Search NASA⌕ Search

SEARCH · Search NASA

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.

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

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

A method for including external feed in depletion calculations with CRAM and implementation into ORIGEN

A method for including external feed with polynomial time dependence in depletion calculations with the Chebyshev Rational Approximation Method (CRAM) is presented and the implementation of CRAM to the ORIGEN module of the SCALE suite is described. In addition to being able to handle time-dependent feed rates, the new solver also adds the capability to perform adjoint calculations. Results obtained with the new CRAM solver and the original depletion solver of ORIGEN are compared to high precision reference calculations, which shows the new solver to be orders of magnitude more accurate. Lastly, in most cases, the new solver is up to several times faster due to not requiring similar substepping as the original one.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

The regulation mechanism of yitJ and metF riboswitches

Riboswitches which function at the transcriptional level are sensitive to cotranscriptional folding. Based on the recently proposed theory of cotranscriptional folding, we developed a transition node approximation method to effectively decrease the conformation space of long RNA chains. Our results indicate that this approximation is reliable for calculating the cotranscriptional folding kinetics of long mRNA chains. We theoretically studied the cotranscriptional folding behavior of the yitJ and metF riboswitches in the absence/presence of S-adenosylmethionine. Although the two S-box riboswitches have similar OFF-state structures and share common features of riboswitches operated at the transcriptional level, their regulation mechanisms are different. The yitJ riboswitch is regulated by a combination of thermodynamic and kinetic mechanisms, while the metF riboswitch is solely kinetically controlled. For the yitJ riboswitch, transcriptional pausing at the U-stretch directly following the terminator decreases the amount of ligand required to trigger the switch. The different regulation mechanisms and binding affinities of the two riboswitches result from the different lengths of the anti-terminator helix, which in yitJ is short and only disrupts helix P1 of the riboswitch aptamer, but in metF is long and breaks both the helices P1 and P4.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Majorant recursions to determine eigenstate bounds of a symmetric exponential quantum anharmonic oscillator

The determination of the energy states is highly studied issue in the quantum mechanics. Based on expectation values dynamics, energy states can be observed. But conditions and calculations vary depending on the created system. In this work, a symmetric exponential anharmonic oscillator is considered and development of a recursive approximation method is studied to find its ground energy state. The use of majorant values facilitates the approximate calculation of expectation values.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Predicting the mineral composition of dust aerosols – Part 2: Model evaluation and identification of key processes with observations

A global compilation of nearly sixty measurement studies is used to evaluate two methods of simulating the mineral composition of dust aerosols in an Earth system model. Both methods are based upon a Mean Mineralogical Table (MMT) that relates the soil mineral fractions to a global atlas of arid soil type. The Soil Mineral Fraction (SMF) method assumes that the aerosol mineral fractions match the fractions of the soil. The MMT is based upon soil measurements after wet sieving, a process that destroys aggregates of soil particles that would have been emitted from the original, undisturbed soil. The second method approximately reconstructs the emitted aggregates. This model is referred to as the Aerosol Mineral Fraction (AMF) method because the mineral fractions of the aerosols differ from those of the wet-sieved parent soil, partly due to reaggregation. The AMF method remedies some of the deficiencies of the SMF method in comparison to observations. Only the AMF method exhibits phyllosilicate mass at silt sizes, where they are abundant according to observations. In addition, the AMF quartz fraction of silt particles is in better agreement with measured values, in contrast to the overestimated SMF fraction. Measurements at distinct clay and silt particle sizes are shown to be more useful for evaluation of the models, in contrast to the sum over all particles sizes that is susceptible to compensating errors, as illustrated by the SMF experiment. Model errors suggest that allocation of the emitted silt fraction of each mineral into the corresponding transported size categories is an important remaining source of uncertainty. Evaluation of both models and the MMT is hindered by the limited number of size-resolved measurements of mineral content that sparsely sample aerosols from the major dust sources. In conclusion, the importance of climate processes dependent upon aerosol mineral composition shows the need for global and routine mineral measurements.

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

Solving high-dimensional partial integral differential equations: The finite expression method

Partial integro-differential equations (PIDEs) have broad applications in the sciences, from electro-magnetism to options pricing. Here, in this paper, we introduce a new finite expression method (FEX) to solve PIDEs. This approach builds upon the original FEX and its inherent advantages with new advances: 1) A novel method of parameter grouping is proposed to reduce the number of coefficients in high-dimensional function approximation; 2) A Taylor series approximation method is implemented to significantly improve the computational efficiency and accuracy of the evaluation of the integral terms of PIDEs. The new FEX based method, denoted FEX-PG to indicate the addition of the parameter grouping (PG) step to the algorithm, provides both high accuracy and interpretable numerical solutions, with the outcome being an explicit equation that facilitates intuitive understanding of the underlying solution structures. These features are often absent in traditional methods, such as finite element methods (FEM) and finite difference methods, as well as in deep learning-based approaches. To benchmark our method against recent advances, we apply the new FEX-PG to solve benchmark PIDEs in the literature. In high-dimensional settings, FEX-PG exhibits strong and robust performance, achieving relative errors on the order of single precision machine epsilon, significantly outperforming existing approaches based on neural networks.

Combinatorial optimization↗
DOE OSTI2020

Depletion capabilities in the OpenMC Monte Carlo particle transport code

A depletion solver has been implemented in OpenMC and is described herein. The depletion solver is implemented in Python and interfaces with OpenMC’s transport solver through a C++ application programming interface, which enables an in-memory transport-depletion coupling. Multiple integration methods for advancing in time have been implemented and exhibit tradeoffs in cost, accuracy, and memory use. For all time integration methods, evaluation of the matrix exponential is performed by using the incomplete partial fraction form of the Chebyshev rational approximation method. Simulations of a pressurized water reactor (PWR) pincell and a sodium-cooled fast reactor (SFR) assembly were carried out with OpenMC and Serpent. For both problems, the use of a high-fidelity depletion chain results in predictions of k eff that agree within 20–30 pcm between OpenMC and Serpent. Predicted actinide concentrations were found to agree to a fraction of a percent, and most fission product concentrations were found to agree within 1%. Here, the few cases where larger differences were observed can be attributed either to differences in how the energy dependence of fission product yields is handled or deficiencies in the nuclear data used. OpenMC simulations of the PWR and SFR problems using a simplified 228-nuclide depletion chain demonstrate that it achieves accuracy close to that of the full, high-fidelity depletion chain with respect to the studied responses.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Analysis of spin frustration in an Fe III 7 cluster using a combination of computational, experimental, and magnetostructural correlation methods

The synthesis, structure, and magnetic properties are reported for [Fe 7 O 3 (O 2 C t Bu) 9 (mda) 3 (H 2 O) 3 ] ( 1 ), where mdaH 2 is N -methyldiethanolamine. 1 was prepared from the reaction of [Fe 3 O(O 2 C t Bu) 6 (H 2 O) 3 ](NO 3 ) with mdaH 2 in a 1:~3 ratio in MeCN. The core of 1 consists of a central octahedral Fe III ion held within a non-planar Fe 6 loop by three μ 3 -O 2- and three μ 2 -RO - arms from the three mda 2- chelates. Variable-temperature dc and ac magnetic susceptibility studies revealed dominant antiferromagnetic coupling, leading to a ground state spin of S = 5 / 2 . The ground state was confirmed by a fit of magnetization data collected in the 0.1–7.0 T and 1.8–10.0 K ranges. The four Fe 2 pairwise exchange parameters ( J 1 - J 4 ) were estimated by independent methods: theoretical calculations using either broken symmetry energy differences (-46.3, -16.2, -3.9, and - 28.1 cm -1 , respectively) or Green’s function approximation methods (-41.4, -14.8, -13.2, and - 24.7 cm -1 ), and a magnetostructural correlation (MSC) previously developed for high nuclearity Fe III /O complexes (-39.5, -13.8, -6.7, and - 23.5 cm -1 ). Additionally, the J 1 - J 4 obtained from the MSC and theoretical methods were used with the program PHI to both simulate χ M T vs T as well as to serve as reasonable input values to fit the experimental data (-41.0, -11.4, -5.0, and - 27.3 cm -1 ). Analysis of the J ij led to identification of the spin frustration effects operative and the resultant spin vector alignments at each Fe III ion, thus allowing for the rationalization of the experimental ground state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Parallel Algebraic Multigrid for Fusion and Higher-Order PDEs

Multigrid methods play a key role in large-scale scientific simulation because they are among the fastest and most scalable approaches for solving the underlying sparse linear systems of equations that arise from a wide array of Partial Differential Equation (PDE) discretizations. Algebraic multigrid (AMG) is a special type of multigrid method that depends only on the description of the linear system, giving it better portability and broader applicability than geometric multigrid, as it requires no explicit knowledge of the problem geometry. Even though these methods are widely used today, there are still applications where further development is needed. In this report, we focus on PDEs with higher-order terms (e.g., fourth order), concentrating on a PDE that arises in tokamak edge plasma simulations (a tokamak is a machine that confines a plasma using magnetic fields and is believed to be the leading plasma confinement concept for future fusion power plants). General multigrid relaxes a linear system on coarser grids and reverses this process with interpolation, but standard AMG methods struggle with the aforementioned higher-order PDEs. We investigate cyclic coarsening and interpolation heuristics, as well as new iterative approximation methods of refining the solution at each grid to improve the existing multigrid approach. To this end, we ensure that these techniques are transferable to a parallelized setting with LLNL’s supercomputers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nev- ertheless, the majority of these studies examine how well deep neural networks can model functions with uniform regularities. In this paper, we explore a different angle: how deep neural networks can adapt to varying degrees of smoothness in functions and nonuni- form data distributions across different locations and scales. More precisely, we focus on a broad class of functions defined by nonlinear tree-based approximation methods. This class encompasses a range of function types, such as functions with uniform regularities and discontinuous functions. We develop nonparametric approximation and estimation theories for this class using deep ReLU networks. Our results show that deep neural networks are adaptive to the nonuniform smoothness of functions and nonuniform data distributions at different locations and scales. We apply our results to several function classes, and derive the corresponding approximation and generalization errors. The validity of our results is demonstrated through numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Comment on: “Solving many-body Schrödinger equations with kinetic energy partition method”, Ann. Phys. 388 (2018) 54–68 by Y-H. Chen and S.D. Chao

We discuss a recent test of the performance of the kinetic energy partition method (KEP) through its application to two separable quantum-mechanical models. We argue that one of the benchmark models is exceedingly simple for testing any realistic approximate method and that almost any reasonable approach yields better results. In the second example our exact benchmark eigenvalues disagree considerably with those chosen by the authors for comparison, which casts doubts on the accuracy of their KEP approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Runge–Kutta method for solving fuzzy differential equations under generalized differentiability

In this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized Characterization Theorem, we investigate the problem of finding a numerical approximation of solutions. The Runge–Kutta approximation method is implemented and its error analysis, which guarantees pointwise convergence, is given. The method applicability is illustrated by solving a linear first-order fuzzy differential equation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Spectral density method to Anderson-Holstein model

Two-parameter spectral density function of a magnetic impurity electron in a non-magnetic metal is calculated within the framework of the Anderson-Holstein model using the spectral density approximation method. The effect of electron-phonon interaction on the spectral function is investigated.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

On a Certain First-Order Differential Equation with Delay

We consider the Cauchy problem for a first-order quasilinear differential equation with delayed argument of neutral type, and obtain sufficient conditions of existence and uniqueness of its solutions. Proofs of the solvability of nonlinear problems, estimates of solutions, and constructions of approximate methods are based on Chaplygin-type theorems on differential inequalities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Assessing an experimental approach for chemical explosive mode and heat release rate using DNS data

Obtaining information about burning characteristics and flame structures by analyzing experimental data is an important issue for understanding combustion processes and pursuing combustion modeling approaches. It has been shown that Raman/Rayleigh measurements of major species and temperature can be used to approximate the local heat release rate and the chemical explosive mode, and that these results are sufficiently accurate for a qualitative assessment of the relative importance of different heat release zones within the same overall flame structure in laminar and mildly turbulent partially premixed flames. The present study uses data from direct numerical simulation (DNS) to extend and quantify the understanding of the approximation method with respect to premixed and stratified-premixed flames with significant turbulence–chemistry interaction (high Karlovitz number). Here, the accuracy of the approximation procedure is assessed as previously applied, using just major species and temperature, as well as with the OH radical included as an additional experimentally accessible species. The accuracy of the local chemical explosive mode and the local heat release rate results from the approximation are significantly improved with OH included, yielding quantitative agreement with the DNS results. Further, a global sensitivity analysis is applied to identify the sensitivity of the heat release rate and chemical explosive mode to experimental uncertainties imprinted upon the DNS data prior to the approximation procedure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Photonic-Doppler-Velocimetry, Paraxial-Scalar Diffraction Theory and Simulation

In this report I describe current progress on a paraxial, scalar-field theory suitable for simulating what is measured in Photonic Doppler Velocimetry (PDV) experiments in three dimensions. I have introduced a number of approximations in this work in order to bring the total computation time for one experiment down to around 20 hours. My goals were: to develop an approximate method of calculating the peak frequency in a spectral sideband at an instant of time based on an optical diffraction theory for a moving target, to compare the ‘measured’ velocity to the ‘input’ velocity to gain insights into how and to what precision PDV measures the component of the mass velocity along the optical axis, and to investigate the effects of small amounts of roughness on the measured velocity. This report illustrates the progress I have made in describing how to perform such calculations with a full three dimensional picture including tilted target, tilted mass velocity (not necessarily in the same direction), and small amounts of surface roughness. With the method established for a calculation at one instant of time, measured velocities can be simulated for a sequence of times, similar to the process of sampling velocities in experiments. Improvements in these methods are certainly possible at hugely increased computational cost. I am hopeful that readers appreciate the insights possible at the current level of approximation.

42 ENGINEERING↗
DOE OSTI2021

Reduction of the molecular hamiltonian matrix using quantum community detection

Abstract Quantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Absence of Coulomb Blockade in the Anderson Impurity Model at the Symmetric Point

In this study, we investigate the characteristics of the electric current in the so-called symmetric Anderson impurity model. We study the nonequilibrium model using two complementary approximate methods, the perturbative quantum master equation approach to the reduced density matrix and a self-consistent equation of motion approach to the nonequilibrium Green's function. We find that, at a particular symmetry point, an interacting Anderson impurity model recovers the same steady-state current as an equivalent noninteracting model, akin a two-band resonant level model. We show this in the Coulomb blockade regime for both high and low temperatures, where either the approximate master equation approach or the Green's function method provides accurate results for the current. We conclude that the steady-state current in the symmetric Anderson model at this regime does not encode characteristics of a many-body interacting system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗