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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Implementation and Performance

Developing theoretical understanding of complex reactions and processes at interfaces requires using methods that go beyond semilocal density functional theory to accurately describe the interactions between solvent, reactants and substrates. Methods based on many-body perturbation theory, such as the random phase approximation (RPA), have previously been limited due to their computational complexity. However, this is now a surmountable barrier due to the advances in computational power available, in particular through modern GPU-based supercomputers. In this work, we describe the implementation of RPA calculations within BerkeleyGW and show its favorable computational performance on large complex systems relevant for catalysis and electrochemistry applications. Our implementation builds off of the static subspace approximation which, by employing a compressed representation of the frequency dependent polarizability, enables the evaluation of the RPA correlation energy with significant acceleration and systematically controllable accuracy. We find that the computational cost of calculating the RPA correlation energy scales only linearly with system size for systems containing up to 50 thousand bands, and is expected to scale quadratically thereafter. We also show excellent strong scaling results across several supercomputers, demonstrating the performance and portability of this implementation.

algorithmic development↗
DOE OSTI2020

Fast Approximate Methods for Modified Gravity Cosmological Simulations

The accelerated expansion of the Universe poses a major theoretical puzzle. Although the assumption of a non-zero cosmological constant provides a minimal extension of general relativity that is consistent with observational data, many theories of modified gravity have been suggested as possible alternatives. Predictions of structure formation for these models in the fully nonlinear regime are very expensive and it is difficult, if not impossible, to explore such a huge space of models and parameters using high-resolution N-body simulations. Even in the mildly nonlinear regime, perturbative methods can become extremely complex. We explore whether simplified dynamical approximations, applicable for a certain set of cosmological probes, can be used to investigate models of modified gravity with acceptable accuracy in the latter instance. For the case of chameleon gravity, we find that these methods can indeed be used to explore the region around the baryon acoustic oscillation scale, k ~ 0:1 hMpc-1 but not much further.

cosmology↗
DOE OSTI2022

Entanglement perspective on the quantum approximate optimization algorithm

Many quantum algorithms seek to output a specific bitstring solving the problem of interest—or a few if the solution is degenerate. It is the case for the quantum approximate optimization algorithm (QAOA) in the limit of large circuit depth, which aims to solve quadratic unconstrained binary optimization problems. Hence, the expected final state for these algorithms is either a product state or a low-entangled superposition involving a few bitstrings. What happens in between the initial N -qubit product state | 0 〉 ⊗ N and the final one regarding entanglement? Here, we consider the QAOA algorithm for solving the paradigmatic MaxCut problem on different types of graphs. We study the entanglement growth and spread resulting from randomized and optimized QAOA circuits and find that there is a volume-law entanglement barrier between the initial and final states. We also investigate the entanglement spectrum in connection with random matrix theory. In addition, we compare the entanglement production with a quantum annealing protocol aiming to solve the same MaxCut problems. Finally, we discuss the implications of our results for the simulation of QAOA circuits with tensor network-based methods relying on low-entanglement for efficiency, such as matrix product states.

Dupont, Maxime↗
DOE OSTI2020

Linear Approximation Line Pack Model for Integrated Electricity and Natural Gas Systems OPF

With the increasing installation of renewable energy electricity generation capacity, the penetration of natural gas fired generation is also substantailly increasing in power systems due to their fast response capability to mitigate system variability and uncertainty. The dependencies between the electricity system and the natural gas system are becoming more important to maintain the reliability of both systems. In integrated electricity and natural gas systems (IEGSs) operations, the nonlinearity of the natural gas system brings challenges to the system operators. In this paper, the IEGSs optimal power flow (OPF) model is proposed that includes the line pack of the gas system via linear approximation. The simulation results demonstrate that the proposed model can obtain optimal solutions efficiently that are comparable in accuracy as the nonlinear line pack model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

A higher order approximate static condensation method for multi-material diffusion problems

The paper studies an approximate static condensation method for the diffusion problem with discontinuous diffusion coefficients. The method allows for a general polygonal mesh which is unfitted to the material interfaces. Moreover, the interfaces can be discontinuous across the mesh edges as typical for numerical reconstructions using the volume or moment-of-fluid methods. We apply a mimetic finite difference method to solve local diffusion problems and use P 1 (mortar) edge elements to couple local problems into the global system. The condensation process and the properties of the resulting algebraic system are discussed. It is demonstrated that the method is second order accurate on smooth solutions and performs well for problems with high contrast in diffusion coefficients. Experiments also show the robustness with respect to position of the material interfaces against the underlying mesh.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fresnel zone plate point spread function approximation for zeroth order mitigation in millimetric field of view x-ray imaging

High spatial and temporal resolution x-ray radiography images are required at the National Ignition Facility (NIF) for high-energy density experiments. One technique that is in development to achieve the required resolution uses Fresnel zone plate (FZP) optics to image an object that is backlit by an x-ray source. The multiple FZP diffraction orders do not focus on the same plane, which increases the background and reduces the contrast. Understanding the point spread function of the different diffraction orders will allow the prediction of the expected background using simulations. We find that the two-dimensional point spread function of the FZP can be approximated by the addition of a sharp Gaussian with a disk. This allowed for the estimation of the background in NIF experimental images of Rayleigh–Taylor spikes and their interpretation. An alternative design of FZP is discussed to allow the inclusion of a zeroth order blocker to reduce the background.

Do, A. (ORCID:0000000174372147)↗
DOE OSTI2023

Approximating large-basis coupled-cluster theory vibrational frequencies using focal-point approximations

The focal-point approximation can be used to estimate a high-accuracy, slow quantum chemistry computation by combining several lower-accuracy, faster computations. We examine the performance of focal-point methods by combining second-order Møller–Plesset perturbation theory (MP2) with coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] for the calculation of harmonic frequencies and that of fundamental frequencies using second-order vibrational perturbation theory (VPT2). In contrast to standard CCSD(T), the focal-point CCSD(T) method approaches the complete basis set (CBS) limit with only triple-ζ basis sets for the coupled-cluster portion of the computation. The predicted harmonic and fundamental frequencies were compared with the experimental values for a set of 20 molecules containing up to six atoms. Here, the focal-point method combining CCSD(T)/aug-cc-pV(T + d)Z with CBS-extrapolated MP2 has mean absolute errors vs experiment of only 7.3 cm −1 for the fundamental frequencies, which are essentially the same as the mean absolute error for CCSD(T) extrapolated to the CBS limit using the aug-cc-pV(Q + d)Z and aug-cc-pV(5 + d)Z basis sets. However, for H 2 O, the focal-point procedure requires only 3% of the computation time as the extrapolated CCSD(T) result, and the cost savings will grow for larger molecules.

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

The matrix product approximation for the dynamic cavity method

Stochastic dynamics of classical degrees of freedom, defined on vertices of locally tree-like graphs, can be studied in the framework of the dynamic cavity method which is exact for tree graphs. Such models correspond for example to spin-glass systems, Boolean networks, neural networks, and other technical, biological, and social networks. The central objects in the cavity method are edge messages—conditional probabilities of two vertex variable trajectories. In this paper, we discuss a rather pedagogical derivation for the dynamic cavity method, give a detailed account of the novel matrix product edge message (MPEM) algorithm for the solution of the dynamic cavity equation as introduced, and present optimizations and extensions. Matrix product approximations of the edge messages are constructed recursively in an iteration over time. Computation costs and precision can be tuned by controlling the matrix dimensions of the MPEM in truncations. Without truncations, the dynamics is exact. Data for Glauber–Ising dynamics shows a linear growth of computation costs in time. In contrast to Monte Carlo simulations, the approach has a much better error scaling. Hence, it gives for example access to low probability events and decaying observables like temporal correlations. Here, we discuss optimized truncation schemes and an extension that allows to capture models which have a continuum time limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Dancoff-based Wigner-Seitz approximation for the subgroup resonance self-shielding in the VERA neutronic simulator MPACT

The MPACT neutronics module of the Virtual Environment for Reactor Analysis (VERA) has used the subgroup method for resonance self-shielding calculation, for which two-dimensional (2D) fixed-source transport calculations are performed using the method of characteristics for resonance energy groups. When considering thermal feedbacks, the subgroup calculation must be performed at each outer iteration. Therefore, the computing time for cross section processing is a significant burden for computational efficiency. The Dancoff-based Wigner-Seitz approximation (DWA) capability has been implemented into MPACT in conjunction with the subgroup method, which has been used in SCALE/XSProc since SCALE version 6.0 and has recently been called an equivalent Dancoff-factor cell (EDC) method. The issue of relatively large reactivity bias in DWA for the gadolinia rods was resolved by introducing multiple Dancoff factors. Benchmark results for the VERA pressurized and boiling water reactor benchmark suites show that the DWA capability would significantly enhance computational efficiency with comparable accuracy. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1977

Validity of approximate methods in molecular scattering. III - Effective potential and coupled states approximations for differential and gas kinetic cross sections

Two dimensionality-reducing approximations, the j sub z-conserving coupled states (sometimes called the centrifugal decoupling) method and the effective potential method, were applied to collision calculations of He with CO and with HCl. The coupled states method was found to be sensitive to the interpretation of the centrifugal angular momentum quantum number in the body-fixed frame, but the choice leading to the original McGuire-Kouri expression for the scattering amplitude - and to the simplest formulas - proved to be quite successful in reproducing differential and gas kinetic cross sections. The computationally cheaper effective potential method was much less accurate.

Monchick, L.↗
NASA NTRS2000

A Posteriori Error Estimation for Finite Volume and Finite Element Approximations Using Broken Space Approximation

We consider a posteriori error estimates for finite volume and finite element methods on arbitrary meshes subject to prescribed error functionals. Error estimates of this type are useful in a number of computational settings: (1) quantitative prediction of the numerical solution error, (2) adaptive meshing, and (3) load balancing of work on parallel computing architectures. Our analysis recasts the class of Godunov finite volumes schemes as a particular form of discontinuous Galerkin method utilizing broken space approximation obtained via reconstruction of cell-averaged data. In this general framework, weighted residual error bounds are readily obtained using duality arguments and Galerkin orthogonality. Additional consideration is given to issues such as nonlinearity, efficiency, and the relationship to other existing methods. Numerical examples are given throughout the talk to demonstrate the sharpness of the estimates and efficiency of the techniques. Additional information is contained in the original.

Barth, Timothy J.↗
DOE OSTI2021

Fourier Neural Networks as Function Approximators and Differential Equation Solvers

We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a straightforward architecture with a single hidden layer. The simplicity of this network architecture facilitates the integration with any other higher-complexity networks, at a data pre- or postprocessing stage. We validate this FNN on naturally periodic smooth functions and on piecewise continuous periodic functions. We showcase the use of this FNN for modeling or solving partial differential equations with periodic boundary conditions. The main advantages of the current approach are the validity of the solution outside the training region, interpretability of the trained model, and simplicity of use.

Fourier decomposition↗
DOE OSTI2022

Simple Approximation for the Ideal Reference State of Gases Adsorbed on Solid-State Surfaces

Reference states are useful as models for facilitating calculations of equilibrium constants, and they may also serve as standard states that are convenient for organizing and tabulating thermodynamic data; however, standard state conventions and appropriate reference states for adsorbed species have received less attention than those for pure substances and solutes. Here, we compare seven choices of reference states for calculations of equilibrium constants and transition state theory rate constants for flat surfaces, in particular (1) an ideal 2D harmonic oscillator, (2) an ideal rigid-molecule harmonic oscillator, (3) an ideal 2D harmonic oscillator with separable surface modes, (4) a 2D ideal gas, (5) an ideal 2D hindered translator, (6) an ideal 2D hindered translator with lowest-order barriers, and (7) a simple ideal 2D hindered translator proposed in this work. The advantage of models 5–7 is that they can treat both mobile and localized adsorbates in a consistent way, whereas models 1–3 are only appropriate for localized adsorbates, and model 4 is only appropriate for a freely translating adsorbate. Furthermore, models 6 and 7 reduce the computational cost without the user having to calculate barrier heights for diffusion. An advantage of the simple ideal 2D hindered translator is that it has a physical high-temperature limit. We also propose a reference state for nonflat surfaces. Here, the user is encouraged to choose a reference state based on the appropriateness of the model and the practicality of the calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Deterministic Linear Time for Maximal Poisson‐Disk Sampling using Chocks without Rejection or Approximation

Abstract We show how to sample uniformly within the three‐sided region bounded by a circle, a radial ray, and a tangent, called a “chock.” By dividing a 2D planar rectangle into a background grid, and subtracting Poisson disks from grid squares, we are able to represent the available region for samples exactly using triangles and chocks. Uniform random samples are generated from chock areas precisely without rejection sampling. This provides the first implemented algorithm for precise maximal Poisson‐disk sampling in deterministic linear time. We prove O(n · M(b) log b), where n is the number of samples, b is the bits of numerical precision and M is the cost of multiplication. Prior methods have higher time complexity, take expected time, are non‐maximal, and/or are not Poisson‐disk distributions in the most precise mathematical sense. We fill this theoretical lacuna.

Mitchell, Scott A.↗