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At least 271 records · Page 15

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DOE OSTI2023

A path integral ground state Monte Carlo algorithm for entanglement of lattice bosons

A ground state path integral quantum Monte Carlo algorithm is introduced that allows for the study of entanglement in lattice bosons at zero temperature. The Rényi entanglement entropy between spatial subregions is explored across the phase diagram of the one dimensional Bose-Hubbard model for systems consisting of up to L=256 L = 256 sites at unit-filling without any restrictions on site occupancy, far beyond the reach of exact diagonalization. The favorable scaling of the algorithm is demonstrated through a further measurement of the Rényi entanglement entropy at the two dimensional superfluid-insulator critical point for large system sizes, confirming the existence of the expected entanglement boundary law in the ground state. The Rényi estimator is extended to measure the symmetry resolved entanglement that is operationally accessible as a resource for experimentally relevant lattice gases with fixed total particle number.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1990

A study of microkinetic adjustments required to match shock wave experiments and Monte Carlo Direct Simulation for a wide Mach number range

Shock wave thickness predictions from Monte Carlo Direct Simulations, using differential scattering and the Maitland-Smith-Aziz interatomic potential, underpredict experiments as shock Mach numbers increase above about 4. Examination of several sources of data has indicated that at relatively high energies the repulsive portion of accepted potentials such as the Maitland-Smith-Aziz may be too steep. An Exponential-6 potential due to Ross, based on high energy molecular beam scattering data and shock velocity measurements in liquid argon, has been combined with the lower energy portion of the Maitland-Smith-Aziz potential. When this hybrid potential is used in Monte Carlo Direct Simulations, agreement with experiments is improved over the previous predictions using the pure Maitland-Smith-Aziz form.

Pham-Van-diep, Gerald C.↗

DOE OSTI2024

A triple junction energy study using an inclination-dependent anisotropic Monte Carlo Potts grain growth model

This work presents a Monte Carlo Potts grain growth model in which the grain boundary (GB) energies depend on the GB inclination. The inclination is calculated using a linear smoothing approach developed by the authors. In bicrystal simulations with a shrinking grain, the grain changes shape to prefer low energy GB inclinations. However, in polycrystal simulations the preferred inclinations depend on the approach used to assign the triple junction (TJ) energies. Approaches that produce unimodal TJ energy distributions result in the expected behavior of preferring low energy GB inclinations. However, approaches that produce bimodal TJ energy distributions result in medium energy or even high energy inclinations being preferred. Overall, this study underscores the importance of TJs in anisotropic grain growth.

Grain boundary inclination↗

DOE OSTI2025

Energy-preserving coupling of explicit particle-in-cell with Monte Carlo collisions

The particle-in-cell (PIC) and Monte Carlo collisions (MCC) methods are workhorses of many numerical simulations of physical systems. Recently, it was pointed out that, while the two methods can be exactly—or nearly—energy-conserving independently, combining the two leads to anomalous numerical heating. This paper reviews the standard explicit PIC-MCC algorithm, elucidates the origins of the anomalous numerical heating, and explains how to couple the two methods such that the anomalous numerical heating is avoided.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Emulators for Scarce and Noisy Data: Application to Auxiliary-Field Diffusion Monte Carlo for Neutron Matter

Understanding the equation of state (EOS) of pure neutron matter is necessary for interpreting multimessenger observations of neutron stars. Reliable data analyses of these observations require well-quantified uncertainties for the EOS input, ideally propagating uncertainties from nuclear interactions directly to the EOS. This, however, requires calculations of the EOS for a prohibitively larger number of nuclear Hamiltonians, solving the nuclear many-body problem for each one. Quantum Monte Carlo methods, such as auxiliary-field diffusion Monte Carlo (AFDMC), provide precise and accurate results for the neutron matter EOS, but they are very computationally expensive, making them unsuitable for the fast evaluations necessary for uncertainty propagation. Here, we employ parametric matrix models to develop fast emulators for AFDMC calculations of neutron matter and use them to directly propagate uncertainties of coupling constants in the Hamiltonian to the EOS. As these uncertainties include estimates of the effective field theory truncation uncertainty, this approach provides robust uncertainty estimates for use in astrophysical data analyses. In conclusion, this Letter will enable novel applications such as using astrophysical observations to put constraints on coupling constants for nuclear interactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Monte Carlo neutronics benchmarks on nuclear fuel depletion: A review

Monte Carlo (MC) neutronics codes are used widely for academic and industrial needs. Several schemes of coupling MC neutronics code with isotope generation and depletion code exist, which are used for performing nuclear fuel depletion simulations. These simulations can estimate the inventory of isotopes in neutron irradiated nuclear reactor fuel. However, the accuracy of these simulations shall be validated through experiments. MC codes are seldom validated by isotopic benchmarks compared to criticality benchmarks. This work compiles and analyzes the fuel depletion benchmarks and validations used to analyze the performance of MC-based fuel depletion neutronics codes. Analyses of these benchmarks and validations showed that the computed concentrations of 133 Cs, 135 Cs, 137 Cs, 148 Nd, 239 Pu, 240 Pu, and 241 Pu in the irradiated fuel by the depletion codes agreed with the measured values within 10% error. However, the computed concentrations of 125 Sb, 242 Cm, 243 Cm, 244 Cm, 245 Cm, and 246 Cm had errors more than 15% compared to the measured values. As a result, Ventina depletion code showed the most accurate predictions for the greatest number of isotope concentrations compared to ORIGEN2 and CINDER90.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo

In this work we develop a new hierarchical multilevel approach to generate Gaussian random field realizations in an algorithmically scalable manner that is well suited to incorporating into multilevel Markov chain Monte Carlo (MCMC) algorithms. This approach builds off of other partial differential equation (PDE) approaches for generating Gaussian random field realizations; in particular, a single field realization may be formed by solving a reaction-diffusion PDE with a spatial white noise source function as the right-hand side. While these approaches have been explored to accelerate forward uncertainty quantification tasks, e.g., multilevel Monte Carlo, the previous constructions are not directly applicable to multilevel MCMC frameworks which build fine-scale random fields in a hierarchical fashion from coarse-scale random fields. Our new hierarchical multilevel method relies on a hierarchical decomposition of the white noise source function in $L^2$ which allows us to form Gaussian random field realizations across multiple levels of discretization in a way that fits into multilevel MCMC algorithmic frameworks. After presenting our main theoretical results and numerical scaling results to showcase the utility of this new hierarchical PDE method for generating Gaussian random field realizations, this method is tested on a four-level MCMC algorithm to explore its feasibility.

algebraic multigrid↗

DOE OSTI2020

Hybridizing pseudo-Hamiltonians and non-local pseudopotentials in diffusion Monte Carlo

An accurate treatment of effective core potentials (ECPs) requires care in continuum quantum Monte Carlo (QMC) methods. While most QMC studies have settled on the use of familiar non-local (NL) pseudopotentials with additional localization approximations, these approaches have been shown to result in moderate residual errors for some classes of molecular and solid state applications. Here, we revisit an idea proposed early in the history of QMC ECPs that does not require localization approximations, namely, a differential class of potentials referred to as pseudo-Hamiltonians. We propose to hybridize NL potentials and pseudo-Hamiltonians to reduce residual non-locality of existing potentials. We derive an approach to recast pseudopotentials for 3d elements as hybrid pseudo-Hamiltonians with optimally reduced NL energy. We demonstrate the fidelity of the hybrid potentials by studying atomic ionization potentials of Ti and Fe and the binding properties of TiO and FeO molecules with diffusion Monte Carlo (DMC). We show that localization errors have been reduced relative to potentials with the same NL channels for Sc–Zn by considering the DMC energy change with respect to the choice of approximate localization. While localization error decreases proportionate to the reduced NL energy without a Jastrow, with a Jastrow, the degree of reduction decreases at higher filling of the d-shell. Our results suggest that a subset of existing ECPs may be recast in this hybrid form to reduce the DMC localization error. They also point to the prospect of further reducing this error by generating ECPs within this hybrid form from the start.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Validation of the TOPAS Monte Carlo toolkit for HDR brachytherapy simulations

The goal of this work is to validate the user-friendly Geant4-based Monte Carlo toolkit TOol for PArticle Simulation (TOPAS) for brachytherapy applications. Brachytherapy simulations performed with TOPAS were systematically compared with published TG-186 reference data. The photon emission energy spectrum, the air-kerma strength, and the dose-rate constant of the model-based dose calculation algorithm (MBDCA)-WG generic Ir-192 source were extracted. For dose calculations, a track-length estimator was implemented. Additionally, the four Joint AAPM/ESTRO/ABG MBDCA-WG test cases were evaluated through histograms of the local and global dose difference volumes. A prostate, a palliative lung, and a breast case were simulated. For each case, the dose ratio map, the histogram of the global dose difference volume, and cumulative dose-volume histograms were calculated. The air-kerma strength was (9.772 ± 0.001) × 10 -8 U Bq -1 (within 0.3% of the reference value). The dose-rate constant was 1.1107 ± 0.0005 cGy h -1 U -1 (within 0.01% of the reference value). For all cases, at least 96.9% of voxels had a local dose difference within [-1%, 1%] and at least 99.9% of voxels had a global dose difference within [-0.1%, 0.1%]. The implemented track-length estimator scorer was more efficient than the default analog dose scorer by a factor of 237. For all clinical cases, at least 97.5% of voxels had a global dose difference within [-1%, 1%]. Dose-volume histograms were consistent with the reference data. TOPAS was validated for high-dose-rate brachytherapy simulations following the TG-186 recommended approach for MBDCAs. Built on top of Geant4, TOPAS provides broad access to a state-of-the-art Monte Carlo code for brachytherapy simulations.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation

The combination of neural networks and quantum Monte Carlo methods has arisen as a promising path forward for highly accurate electronic structure calculations. Previous proposals have combined equivariant neural network layers with a final antisymmetric layer in order to satisfy the antisymmetry requirements of the electronic wavefunction. However, to date it is unclear if one can represent antisymmetric functions of physical interest, and it is difficult to precisely measure the expressiveness of the antisymmetric layer. Here, this work attempts to address this problem by introducing explicitly antisymmetrized universal neural network layers. This approach has a computational cost which increases factorially with respect to the system size, but we are nonetheless able to apply it to small systems to better understand how the structure of the antisymmetric layer affects its performance. We first introduce a generic antisymmetric (GA) neural network layer, which we use to replace the entire antisymmetric layer of the highly accurate ansatz known as the FermiNet. We demonstrate that the resulting FermiNet-GA architecture can yield effectively the exact ground state energy for small atoms and molecules. We then consider a factorized antisymmetric (FA) layer which more directly generalizes the FermiNet by replacing the products of determinants with products of antisymmetrized neural networks. We find, interestingly, that the resulting FermiNet-FA architecture does not significantly outperform the FermiNet. This strongly suggests that the sum of products of antisymmetries is a key limiting aspect of the FermiNet architecture. To explore this further, we investigate a slight modification of the FermiNet, called the full determinant mode, which replaces each product of determinants with a single combined determinant. We find that the full single-determinant FermiNet closes a large part of the gap between the standard single-determinant FermiNet and FermiNet-GA on small atomic and molecular problems. Surprisingly, on the nitrogen molecule at a dissociating bond length of 4.0 Bohr, the full single-determinant FermiNet can outperform the largest standard FermiNet calculation with 64 determinants.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Using Importance Sampling Monte Carlo to Analyze Aircraft Takeoff and Landing

Aircraft have achieved high levels of reliability, so the probability of undesirable dynamics is very low. The low probability of a bad takeoff or landing challenges nondeterministic methods to quantify the uncertainty of these improbable events. In the present work, a Monte Carlo method is defined to more effectively quantify these unlikely events that is suitable for uncertainty analysis of a mature design with many uncertainty parameters. The proposed Monte Carlo method has been applied to the takeoff and landing of the X-59 Quiet SuperSonic Technology (QueSST). Takeoff and landing simulation profiles were defined using a combination of industry standards and piloted simulation experience. The proposed method is shown to be able to quantify events with significantly fewer samples than would be required with conventional Monte Carlo. These results improve understanding of the sensitivity of the takeoff and landing dynamics to inform further studies and test planning.

Jeffrey Ouellette↗

NASA NTRSDate not supplied

Using Importance Sampling Monte Carlo to Analyze Aircraft Takeoff and Landing

Jeffrey Ouellette↗

NASA NTRS2022

Parallel Grand-Canonical Monte Carlo (ParaGrandMC) User’s Manual Version 2.0

This manual describes the commands and command line options for the Parallel Grand Canonical Monte Carlo version 2.0 (ParaGrandMC.2.0) simulation code. This is a highly scalable parallel FORTRAN 2003 code for simulating the thermodynamic evolution of materials at the atomic level, and predicting their thermodynamic state, phase diagram, chemical composition and mechanical properties. The code is specifically designed to simulate multi-component alloy systems, predict solid-state phase transformations such as austenite-martensite transformations, precipitate formation, recrystallization, capillary effects at interfaces, surface absorption, etc., which can aid the design of novel metallic alloys. While the software is mainly tailored for modeling metal alloys, it can also be used for other types of solid-state systems, and to some degree for liquid or gaseous systems, including multiphase systems forming solid-liquid-gas interfaces. In addition to performing Monte Carlo (MC) simulations, the code can also perform Molecular Dynamics (MD) and Langevin Dynamics (LD) simulations, which can be combined and interchanged with MC for faster and more efficient system evolution. A detailed description of the MC part of the code is provided in the NASA ParaGrandMC report: NASA/CR–2016-219202; http://www.sti.nasa.gov.

High performance computing↗

DOE OSTI2022

A High-Performance Design for Hierarchical Parallelism in the QMCPACK Monte Carlo code

We introduce a new high-performance design for parallelism within the Quantum Monte Carlo code QMCPACK. We demonstrate that the new design is better able to exploit the hierarchical parallelism of heterogeneous architectures compared to the previous GPU implementation. The new version is able to achieve higher GPU occupancy via the new concept of crowds of Monte Carlo walkers, and by enabling more host CPU threads to effectively offload to the GPU. The higher performance is expected to be achieved independent of the underlying hardware, significantly improving developer productivity and reducing code maintenance costs. Scientific productivity is also improved with full support for fallback to CPU execution when GPU implementations are not available or CPU execution is more optimal.

Luo, Ye↗

NASA NTRS1980

Methods for Monte Carlo simulation of the exospheres of the moon and Mercury

A general form of the integral equation of exospheric transport on moon-like bodies is derived in a form that permits arbitrary specification of time varying physical processes affecting atom creation and annihilation, atom-regolith collisions, adsorption and desorption, and nonplanetocentric acceleration. Because these processes usually defy analytic representation, the Monte Carlo method of solution of the transport equation, the only viable alternative, is described in detail, with separate discussions of the methods of specification of physical processes as probabalistic functions. Proof of the validity of the Monte Carlo exosphere simulation method is provided in the form of a comparison of analytic and Monte Carlo solutions to three classical, and analytically tractable, exosphere problems. One of the key phenomena in moonlike exosphere simulations, the distribution of velocities of the atoms leaving a regolith, depends mainly on the nature of collisions of free atoms with rocks. It is shown that on the moon and Mercury, elastic collisions of helium atoms with a Maxwellian distribution of vibrating, bound atoms produce a nearly Maxwellian distribution of helium velocities, despite the absence of speeds in excess of escape in the impinging helium velocity distribution.

Hodges, R. R., Jr.↗

NASA NTRS1971

Computer simulation of supersonic rarefied gas flow in the transition region, about a spherical probe; a Monte Carlo approach with application to rocket-borne ion probe experiments

This report describes a Monte Carlo simulation of transition flow around a sphere. Conditions for the simulation correspond to neutral monatomic molecules at two altitudes (70 and 75 km) in the D region of the ionosphere. Results are presented in the form of density contours, velocity vector plots and density, velocity and temperature profiles for the two altitudes. Contours and density profiles are related to independent Monte Carlo and experimental studies, and drag coefficients are calculated and compared with available experimental data. The small computer used is a PDP-15 with 16 K of core, and a typical run for 75 km requires five iterations, each taking five hours. The results are recorded on DECTAPE to be printed when required, and the program provides error estimates for any flow field parameter.

Horton, B. E.↗

DOE OSTI2023

Prediction and uncertainty quantification of shale well performance using multifidelity Monte Carlo

Uncertainty quantification is an integral component of reservoir management, especially considering the inherent uncertainty in subsurface systems. While a standard practice to estimate the uncertainty, Monte Carlo (MC) simulation is computationally intense when the sampling population comprises high-fidelity simulations. Alternatively, the Multi-fidelity Monte Carlo (MFMC) simulation overcomes this computational intensity by integrating low- and high-fidelity simulations. Our goal is to minimize the number of expensive high-fidelity simulations while maintaining accuracy and using numerous fast and cheap low-fidelity simulations to efficiently sample to input parameter space of interest. We selected gas production from unconventional wells to demonstrate the potential speedups and accuracy of the MFMC approach. The model fidelity usually determines the trade-off between accuracy and efficiency. While the high-fidelity model is more accurate, the low-fidelity model is more efficient. Our high-fidelity simulation includes reservoir simulations of a hydraulically fractured well. On the other hand, our low-fidelity model comprises the parallel-plate flow model. We used differential programming to efficiently solve the 1D flow model, where automatic differentiation is used to efficiently compute the gradients. We matched the production profile of high-fidelity simulations with our low-fidelity simulations. Then, we used a support vector regression to map the high- and low-fidelity input parameters. The mapping function is essential to tune the low-dimensional parameter space of the low-fidelity model to the high-dimensional parameter space of the high-fidelity model. We found that we can use a combination of 9 high fidelity and 10,000 low fidelity simulations to efficiently and accurately simulate pressure management. This method is at least two orders of magnitude faster than only using high-fidelity simulations. Finally, from a broader perspective, MFMC could efficiently estimate the uncertainty of various systems and models, integrating low- and high-fidelity models.

04 OIL SHALES AND TAR SANDS↗

DOE OSTI2024

Enhanced Twist-Averaging Technique for Magnetic Metals: Applications Using Quantum Monte Carlo

In this study, we propose an improved twist-averaging (TA) scheme for quantum Monte Carlo methods that use converged Kohn–Sham or Hartree–Fock orbitals as the reference. This TA technique is tailored to sample the Brillouin zone of magnetic metals, although it naturally extends to nonmagnetic (NM) conducting systems. The proposed scheme aims to reproduce the reference magnetization and achieves charge neutrality by construction, thus avoiding the large energy fluctuations and the postprocessing needed to correct the energies. It shows the most robust convergence of total energy and magnetism to the thermodynamic limit (TDL) when compared to four other TA schemes. Diffusion Monte Carlo applications are shown on NM Al and ferromagnetic α-Fe. The cohesive energy of Al in the TDL shows an excellent agreement with the experimental result. Furthermore, the magnetic moments in α-Fe exhibit rapid convergence with an increasing number of twists.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗