than SCALE 6.1),• Spent fuel characterization with 1470 new reactor-specific libraries for ORIGEN,• Modernization of ORIGEN (Chebyshev Rational Approximation Method [CRAM] solver, API for high-performance depletion, new keyword input format)• Extension of the maximum mixture number to values well beyond the previous limit of 2147 to ~2 billion,• Nuclear data formats enabling the use of more than 999 energy groups,• Updated standard composition library to provide more accurate use of natural abundances, andvi• Numerous other enhancements for improved usability and stability.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2018

Modified Steklov Functions and Numerical Differentiation Formulas

We consider an approximation method based on Steklov functions of the first and second order. We obtain estimates for the norms in the space C of continuous periodic functions and clarify how they connect with numerical differentiation formulas.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

A low tritium hydride bed inventory estimation technique

Low tritium hydride beds were developed and deployed into tritium service in Savannah River Site. Process beds to be used for low concentration tritium gas were not fitted with instrumentation to perform the steady-state, flowing gas calorimetric inventory measurement method. Low tritium beds contain less than the detection limit of the IBA (In-Bed Accountability) technique used for tritium inventory. This paper describes two techniques for estimating tritium content and uncertainty for low tritium content beds to be used in the facility's physical inventory (PI). PI are performed periodically to assess the quantity of nuclear material used in a facility. The first approach (Mid-point approximation method - MPA) assumes the bed is half-full and uses a gas composition measurement to estimate the tritium inventory and uncertainty. The second approach utilizes the bed's hydride material pressure-composition-temperature (PCT) properties and a gas composition measurement to reduce the uncertainty in the calculated bed inventory.

07 ISOTOPE AND RADIATION SOURCES↗