SEARCH · Search NASA

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.

SourceResearch connectionFrom yearThrough year

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

At least 829 records · Page 46

All sources NASA NTRS DOE OSTI

DOE OSTI2025

Computation of Auger Electron Spectra in Organic Molecules with Multiconfiguration Pair-Density Functional Theory

Efficient and accurate computation of molecular Auger electron spectra for larger systems is limited by the rapid increase in the number of doubly ionized final states as the system size grows. Here, in this work, we benchmark the application of multiconfiguration pair-density functional theory with a restricted active space (RAS) reference wave function for computing the carbon K-edge decay spectra of 20 organic molecules. Decay rates are computed within the one-center approximation. We evaluate the performance of different basis sets and on-top functionals and find that multiconfiguration pair-density functional theory achieves accuracy comparable to RAS followed by second-order perturbation theory, but at significantly lower computational cost.

Fouda, Adam E. A. [Argonne National Laboratory (AN↗

DOE OSTI2015

EMMA: an adaptive mesh refinement cosmological simulation code with radiative transfer

EMMA is a cosmological simulation code aimed at investigating the reionization epoch. It handles simultaneously collisionless and gas dynamics, as well as radiative transfer physics using a moment-based description with the M1 approximation. Field quantities are stored and computed on an adaptive three-dimensional mesh and the spatial resolution can be dynamically modified based on physically motivated criteria. Physical processes can be coupled at all spatial and temporal scales. We also introduce a new and optional approximation to handle radiation: the light is transported at the resolution of the non-refined grid and only once the dynamics has been fully updated, whereas thermo-chemical processes are still tracked on the refined elements. Such an approximation reduces the overheads induced by the treatment of radiation physics. A suite of standard tests are presented and passed by EMMA, providing a validation for its future use in studies of the reionization epoch. The code is parallel and is able to use graphics processing units (GPUs) to accelerate hydrodynamics and radiative transfer calculations. Depending on the optimizations and the compilers used to generate the CPU reference, global GPU acceleration factors between ×3.9 and ×16.9 can be obtained. As a result, vectorization and transfer operations currently prevent better GPU performance and we expect that future optimizations and hardware evolution will lead to greater accelerations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Large-scale harmonic balance simulations with Krylov subspace and preconditioner recycling

The multi-harmonic balance method combined with numerical continuation provides an efficient framework to compute a family of time-periodic solutions, or response curves, for large-scale, nonlinear mechanical systems. The predictor and corrector steps repeatedly solve a sequence of linear systems that scale by the model size and number of harmonics in the assumed Fourier series approximation. In this paper, a novel Newton–Krylov iterative method is embedded within the multi-harmonic balance and continuation algorithm to efficiently compute the approximate solutions from the sequence of linear systems that arise during the prediction and correction steps. Further, the method recycles, or reuses, both the preconditioner and the Krylov subspace generated by previous linear systems in the solution sequence. A delayed frequency preconditioner refactorizes the preconditioner only when the performance of the iterative solver deteriorates. The GCRO-DR iterative solver recycles a subset of harmonic Ritz vectors to initialize the solution subspace for the next linear system in the sequence. The performance of the iterative solver is demonstrated on two exemplars with contact-type nonlinearities and benchmarked against a direct solver with traditional Newton–Raphson iterations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Eccentric Form of the Loss of Stability of a Rotating Elastoplastic Radially Inhomogeneous Stepped Circular Disk

We propose a procedure for the investigation of the possible loss of stability of a rotating elastoplastic radially inhomogeneous stepped circular disk by the method of small parameter. The characteristic equation for the critical radius of the plastic zone is obtained in the first approximation. The values of the critical angular rotational velocity are numerically found for various parameters of the disk.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Exact sum rules with approximate ground states

Electromagnetic and weak transitions tell us a great deal about the structure of atomic nuclei. Yet modeling transitions can be difficult: it is often easier to compute the ground state, if only as an approximation, than excited states. One alternative is through transition sum rules, in particular the non-energy-weighted and energy-weighted sum rules, which can be computed as expectation values of operators. We investigate by computing sum rules for a variety of nuclei, comparing the numerically exact full configuration-interaction shell model, as a reference, to Hartree-Fock, projected Hartree-Fock, and the nucleon pair approximation. Furthermore, these approximations yield reasonable agreement, which we explain by prior work on the systematics of transition moments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator

Our manuscript demonstrates a technique for efficiently solving the classical wave equation, the shallow water equations, and, more generally, equations of the form ∂u/∂t=Lu∂u/∂t=Lu, where LL is a skew-Hermitian differential operator. The idea is to explicitly construct an approximation to the time-evolution operator exp(τL)exp(τL) for a relatively large time-step ττ. Recently developed techniques for approximating oscillatory scalar functions by rational functions, and accelerated algorithms for computing functions of discretized differential operators are exploited. Principal advantages of the proposed method include: stability even for large time-steps, the possibility to parallelize in time over many characteristic wavelengths and large speed-ups over existing methods in situations where simulation over long times are required. Numerical examples involving the 2D rotating shallow water equations and the 2D wave equation in an inhomogenous medium are presented, and the method is compared to the 4th order Runge–Kutta (RK4) method and to the use of Chebyshev polynomials. The new method achieved high accuracy over long-time intervals, and with speeds that are orders of magnitude faster than both RK4 and the use of Chebyshev polynomials.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Applications of Analytic Models to Spent Fuel Cask Analysis

The advent of high performance computing has changed the way scientists and engineers solve problems. Scientists previously would make a tremendous effort to simplify a complex problem to it’s essence by reducing geometry, neglecting changes and only preserving first-order effects. Now, scientist are able to leave the details in the problem and computationally arrive at a result. To develop the computational physics programs used by scientists, developers make assumptions and use approximation to reduce complex, continuous calculus to algebraic expressions which computers are able to solve.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Low rank approximation in simulations of quantum algorithms

Simulating quantum algorithms on classical computers is challenging when the system size, i.e., the number of qubits used in the quantum algorithm, is moderately large. However, some quantum algorithms and the corresponding quantum circuits can be simulated efficiently on a classical computer if the input quantum state is a low rank tensor and all intermediate states of the quantum algorithm can be represented or approximated by low rank tensors. Here, in this paper, we examine the possibility of simulating a few quantum algorithms by using low-rank canonical polyadic (CP) decomposition to represent the input and all intermediate states of these algorithms. Two rank reduction algorithms are used to enable efficient simulation. We show that some of the algorithms preserve the low rank structure of the input state and can thus be efficiently simulated on a classical computer. However, the rank of the intermediate states in other quantum algorithms can increase rapidly, making efficient simulation more difficult. To some extent, such difficulty reflects the advantage or superiority of a quantum computer over a classical computer. As a result, understanding the low rank structure of a quantum algorithm allows us to identify algorithms that can benefit significantly from quantum computers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Data-driven quantum approximate optimization algorithm for power systems

Abstract Quantum technology provides a ground-breaking methodology to tackle challenging computational issues in power systems. It is especially promising for Distributed Energy Resources (DERs) dominant systems that have been widely developed to promote energy sustainability. In those systems, knowing the maximum sections of power and data delivery is essential for monitoring, operation, and control. However, high computational effort is required. By leveraging quantum resources, Quantum Approximate Optimization Algorithm (QAOA) provides a means to search for these sections efficiently. However, QAOA performance relies heavily on critical parameters, especially for weighted graphs. Here we present a data-driven QAOA, which transfers quasi-optimal parameters between weighted graphs based on the normalized graph density. We verify the strategy with 39,774 expectation value calculations. Without parameter optimization, our data-driven QAOA is comparable with the Goemans-Williamson algorithm. This work advances QAOA and pilots its practical application to power systems in noisy intermediate-scale quantum devices.

Jing, Hang (ORCID:0000000256343489)↗

DOE OSTI2018

Combining the ensemble and Franck-Condon approaches for calculating spectral shapes of molecules in solution

The correct treatment of vibronic effects is vital for the modeling of absorption spectra of many solvated dyes. Vibronic spectra for small dyes in solution can be easily computed within the Franck-Condon approximation using an implicit solvent model. However, implicit solvent models neglect specific solute-solvent interactions on the electronic excited state. On the other hand, a straightforward way to account for solute-solvent interactions and temperature-dependent broadening is by computing vertical excitation energies obtained from an ensemble of solute-solvent conformations. Ensemble approaches usually do not account for vibronic transitions and thus often produce spectral shapes in poor agreement with experiment. Here we address these shortcomings by combining zero-temperature vibronic fine structure with vertical excitations computed for a room-temperature ensemble of solute-solvent configurations. In this combined approach, all temperature-dependent broadening is treated classically through the sampling of configurations and quantum mechanical vibronic contributions are included as a zero-temperature correction to each vertical transition. In our calculation of the vertical excitations, significant regions of the solvent environment are treated fully quantum mechanically to account for solute-solvent polarization and charge-transfer. For the Franck-Condon calculations, a small amount of frozen explicit solvent is considered in order to capture solvent effects on the vibronic shape function. We test the proposed method by comparing calculated and experimental absorption spectra of Nile red and the green fluorescent protein chromophore in polar and non-polar solvents. For systems with strong solute-solvent interactions, the combined approach yields significant improvements over the ensemble approach. For systems with weak to moderate solute-solvent interactions, both the high-energy vibronic tail and the width of the spectra are in excellent agreement with experiments

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Mana and thermalization: Probing the feasibility of near-Clifford Hamiltonian simulation

Quantum hydrodynamics is the emergent classical dynamics governing transport of conserved quantities in generic strongly interacting quantum systems. Here, recent matrix product operator methods [1,2] have made simulations of quantum hydrodynamics in 1+1D tractable, but they do not naturally generalize to 2+1D or higher, and they offer limited guidance as to the difficulty of simulations on quantum computers. Near-Clifford simulation algorithms are not limited to one dimension, and future error-corrected quantum computers will likely be bottlenecked by non-Clifford operations. We therefore investigate the non-Clifford resource requirements for simulation of quantum hydrodynamics using mana, a resource theory of non-Clifford operations. For infinite-temperature starting states, we find that the mana of subsystems quickly approaches zero, while for starting states with energy above some threshold the mana approaches a nonzero value. Surprisingly, in each case the finite-time mana is governed by the subsystem entropy, not the thermal state mana; we argue that this is because mana is a sensitive diagnostic of finite-time deviations from canonical typicality.

1-dimensional spin chains↗

DOE OSTI2018

Convergence of Probability Densities Using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification

Here, we analyze the convergence of probability density functions utilizing approximate models for both forward and inverse problems. We consider the standard forward uncertainty quantification problem where an assumed probability density on parameters is propagated through the approximate model to produce a probability density, often called a push-forward probability density, on a set of quantities of interest (QoI). The inverse problem considered in this paper seeks to update an initial probability density assumed on model input parameters such that the subsequent push-forward of this updated density through the parameter-to-QoI map matches a given probability density on the QoI. We prove that the densities obtained from solving the forward and inverse problems, using approximate models, converge to the true densities as the approximate models converge to the true models. Numerical results are presented to demonstrate convergence rates of densities for sparse grid approximations of parameter-to-QoI maps and standard spatial and temporal discretizations of PDEs and ODEs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

A generalized framework for in-line energy deposition during steady-state Monte Carlo radiation transport

A rigorous treatment of energy deposition in a Monte Carlo transport calculation, including coupled transport of all secondary and tertiary radiations, increases the computational cost of a simulation dramatically, making fully-coupled heating impractical for many large calculations, such as 3-D analysis of nuclear reactor cores. However, in some cases, the added benefit from a full-fidelity energy-deposition treatment is negligible, especially considering the increased simulation run time. In this paper we present a generalized framework for the in-line calculation of energy deposition during steady-state Monte Carlo transport simulations. This framework gives users the ability to select among several energy-deposition approximations with varying levels of fidelity. The paper describes the computational framework, along with derivations of four energy-deposition treatments. Each treatment uses a unique set of self-consistent approximations, which ensure that energy balance is preserved over the entire problem. By providing several energy-deposition treatments, each with different approximations for neglecting the energy transport of certain secondary radiations, the proposed framework provides users the flexibility to choose between accuracy and computational efficiency. Numerical results are presented, comparing heating results among the four energy-deposition treatments for a simple reactor/compound shielding problem. The results illustrate the limitations and computational expense of each of the four energy-deposition treatments. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Hybrid immersed interface-immersed boundary methods for AC dielectrophoresis

Dielectrophoresis, a nonlinear electrokinetic transport mechanism, has become popular in many engineering applications including manipulation, characterization and actuation of biomaterials, particles and biological cells. In this paper, we present a hybrid immersed interface–immersed boundary method to study AC dielectrophoresis where an algorithm is developed to solve the complex Poisson equation using a real variable formulation. An immersed interface method is employed to obtain the AC electric field in a fluid media with suspended particles and an immersed boundary method is used for the fluid equations and particle transport. The convergence of the proposed algorithm as well as validation of the hybrid scheme with experimental results is presented. In this paper, the Maxwell stress tensor is used to calculate the dielectrophoretic force acting on particles by considering the physical effect of particles in the computational domain. Thus, this study eliminates the approximations used in point dipole methods for calculating dielectrophoretic force. A comparative study between Maxwell stress tensor and point dipole methods for computing dielectrophoretic forces are presented. The hybrid method is used to investigate the physics of dielectrophoresis in microfluidic devices using an AC electric field. The numerical results show that with proper design and appropriate selection of applied potential and frequency, global electric field minima can be obtained to facilitate multiple particle trapping by exploiting the mechanism of negative dielectrophoresis. Our numerical results also show that electrically neutral particles form a chain parallel to the applied electric field irrespective of their initial orientation when an AC electric field is applied. This proposed hybrid numerical scheme will help to better understand dielectrophoresis and to design and optimize microfluidic devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

PDG: A Composite Method Based on the Resolution of the Identity

The Gaussian-3 (G3) composite approach for thermochemical properties is revisited in light of the enhanced computational efficiency and reduced memory costs by applying the resolution-of-the-identity (RI) approximation for two-electron repulsion integrals (ERIs) to the computationally demanding component methods in the G3 model: the energy and gradient computations via the second-order Møller–Plesset perturbation theory (MP2) and the energy computations using the coupled-cluster singles–doubles method augmented with noniterative triples corrections [CCSD(T)]. Efficient implementation of the RI-based methods is achieved by employing a hybrid distributed/shared memory model based on MPI and OpenMP. The new variant of the G3 composite approach based on the RI approximation is termed the RI-G3 scheme, or alternatively the PDG method. The accuracy of the new RI-G3/PDG scheme is compared to the “standard” G3 composite approach that employs the memory-expensive four-center ERIs in the MP2 and CCSD(T) calculations. Taking the computation of the heats of formation of the closed-shell molecules in the G3/99 test set as a test case, it is demonstrated that the RI approximation introduces negligible changes to the mean absolute errors relative to the standard G3 model (less than 0.1 kcal/mol), while the standard deviations remain unaltered. Furthermore, the efficiency and memory requirements for the RI-MP2 and RI-CCSD(T) methods are compared to the standard MP2 and CCSD(T) approaches, respectively. The hybrid MPI/OpenMP-based RI-MP2 energy plus gradient computation is found to attain a 7.5× speedup over the standard MP2 calculations. For the most demanding CCSD(T) calculations, the application of the RI approximation is found to nearly halve the memory demand, confer about a 4–5× speedup for the CCSD iterations, and reduce the computational time for the compute-intensive triples correction step by several hours.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

The use of Jacobi wavelets for constrained approximation of rational Bézier curves

This paper presents an efficient method to solve the approximation problem of the rational Bézier curve by continuous piecewise polynomial curve in L{sub 2}-norm. For this purpose, extended Jacobi wavelets together with the Gauss–Jacobi quadrature rules are employed. The proposed technique has some advantages such as: simplicity, high accuracy and fast computation. Also, the method in the paper performs multi-degree reduction at one time and does not need the stepwise computing. Several examples are given to illustrate the effectiveness of the algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

HPC Annual Report 2017

Sandia National Laboratories has a long history of significant contributions to the high performance community and industry. Our innovative computer architectures allowed the United States to become the first to break the teraFLOP barrier—propelling us to the international spotlight. Our advanced simulation and modeling capabilities have been integral in high consequence US operations such as Operation Burnt Frost. Strong partnerships with industry leaders, such as Cray, Inc. and Goodyear, have enabled them to leverage our high performance computing (HPC) capabilities to gain a tremendous competitive edge in the marketplace. As part of our continuing commitment to providing modern computing infrastructure and systems in support of Sandia missions, we made a major investment in expanding Building 725 to serve as the new home of HPC systems at Sandia. Work is expected to be completed in 2018 and will result in a modern facility of approximately 15,000 square feet of computer center space. The facility will be ready to house the newest National Nuclear Security Administration/Advanced Simulation and Computing (NNSA/ASC) Prototype platform being acquired by Sandia, with delivery in late 2019 or early 2020. This new system will enable continuing advances by Sandia science and engineering staff in the areas of operating system R&D, operation cost effectiveness (power and innovative cooling technologies), user environment and application code performance.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Monte Carlo methods and their analysis for Coulomb collisions in multicomponent plasmas

Highlights: •A general approach to Monte Carlo methods for multicomponent plasmas is proposed. •We show numerical tests for the two-component (electrons and ions) case. •An optimal choice of parameters for speeding up the computations is discussed. •A rigorous estimate of the error of approximation is proved. -- Abstract: A general approach to Monte Carlo methods for Coulomb collisions is proposed. Its key idea is an approximation of Landau–Fokker–Planck equations by Boltzmann equations of quasi-Maxwellian kind. It means that the total collision frequency for the corresponding Boltzmann equation does not depend on the velocities. This allows to make the simulation process very simple since the collision pairs can be chosen arbitrarily, without restriction. It is shown that this approach includes the well-known methods of Takizuka and Abe (1977) [12] and Nanbu (1997) as particular cases, and generalizes the approach of Bobylev and Nanbu (2000). The numerical scheme of this paper is simpler than the schemes by Takizuka and Abe [12] and by Nanbu. We derive it for the general case of multicomponent plasmas and show some numerical tests for the two-component (electrons and ions) case. An optimal choice of parameters for speeding up the computations is also discussed. It is also proved that the order of approximation is not worse than O(√(ε)), where ε is a parameter of approximation being equivalent to the time step Δt in earlier methods. A similar estimate is obtained for the methods of Takizuka and Abe and Nanbu.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗