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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Bayesian projection pursuit regression

In projection pursuit regression (PPR), a univariate response variable is approximated by the sum of $M$ “ridge functions,” which are flexible functions of one-dimensional projections of a multivariate input variable. Traditionally, optimization routines are used to choose the projection directions and ridge functions via a sequential algorithm, and $M$ is typically chosen via cross-validation. Here, we introduce a novel Bayesian version of PPR, which has the benefit of accurate uncertainty quantification. To infer appropriate projection directions and ridge functions, we apply novel adaptations of methods used for the single ridge function case ($M$=1), called the Bayesian Single Index Model; and use a Reversible Jump Markov chain Monte Carlo algorithm to infer the number of ridge functions $M$. We evaluate the predictive ability of our model in 20 simulated scenarios and for 23 real datasets, in a bake-off against an array of state-of-the-art regression methods. Finally, we generalize this methodology and demonstrate the ability to accurately model multivariate response variables. Its effective performance indicates that Bayesian Projection Pursuit Regression is a valuable addition to the existing regression toolbox.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Influence of temporal variations in plasma conditions on the electric potential near self-organized dust chains

Self-organization of dust grains into stable filamentary dust structures (or “chains”) largely depends on dynamic interactions between individual charged dust grains and complex electric potential arising from the distribution of charges within a local plasma environment. Recent studies have shown that the positive column of the gas discharge plasma in the Plasmakristall-4 (PK-4) experiment at the International Space Station supports the presence of fast-moving ionization waves, which lead to variations of plasma parameters by up to an order of magnitude from the average background values. The highly variable environment resulting from ionization waves may have interesting implications for the dynamics and self-organization of dust particles, particularly concerning the formation and stability of dust chains. Here, we investigate the electric potential surrounding dust chains in the PK-4 experiment by employing a molecular dynamics model of the dust and ions with boundary conditions supplied by a particle-in-cell with Monte Carlo collision simulation of the ionization waves. The model is used to examine the effects of the plasma conditions within different regions of the ionization wave and compare the resulting dust structure to that obtained by employing the time-averaged plasma conditions. Here, the comparison between simulated dust chains and experimental data from the PK-4 experiment shows that the time-averaged plasma conditions do not accurately reproduce observed results for dust behavior, indicating that more careful treatment of plasma conditions in the presence of ionization waves is required. It is further shown that commonly used analytic forms of the electric potential do not accurately describe the electric potential near charged dust grains under these plasma conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Comparative study of the superconductivity in the Holstein and optical Su-Schrieffer-Heeger models

Theoretical studies suggest that Su-Schrieffer-Heeger-like electron-phonon (e-ph) interactions can mediate high-temperature bipolaronic superconductivity that is robust against repulsive electron-electron interactions. Here we present a comparative analysis of the pairing and competing charge/bond correlations in the two-dimensional Holstein and optical Su-Schrieffer-Heeger (SSH) models using numerically exact determinant quantum Monte Carlo. We find that the SSH interactions support light bipolarons and strong superconducting correlations out to relatively large values of the e-ph coupling λ and densities near half-filling, while the Holstein interaction does not due to the formation of heavy bipolarons and competing charge-density-wave order. We further find that the Holstein and SSH models have comparable pairing correlations in the weak coupling limit for carrier concentrations < n > <<1, where competing orders and polaronic effects are absent. These results support the proposal that SSH (bi)polarons can support superconductivity to larger values of λ in comparison to the Holstein polaron, but that the resulting T c gains are small in the weak coupling limit. We also find that the SSH model's pairing correlations are suppressed after including a weak on-site Hubbard repulsion. Furthermore, these results have important implications for identifying and engineering bipolaronic superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2013

Estimating the Properties of Hard X-Ray Solar Flares by Constraining Model Parameters

We wish to better constrain the properties of solar flares by exploring how parameterized models of solar flares interact with uncertainty estimation methods. We compare four different methods of calculating uncertainty estimates in fitting parameterized models to Ramaty High Energy Solar Spectroscopic Imager X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method is also based on the difference between the data and the model, but instead uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra are modeled: one from the Geostationary Operational Environmental Satellite X1.3 class flare of 2005 January 19, and the other from the X4.8 flare of 2002 July 23.We find that the four methods give approximately the same uncertainty estimates for the 2005 January 19 spectral fit parameters, but lead to very different uncertainty estimates for the 2002 July 23 spectral fit. This is because each method implements different analyses of the hypersurface, yielding method-dependent results that can differ greatly depending on the shape of the hypersurface. The hypersurface arising from the 2005 January 19 analysis is consistent with a normal distribution; therefore, the assumptions behind the three non- Bayesian uncertainty estimation methods are satisfied and similar estimates are found. The 2002 July 23 analysis shows that the hypersurface is not consistent with a normal distribution, indicating that the assumptions behind the three non-Bayesian uncertainty estimation methods are not satisfied, leading to differing estimates of the uncertainty. We find that the shape of the hypersurface is crucial in understanding the output from each uncertainty estimation technique, and that a crucial factor determining the shape of hypersurface is the location of the low-energy cutoff relative to energies where the thermal emission dominates. The Bayesian/MCMC approach also allows us to provide detailed information on probable values of the low-energy cutoff, Ec, a crucial parameter in defining the energy content of the flare-accelerated electrons. We show that for the 2002 July 23 flare data, there is a 95% probability that Ec lies below approximately 40 keV, and a 68% probability that it lies in the range 7-36 keV. Further, the low-energy cutoff is more likely to be in the range 25-35 keV than in any other 10 keV wide energy range. The low-energy cutoff for the 2005 January 19 flare is more tightly constrained to 107 +/- 4 keV with 68% probability.

X-rays↗
DOE OSTI2023

Modeling Enhancements and Demonstration of Shift Capabilities for PBRs and MSRs

This technical report documents the modeling enhancements and demonstrations with the Shift Monte Carlo (MC) code targeted at pebble-bed reactors (PBRs) and molten salt reactors (MSRs) under the US Department of Energy (DOE) Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in fiscal year (FY) 2023. The work performed included several enhancements, such as improvements for multigroup cross section generation, a new eigenvalue mode considering only prompt fission neutrons, and enhancements to the Titan frontend for Shift to allow for new geometry types and tally functionality. Additionally, new PBR equilibrium core search reference calculations were generated with Shift and compared to Serpent calculations provided by Idaho National Laboratory (INL). These enhancements provide a robust foundation for applying Shift for both reference and two-step neutronics analysis for advanced reactor simulation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Forward Modeling of Gamma Reaction History Signatures From Anticipated Deuterium-Tritium Filled MagLIF Implosions on Sandia’s Z-Machine

Nuclear reaction history measurements provide a bang time and burn width of Inertial Confinement Fusion (ICF) implosions and are essential for understanding implosion performance to constrain ICF capsule design. When fusion fuel contains Deuterium (D) and Tritium (T) gas, reaction history is informed by measuring the 16.75 MeV gamma rays generated from the D(T,γ) 5 He reaction. Such DT based reaction history measurements have not been made on the Magnetized Laser Inertial Fusion (MagLIF) platform on Sandia’s Z-Machine due to the lack of Tritium being used. The recent development of ICF implosions with tritiated fuel will open the possibility of measuring the gamma reaction history on the Z-Machine. A forward model of the Gamma Reaction History diagnostic on Z (GRH-Z) has been developed using the MCNP6.3 (Monte-Carlo N-Particle) radiation transport code. The model included the Z-Machine geometry of interest to characterize the impact of neutron induced gamma rays on the DT reaction history measurements. In addition, the impulse response functions of the GRH-Z diagnostic to understand the temporal response of the detector, and the minimum yields required to make a reaction history measurement were calculated. This approach also predicted that with T 2 gas doping of MagLIF implosions a reaction history may be made for high performance shots >8e12-2.4e13 depending on the chosen threshold for the detector, with a maximum signal to background ratio of 25%. It was found that for long duration ICF implosions that additional collimation will be needed to prevent the neutron induced gamma rays from modifying the shape of the measured DT reaction history curve.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1994

Radiative interactions in multi-dimensional chemically reacting flows using Monte Carlo simulations

The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. The amount and transfer of the emitted radiative energy in a finite volume element within a medium are considered in an exact manner. The spectral correlation between transmittances of two different segments of the same path in a medium makes the statistical relationship different from the conventional relationship, which only provides the non-correlated results for nongray methods is discussed. Validation of the Monte Carlo formulations is conducted by comparing results of this method of other solutions. In order to further establish the validity of the MCM, a relatively simple problem of radiative interactions in laminar parallel plate flows is considered. One-dimensional correlated Monte Carlo formulations are applied to investigate radiative heat transfer. The nongray Monte Carlo solutions are also obtained for the same problem and they also essentially match the available analytical solutions. the exact correlated and non-correlated Monte Carlo formulations are very complicated for multi-dimensional systems. However, by introducing the assumption of an infinitesimal volume element, the approximate correlated and non-correlated formulations are obtained which are much simpler than the exact formulations. Consideration of different problems and comparison of different solutions reveal that the approximate and exact correlated solutions agree very well, and so do the approximate and exact non-correlated solutions. However, the two non-correlated solutions have no physical meaning because they significantly differ from the correlated solutions. An accurate prediction of radiative heat transfer in any nongray and multi-dimensional system is possible by using the approximate correlated formulations. Radiative interactions are investigated in chemically reacting compressible flows of premixed hydrogen and air in an expanding nozzle. The governing equations are based on the fully elliptic Navier-Stokes equations. Chemical reaction mechanisms were described by a finite rate chemistry model. The correlated Monte Carlo method developed earlier was employed to simulate multi-dimensional radiative heat transfer. Results obtained demonstrate that radiative effects on the flowfield are minimal but radiative effects on the wall heat transfer are significant. Extensive parametric studies are conducted to investigate the effects of equivalence ratio, wall temperature, inlet flow temperature, and nozzle size on the radiative and conductive wall fluxes.

Liu, Jiwen↗
DOE OSTI2022

Behavioral and Population Data-Driven Distribution System Load Modeling

Distribution system residential load modeling and analysis for different geographic areas within a utility or an independent system operator territory are critical for enabling small-scale, aggregated distributed energy resources to participate in grid services under Federal Energy Regulatory Commission Order No. 2222 [1]. In this study, we develop a methodology of modeling residential load profiles in different geographic areas with a focus on human behavior impact. First, we construct a behavior-based load profile model leveraging state-of-the-art appliance models. We simulate human activity and occupancy using Markov chain Monte Carlo methods calibrated with the American Time Use Survey data set. Second, we link our model with cleaned Current Population Survey data from the U.S. Census Bureau. Finally, we populate two sets of 500 households using California and Texas census data, respectively, to perform an initial analysis of the load in different geographic areas with various group features (e.g., different income levels). To distinguish the effect of population behavior differences on aggregated load, we simulate load profiles for both sets assuming fixed physical household parameters and weather data. Analysis shows that average daily load profiles vary significantly by income and income dependency varies by locality.

American Time Use Survey↗
DOE OSTI2025

The Fluid Dynamics Uncertainty Quantification Challenge Problem: XFOIL vs. MFOIL

Uncertainty quantification (UQ) has become more critical in aerospace engineering due to the growing dependence on computational tools for design optimization and performance analyses of aerospace vehicles. Even though the significance of UQ in assessing the credibility of computational analyses is well recognized, its costs and complexity impede its integration into standard practices, particularly in computational fluid dynamics (CFD) and other fluid analyses. This paper presents a UQ study for low-fidelity computational aerodynamics analyses with XFOIL and mfoil (i.e., the MATLAB version of XFOIL with several implementation modifications); these tools are utilized widely in both research and education. The main contributions of this paper are as follows: 1) improved precision in quantifying the uncertainty of the baseline Monte Carlo results used to benchmark surrogate modeling techniques for UQ, 2) quantification of the effect of the implementation differences between XFOIL and mfoil on solution quantities of interest (QoIs), such as lift and pitching moment coefficients, and 3) development of an open-source UQ library for use with XFOIL and mfoil, which has educational values and helps promote UQ for fluid analyses with aerospace applications. Results and discussions revolve around cases 1-4 of the challenge problem posed by the AIAA Fluid Dynamics Technical Committee’s Uncertainty Quantification Discussion Group (UQDG). In case 3, this work employs CFDverify, an open-source solution verification software, to quantify the discretization error and evaluate the extrapolated QoIs based on the grid convergence index (GCI). This UQ study differentiates itself from previous studies in the rigor of handling baseline Monte Carlo uncertainty and in including mfoil, which is a more accessible alternative to XFOIL. Finally, despite the growing computing power, low-fidelity computational tools remain valuable, such as for aerodynamic shape optimization at Mach numbers below 0.65 and low-to-mid Reynolds numbers.

Lay, Aidan S [University of Tennessee, Knoxville (↗
NASA NTRS1973

Monte Carlo calculations of lunar regolith thickness distributions.

It is pointed out that none of the existing models of lunar regolith evolution take into account the relationship between regolith thickness, crater shape, and volume of debris ejected. The results of a Monte Carlo computer simulation of regolith evolution are presented. The simulation was designed to consider the full effect of the buffering regolith through calculation of the amount of debris produced by any given crater as a function of the amount of debris present at the site of the crater at the time of crater formation. The method is essentially an improved version of the Oberbeck and Quaide (1968) model.

Oberbeck, V. R.↗
NASA NTRSDate not supplied

Launch Vehicle Design and Requirements Verification Using Statistical Methods

- This presentation applies statistics to launch vehicle design, but the methods may be used for other engineering applications - Vehicle Models: What do we know when? How to separate parameters for making Monte Carlo runs - Known when assembling the vehicle but not during design - Known prior to committing to flight - Unknown at lift off - How do we correctly model the vehicle during the design phases? - Number of Monte Carlo samples - Requirements success - Design parameter values

Monte Carlo↗
NASA NTRS2014

Kinematic Modeling of Separation Compression for Paired Approaches to Closely-Spaced Parallel Runways

In a simultaneous paired approach to closely-spaced parallel runways, a pair of aircraft flies in close proximity on parallel approach paths. The longitudinal separation between the aircraft must be maintained within a range that avoids wake encounters and, if one of the aircraft blunders, avoids collision. To increase operational availability, the approach procedure must accommodate a mixture of aircraft sizes and, consequently, approach speeds. In these procedures, the slower aircraft is placed in the lead position. The faster aircraft maintains separation from the slow aircraft in a dependent operation until final approach and flies independently afterward. Due to the higher approach speed of the fast aircraft, longitudinal separation will decrease during final approach. Therefore, the fast aircraft must position itself before the final approach so that it will remain within the safe range of separation as separation decreases. Given the approach geometry and speed schedule for each aircraft, one can use kinematics to estimate the separation loss between a pair of aircraft. A kinematic model can complement fast-time Monte-Carlo simulations of the approach by enabling a tailored reduction in the variation of starting position for the fast aircraft. One could also implement the kinematic model in ground-based or on-board decision support tools to compute the optimal initial separation for a given pair of aircraft. To better match the auto-coupled flight of real aircraft, the paper derives a kinematic model where the speed schedule is flown using equivalent airspeed. The predicted time of flight using the equivalent airspeed kinematic model compares well against a high-fidelity aircraft simulation performing the same approach. This model also demonstrates a modest increase in the predicted loss of separation when contrasted against a kinematic model that assumes the scheduled speed is true airspeed.

Madden, Michael M.↗
DOE OSTI2026

On the Statistical Uncertainty of Monte Carlo-Calculated Scattering Sensitivities

Sensitivity coefficients calculated with Monte Carlo codes are widely used for nuclear data uncertainty quantification in the modeling and simulation of complex 3D reactor systems. This study systematically compares sensitivity coefficients and associated statistical uncertainties for the multiplication factor and fuel temperature reactivity across multiple Monte Carlo codes (SCALE/KENO, SCALE/Shift, MCNP, and Serpent) using simple models representing light-water reactors and advanced reactor concepts. For multiplication factor sensitivities, statistical uncertainties are generally acceptable, although scattering sensitivities show significantly larger statistical uncertainties than, for example, fission and capture reactions. Fuel temperature reactivity sensitivities show significantly larger statistical uncertainties across all reactions. Elastic scattering sensitivities are the most problematic: all Monte Carlo codes fail to resolve energy-dependent coefficients, and they produce dramatically different energy-collapsed values. Critically, the use of these sensitivity coefficients in nuclear data uncertainty propagation leads to reduced statistical uncertainties in individual uncertainty contributions. This can lead to the masking of unusable sensitivity coefficients and producing misleading uncertainty results. The findings of this study show that new or enhanced methods are needed to improve Monte Carlo elastic scattering sensitivity calculations. Additionally, this study shows the relevance of verifying sensitivity coefficients through direct perturbation calculations for individual nuclide reactions, instead of only for total cross sections as commonly done.

Bostelmann, Rike [ORNL] (ORCID:0000000165968088)↗
DOE OSTI2022

TAUOLA update for decay channels with e + e – pairs in the final state

With the arrival of high luminosity B-factories like the Belle II experiment, τ decay measurements have become more precise than ever, allowing rarer processes to be explored, and finer details of τ decays to be studied. These are important to understand the spectrum of intermediate particles produced in τ decays. Therefore Monte Carlo generators, like the TAUOLA program, have to facilitate precision analysis as well as confront new models that constantly emerge with the availability of high statistics experimental data. New decay channels and models may lead to large variation of matrix elements size within the available phase space, as in the case when e + e - pairs are present in final state. It requires appropriate presampler of the phase space generator and a proper documentation to help users introduce their own models. While releasing a new update, it is important for the TAUOLA Monte Carlo library to maintain the general structure of the previous versions to preserve backward compatibility. The aim is to minimize changes from the user perspective. Finally, this paper presents a demonstration of new models implementation facilitated by the current update.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1993

The power spectrum of IRAS galaxies

A technique is presented for removing the power spectrum in flux-limited galaxy catalogs is presented and tested using Monte Carlo simulations of the IRAS survey based on N-body realizations of a standard CDM universe. The technique is applied to the 1.2 Jy IRAS catalog, comparing the resulting IRAS power spectrum with previous results in the literature. A qualitative comparison of the IRAS power spectrum with various theoretical models is shown. An extensive set of Monte Carlo experiments designed to test quantitatively the validity of standard CDM on large scales is described.

Fisher, Karl B.↗
NASA NTRS1977

A model for simulating random atmospheres as a function of latitude, season, and time

An empirical stochastic computer model was developed with the capability of generating random thermodynamic profiles of the atmosphere below an altitude of 99 km which are characteristic of any given season, latitude, and time of day. Samples of temperature, density, and pressure profiles generated by the model are statistically similar to measured profiles in a data base of over 6000 rocket and high-altitude atmospheric soundings; that is, means and standard deviations of modeled profiles and their vertical gradients are in close agreement with data. Model-generated samples can be used for Monte Carlo simulations of aircraft or spacecraft trajectories to predict or account for the effects on a vehicle's performance of atmospheric variability. Other potential uses for the model are in simulating pollutant dispersion patterns, variations in sound propagation, and other phenomena which are dependent on atmospheric properties, and in developing data-reduction software for satellite monitoring systems.

Campbell, J. W.↗
NASA NTRS2001

Free Vibration of Uncertain Unsymmetrically Laminated Beams

Monte Carlo Simulation and Stochastic FEA are used to predict randomness in the free vibration response of thin unsymmetrically laminated beams. For the present study, it is assumed that randomness in the response is only caused by uncertainties in the ply orientations. The ply orientations may become random or uncertain during the manufacturing process. A new 16-dof beam element, based on the first-order shear deformation beam theory, is used to study the stochastic nature of the natural frequencies. Using variational principles, the element stiffness matrix and mass matrix are obtained through analytical integration. Using a random sequence a large data set is generated, containing possible random ply-orientations. This data is assumed to be symmetric. The stochastic-based finite element model for free vibrations predicts the relation between the randomness in fundamental natural frequencies and the randomness in ply-orientation. The sensitivity derivatives are calculated numerically through an exact formulation. The squared fundamental natural frequencies are expressed in terms of deterministic and probabilistic quantities, allowing to determine how sensitive they are to variations in ply angles. The predicted mean-valued fundamental natural frequency squared and the variance of the present model are in good agreement with Monte Carlo Simulation. Results, also, show that variations between plus or minus 5 degrees in ply-angles can affect free vibration response of unsymmetrically and symmetrically laminated beams.

Kapania, Rakesh K.↗
DOE OSTI2022

Bilayer Hubbard model: Analysis based on the fermionic sign problem

The bilayer Hubbard model describes the antiferromagnet to spin singlet transition and, potentially, aspects of the physics of unconventional superconductors. Despite these important applications, significant aspects of its phase diagram in the interplane hopping t ⊥ versus on-site interaction U parameter space, at half filling, are largely in disagreement. Here we provide an analysis making use of the average sign of weights over the course of the importance sampling in quantum Monte Carlo simulations to resolve several central open questions. Specifically, this metric of the weights clarifies the finite-sized metallic regimes at small U. Furthermore, at strong interactions, it points to the existence of a crossover from a correlated to uncorrelated band insulator not yet explored in a variety of existing, unbiased numerical methods. Our paper demonstrates the versatility of using properties of the weights in quantum Monte Carlo simulations to reveal important physical characteristics of the models under study.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗