Search NASA⌕ Search

SEARCH · Search NASA

Results for “Monte Carlo approximation”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Conditional Probability And The Sparse Distributed Memory

Report presents conditional-probability interpretation of Kanerva's sparse distributed memory (SDM). SDM is conceptual digital electronic memory in which addresses chosen sparsely in space of many dimensions and content of memory at each address positive or negative integer written (incremented or decremented) or read according to special rules. Contents of SDM constitute Monte Carlo approximation to multidimensional conditional-probability integral.

Anderson, Charles H.↗
NASA NTRS2003

Energetics of Single Substitutional Impurities in NiTi

Shape-memory alloys are of considerable current interest, with applications ranging from stents to Mars rover components. In this work, we present results on the energetics of single substitutional impurities in B2 NiTi. Specifically, energies of Pd, Pt, Zr and Hf impurities at both Ni and Ti sites are computed. All energies are computed using the CASTEP ab initio code, and, for comparison, using the quantum approximate energy method of Bozzolo, Ferrante and Smith. Atomistic relaxation in the vicinity of the impurities is investigated via quantum approximate Monte Carlo simulation, and in cases where the relaxation is found to be important, the resulting relaxations are applied to the ab initio calculations. We compare our results with available experimental work.

Good, Brian S.↗
DOE OSTI2015

Beyond chemical accuracy: The pseudopotential approximation in diffusion Monte Carlo calculations of the HCP to BCC phase transition in beryllium.

Motivated by the disagreement between recent diffusion Monte Carlo calculations of the phase transition pressure between the ambient and beta-Sn phases of silicon and experiments, we present a study of the HCP to BCC phase transition in beryllium. This lighter element provides an opportunity for directly testing many of the approximations required for calculations on silicon and may suggest a path towards increasing the practical accuracy of diffusion Monte Carlo calculations of solids in general. We demonstrate that the single largest approximation in these calculations is the pseudopotential approximation and after removing this we find excellent agreement with experiment for the ambient HCP phase and results similar to careful calculations using density functional theory for the phase transition pressure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model

In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO{sub 2}(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Grid-based diffusion Monte Carlo for fermions without the fixed-node approximation

A diffusion Monte Carlo algorithm is introduced that can determine the correct nodal structure of the wave function of a few-fermion system and its ground-state energy without an uncontrolled bias. This is achieved by confining signed random walkers to the points of a uniform infinite spatial grid, allowing them to meet and annihilate one another to establish the nodal structure without the fixed-node approximation. An imaginary-time propagator is derived rigorously from a discretized Hamiltonian, governing a non-Gaussian, sign-flipping, branching, and mutually annihilating random walk of particles. The accuracy of the resulting stochastic representations of a fermion wave function is limited only by the grid and imaginary-time resolutions and can be improved in a controlled manner. Here, the method is tested for a series of model problems including fermions in a harmonic trap as well as the He atom in its singlet or triplet ground state. For the latter case, the energies approach from above with increasing grid resolution and converge within 0.015 E h of the exact basis-set-limit value for the grid spacing of 0.08 a.u. with a statistical uncertainty of 10 –5 E h without an importance sampling or Jastrow factor.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

Benchmarking the pseudopotential and fixed-node approximations in diffusion Monte Carlo calculations of molecules and solids

Diffusion Monte Carlo (DMC) calculations of the spectroscopic properties of a large set of molecules were performed, assessing the effect of different approximations. In systems containing elements with large atomic numbers, we show that the errors associated with the use of nonlocal mean-field-based pseudopotentials in DMC calculations can be significant and may surpass the fixed-node error. We suggest practical guidelines for reducing these pseudopotential errors, which allow us to obtain DMC-computed spectroscopic parameters of molecules and equation of state properties of solids in excellent agreement with experiment.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A Monte Carlo Approach to Approximating the Effects of Pore Geometry on the Phase Behavior of Soil Freezing

Abstract Freezing in porous media is associated with a host of dynamic phenomena that stem from the presence and mobility of premelted liquid at subzero temperatures. Accurate assessments of the progressive liquid‐ice phase transition is required for predictive models of frost damage, glacier‐till coupling, and many other cold regions processes, as well as for evaluating the capacity for water storage in near‐surface extraterrestrial environments. We use a Monte Carlo approach to sample the pore space in a synthetic 3D packing of poly‐dispersed spherical particles and evaluate local geometrical constraints that allow us to assess changes in the relative proportions of pore fluid and ice. By approximating the phase boundary geometry in fine‐grained pores while considering both the curvature of the liquid‐ice interface and wetting interactions with matrix particles, our model predicts changes in phase equilibrium in granular media over a broad temperature range, where present accounting for the colligative effects of chloride and perchlorate solutes. In addition to formulating the constitutive behavior needed to better understand properties and processes in frozen soils, our results also provide insight into other aspects of phase equilibria in porous media, including the formation of methane hydrates in permafrost and marine sediments, and the partitioning between liquid water and vapor in the vadose zone.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids—A case study in diamond

While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for ab initio electronic structure calculations, in practice, the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros). This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wavefunctions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. A simple protocol in which both exact and approximate results for finite supercells are used to extrapolate to the thermodynamic limit is introduced. This approach is illustrated in the case of the carbon diamond using Slater–Jastrow trial wavefunctions including up to one million Slater determinants. Fixed-node DMC energies obtained with such large expansions are much improved, and the fixed-node error is found to decrease monotonically and smoothly as a function of the number of determinants in the trial wavefunction, a property opening the way to a better control of this error. The cohesive energy extrapolated to the thermodynamic limit is in close agreement with the estimated experimental value. Interestingly, this is also the case at the single-determinant level, thus, indicating a very good error cancellation in carbon diamond between the bulk and atomic total fixed-node energies when using single-determinant nodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Density scaling approximation for Monte-Carlo simulations of radioactive plumes

The release of radioactive gas into the atmosphere can diffuse into large volumes of air downwind from the point of release. The extent of radioactivity can cover thousands of cubic meters of air. For such large volumes, the weather models used to predict the down-wind distribution of the plume and the radiation transport models used to predict the radiation reaching ground-level from the plume can take tens of hours of computer time on multi-node institutional High-Performance Computing facilities. In this paper we focus on the radiation transport aspect of plume modeling. Here, we describe a phenomenological method for approximating the amounts of radiation that reach ground level from large volumes of a static radioactive plume that can be calculated on a stand-alone personal computer in much shorter computation times than those usually needed for such large volume evaluations. We refer to this method as the Density Scaling Approximation (DSA). Its ability to approximate ground-level count rates of large plumes comes from using a small-plume volume with a scaled-up value of air density to simulate the same number of scatterings that occur during transport in larger plume volumes at normal air density. We demonstrate the DSA by using a 100 m-diameter air-filled hemispherical dome geometry with a uniform volumetric activity of 135 Xe gas throughout the air-filled volume. The DSA for a larger dome diameter is obtained by evaluating the 100 m dome with an air density scaled up by the linear ratio of the larger diameter to the 100 m diameter. We find that this approximation works well for dome diameters up to 1200 m – the largest diameter studied and a size more than sufficient for accounting for all the radiation from 135 Xe. Moreover, most of our DSA results can be calculated over 500 times faster than corresponding full-sized geometry with normal air density. To help evaluate the accuracy of the DSA and gain insight into how well it can reproduce different regions of the spectra, we use three, easily understood regions of interest to compare the DSA results to the full-sized geometry at normal air density results. These regions are the full-energy peak, the region of single-Compton scattering, and the region of multiple-Compton scattering. We show how the dominance of the Compton scattering mechanism determines this division and thus provides insight into how Compton scattering is manifested in spectra from photon scattering through air in general, and how well the DSA approximation works.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Beyond the Born-Oppenheimer approximation with quantum Monte Carlo methods

Here, we develop tools that enable the study of non-adiabatic effects with variational and diffusion Monte Carlo methods. We propose a highly accurate wave function ansatz for electron-ion systems that can involve a combination of both fixed and quantum ions. We explicitly calculate the ground state energies of H 2 , LiH, H 2 O and FHF - using fixed-node quantum Monte Carlo with wave function nodes that explicitly depend on the ion positions. The obtained energies implicitly include the effects arising from quantum nuclei and electron-nucleus coupling. We compare our findings to the best theoretical and experimental results available and find excellent agreement.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Quantitative estimation of localization errors of 3d transition metal pseudopotentials in diffusion Monte Carlo

The necessarily approximate evaluation of non-local pseudopotentials in diffusion Monte Carlo (DMC) introduces localization errors. In this paper, we estimate these errors for two families of non-local pseudopotentials for the first-row transition metal atoms Sc–Zn using an extrapolation scheme and multideterminant wavefunctions. Sensitivities of the error in the DMC energies to the Jastrow factor are used to estimate the quality of two sets of pseudopotentials with respect to locality error reduction. The locality approximation and T-moves scheme are also compared for accuracy of total energies. After estimating the removal of the locality and T-moves errors, we present the range of fixed-node energies between a single determinant description and a full valence multideterminant complete active space expansion. The results for these pseudopotentials agree with previous findings that the locality approximation is less sensitive to changes in the Jastrow than T-moves yielding more accurate total energies, however not necessarily more accurate energy differences. For both the locality approximation and T-moves, we find decreasing Jastrow sensitivity moving left to right across the series Sc–Zn. The recently generated pseudopotentials of Krogel et al. reduce the magnitude of the locality error compared with the pseudopotentials of Burkatzki et al. by an average estimated 40% using the locality approximation. The estimated locality error is equivalent for both sets of pseudopotentials when T-moves is used. Finally, for the Sc–Zn atomic series with these pseudopotentials, and using up to three-body Jastrow factors, our results suggest that the fixed-node error is dominant over the locality error when a single determinant is used.

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

The Impulse Approximation Scattering Function and Its Use in Monte Carlo Photon Transport Simulations

The viability of using the impulse approximation scattering function in Monte Carlo photon transport simulations is explored. This scattering function can be constructed from the double differential incoherent scattering cross section developed by Ribberfors and Berggren. A commonly used method for modeling photon Doppler broadening, which is referred to as the hybrid Doppler broadening method, can also be derived from this cross section. A new photon Doppler broadening method, called the consistent Doppler broadening method, is derived and discussed. This method eliminates some of the commonly employed approximations in the hybrid Doppler broadening method, in part, by using the impulse approximation scattering function. Integrated incoherent cross sections generated using the impulse approximation scattering function and the widely used Waller-Hartree scattering function are in good agreement above 20 keV. Below 20 keV, differences as high as 70% are observed, which differs from the roughly 5% differences observed by Ribberfors for some of the materials. Integral and spectral quantities for two problems are also generated using the Monte Carlo photon transport capabilities of the Framework for REsearch in Nuclear ScIence and Engineering (FRENSIE). Due to the small, relative result differences observed when using the impulse approximation scattering function, it is considered a viable alternative to the Waller-Hartree scattering function. In addition, some small, but expected, differences in spectral fluxes at low energies can be avoided by adopting the consistent Doppler broadening method.

42 ENGINEERING↗
DOE OSTI2015

Combination of the pair density approximation and the Takahashi–Imada approximation for path integral Monte Carlo simulations

We construct an accurate imaginary time propagator for path integral Monte Carlo simulations for heterogeneous systems consisting of a mixture of atoms and molecules. We combine the pair density approximation, which is highly accurate but feasible only for the isotropic interactions between atoms, with the Takahashi–Imada approximation for general interactions. We present finite temperature simulations results for energy and structure of molecules–helium clusters X{sup 4}He{sub 20} (X=HCCH and LiH) which show a marked improvement over the Trotter approximation which has a 2nd-order time step bias. We show that the 4th-order corrections of the Takahashi–Imada approximation can also be applied perturbatively to a 2nd-order simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. Rather than focusing on constructing exactly the stochastic trajectories, our approach relies on approximating the evolution of observables, such as density, coverage, correlations and so on. More specifically, we develop a spatial domain decomposition of the Markov operator (generator) that describes the evolution of all observables according to the kinetic Monte Carlo algorithm. This domain decomposition corresponds to a decomposition of the Markov generator into a hierarchy of operators and can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). Based on this operator decomposition, we formulate parallel Fractional step kinetic Monte Carlo algorithms by employing the Trotter Theorem and its randomized variants; these schemes, (a) are partially asynchronous on each fractional step time-window, and (b) are characterized by their communication schedule between processors. The proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules. We carry out a detailed benchmarking of the parallel KMC schemes using available exact solutions, for example, in Ising-type systems and we demonstrate the capabilities of the method to simulate complex spatially distributed reactions at very large scales on GPUs. Finally, we discuss work load balancing between processors and propose a re-balancing scheme based on probabilistic mass transport methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Solutions of the two-dimensional Hubbard model: Benchmarks and results from a wide range of numerical algorithms

Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Furthermore, cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗