A Monte Carlo Background Covariance Localization Method for an Ensemble–Variational Assimilation System
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Ivo Pasmans↗
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Results for “Monte Carlo method”
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Investigation of Doppler Broadening Methods Within the Shift Monte Carlo Radiation Transport Code
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Evans, Thomas↗
Validation of Linear Covariance Techniques for Mars Entry, Descent, and Landing Guidance and Navigation Performance Analysis
Current Monte Carlo-based uncertainty analysis methods may require significant computational resources to evaluate the performance of a closed-loop guidance, navigation, and control system. An attractive alternative, particularly during the preliminary and conceptual design phase, is to use linear covariance analysis, which can provide the same statistical information as Monte Carlo methods at a fraction of the computational load. Linear covariance has already been demonstrated in various spaceflight regimes, but only recently has it been applied to atmospheric flight. In this study, a 6-degree-of-freedom formulation of both a linear covariance and Monte Carlo analysis tools are utilized for a Mars entry, descent, and landing scenario which capture both atmospheric and powered flight phases to support precision landing. Comparison of the performance results shows close agreement between the linear covariance and traditional Monte Carlo methods when incorporating an assortment of guidance algorithms and processing a variety of inertial and relative sensor measurements onboard the lander's navigation filter.
James W. Williams↗
Some Developments of the Equilibrium Particle Simulation Method for the Direct Simulation of Compressible Flows
The direct simulation Monte Carlo (DSMC) method is the established technique for the simulation of rarefied gas flows. In some flows of engineering interest, such as occur for aero-braking spacecraft in the upper atmosphere, DSMC can become prohibitively expensive in CPU time because some regions of the flow, particularly on the windward side of blunt bodies, become collision dominated. As an alternative to using a hybrid DSMC and continuum gas solver (Euler or Navier-Stokes solver) this work is aimed at making the particle simulation method efficient in the high density regions of the flow. A high density, infinite collision rate limit of DSMC, the Equilibrium Particle Simulation method (EPSM) was proposed some 15 years ago. EPSM is developed here for the flow of a gas consisting of many different species of molecules and is shown to be computationally efficient (compared to DSMC) for high collision rate flows. It thus offers great potential as part of a hybrid DSMC/EPSM code which could handle flows in the transition regime between rarefied gas flows and fully continuum flows. As a first step towards this goal a pure EPSM code is described. The next step of combining DSMC and EPSM is not attempted here but should be straightforward. EPSM and DSMC are applied to Taylor-Couette flow with Kn = 0.02 and 0.0133 and S(omega) = 3). Toroidal vortices develop for both methods but some differences are found, as might be expected for the given flow conditions. EPSM appears to be less sensitive to the sequence of random numbers used in the simulation than is DSMC and may also be more dissipative. The question of the origin and the magnitude of the dissipation in EPSM is addressed. It is suggested that this analysis is also relevant to DSMC when the usual accuracy requirements on the cell size and decoupling time step are relaxed in the interests of computational efficiency.
Macrossan, M. N.↗
Probabilistic Analysis of a Composite Crew Module
An approach for conducting reliability-based analysis (RBA) of a Composite Crew Module (CCM) is presented. The goal is to identify and quantify the benefits of probabilistic design methods for the CCM and future space vehicles. The coarse finite element model from a previous NASA Engineering and Safety Center (NESC) project is used as the baseline deterministic analysis model to evaluate the performance of the CCM using a strength-based failure index. The first step in the probabilistic analysis process is the determination of the uncertainty distributions for key parameters in the model. Analytical data from water landing simulations are used to develop an uncertainty distribution, but such data were unavailable for other load cases. The uncertainty distributions for the other load scale factors and the strength allowables are generated based on assumed coefficients of variation. Probability of first-ply failure is estimated using three methods: the first order reliability method (FORM), Monte Carlo simulation, and conditional sampling. Results for the three methods were consistent. The reliability is shown to be driven by first ply failure in one region of the CCM at the high altitude abort load set. The final predicted probability of failure is on the order of 10-11 due to the conservative nature of the factors of safety on the deterministic loads.
FROM↗
Independent pixel and Monte Carlo estimates of stratocumulus albedo
Monte Carlo radiative transfer methods are employed here to estimate the plane-parallel albedo bias for marine stratocumulus clouds. This is the bias in estimates of the mesoscale-average albedo, which arises from the assumption that cloud liquid water is uniformly distributed. The authors compare such estimates with those based on a more realistic distribution generated from a fractal model of marine stratocumulus clouds belonging to the class of 'bounded cascade' models. In this model the cloud top and base are fixed, so that all variations in cloud shape are ignored. The model generates random variations in liquid water along a single horizontal direction, forming fractal cloud streets while conserving the total liquid water in the cloud field. The model reproduces the mean, variance, and skewness of the vertically integrated cloud liquid water, as well as its observed wavenumber spectrum, which is approximately a power law. The Monte Carlo method keeps track of the three-dimensional paths solar photons take through the cloud field, using a vectorized implementation of a direct technique. The simplifications in the cloud field studied here allow the computations to be accelerated. The Monte Carlo results are compared to those of the independent pixel approximation, which neglects net horizontal photon transport. Differences between the Monte Carlo and independent pixel estimates of the mesoscale-average albedo are on the order of 1% for conservative scattering, while the plane-parallel bias itself is an order of magnitude larger. As cloud absorption increases, the independent pixel approximation agrees even more closely with the Monte Carlo estimates. This result holds for a wide range of sun angles and aspect ratios. Thus, horizontal photon transport can be safely neglected in estimates of the area-average flux for such cloud models. This result relies on the rapid falloff of the wavenumber spectrum of stratocumulus, which ensures that the smaller-scale variability, where the radiative transfer is more three-dimensional, contributes less to the plane-parallel albedo bias than the larger scales, which are more variable. The lack of significant three-dimensional effects also relies on the assumption of a relatively simple geometry. Even with these assumptions, the independent pixel approximation is accurate only for fluxes averaged over large horizontal areas, many photon mean free paths in diameter, and not for local radiance values, which depend strongly on the interaction between neighboring cloud elements.
Cahalan, Robert F.↗
Scale translation yields insights into gas adsorption under nanoconfinement
This work describes a scale-translating simulation framework to investigate gas adsorption behavior in nanoconfined pores. The framework combines molecular simulations (MSs), equation of state (EoS), and lattice Boltzmann (LB) simulations. MSs reveal the physics of methane adsorption in nano-sized pores, where input values of fugacity coefficients are optimized based on EoS predictions. Then, an LB free-energy model, which incorporates a viral EoS, upscales intermolecular forces and estimates adsorption behavior via a proposed fluid–wall interaction model. Armed with the values of the LB interaction parameter as a function of pressure, the LB model is used to predict fluid behavior in irregular nanopores, and the results are validated against reference MS data. The LB model is then used to study adsorption behavior at a continuum scale in representative organic shale nanopores based on finely characterized Vaca Muerta shale samples. Furthermore, the results show that methane adsorption could significantly increase contained fluids by 10%–25% in pores smaller than 20 nm. However, in larger pores (40 nm to 90 nm), adsorption's impact diminishes to 2%–3%, suggesting sorption's negligible role beyond a 40 nm pore size.
74 ATOMIC AND MOLECULAR PHYSICS↗
Application of the Probabilistic Dynamic Synthesis Method to Realistic Structures
The Probabilistic Dynamic Synthesis method is a technique for obtaining the statistics of a desired response engineering quantity for a structure with non-deterministic parameters. The method uses measured data from modal testing of the structure as the input random variables, rather than more "primitive" quantities like geometry or material variation. This modal information is much more comprehensive and easily measured than the "primitive" information. The probabilistic analysis is carried out using either response surface reliability methods or Monte Carlo simulation. In previous work, the feasibility of the PDS method applied to a simple seven degree-of-freedom spring-mass system was verified. In this paper, extensive issues involved with applying the method to a realistic three-substructure system are examined, and free and forced response analyses are performed. The results from using the method are promising, especially when the lack of alternatives for obtaining quantitative output for probabilistic structures is considered.
Brown, Andrew M.↗
On numerical energy conservation for an implicit particle-in-cell method coupled with a binary Monte-Carlo algorithm for Coulomb collisions
We report conventional particle-in-cell (PIC) methods suffer from enhanced numerical heating (explicit PIC) or cooling (semi-implicit PIC) when coupled with a binary Monte-Carlo algorithm for Coulomb collisions. In this work, a fully-implicit θ-PIC scheme (with adjustable time-biasing parameter 1/2 ≤ θ ≤) is considered. The discrete change in energy of a closed system after a time step for this scheme scales with (1/2 - θ)C θ , where C θ is a positive definite quantity that depends on the frequency spectrum of the energy in the fields. Collisions lead to additional energy in the field fluctuations associated with high-frequency light waves produced by a numerical Bremsstrahlung process, which can result in a large increase in the numerical cooling rate for θ > 1/2. However, for θ = 1/2, energy is exactly conserved. The energy in the field fluctuations on long time scales agrees with that calculated using the equipartition theorem for a classical system in thermodynamic equilibrium.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Characterizing Epistemic Uncertainty for Launch Vehicle Designs
NASA Probabilistic Risk Assessment (PRA) has the task of estimating the aleatory (randomness) and epistemic (lack of knowledge) uncertainty of launch vehicle loss of mission and crew risk and communicating the results. Launch vehicles are complex engineered systems designed with sophisticated subsystems that are built to work together to accomplish mission success. Some of these systems or subsystems are in the form of heritage equipment, while some have never been previously launched. For these cases, characterizing the epistemic uncertainty is of foremost importance, and it is anticipated that the epistemic uncertainty of a modified launch vehicle design versus a design of well understood heritage equipment would be greater. For reasons that will be discussed, standard uncertainty propagation methods using Monte Carlo simulation produce counter intuitive results and significantly underestimate epistemic uncertainty for launch vehicle models. Furthermore, standard PRA methods such as Uncertainty-Importance analyses used to identify components that are significant contributors to uncertainty are rendered obsolete since sensitivity to uncertainty changes are not reflected in propagation of uncertainty using Monte Carlo methods.This paper provides a basis of the uncertainty underestimation for complex systems and especially, due to nuances of launch vehicle logic, for launch vehicles. It then suggests several alternative methods for estimating uncertainty and provides examples of estimation results. Lastly, the paper shows how to implement an Uncertainty-Importance analysis using one alternative approach, describes the results, and suggests ways to reduce epistemic uncertainty by focusing on additional data or testing of selected components.
Novack, Steven D.↗
Nuclear Responses with Neural-Network Quantum States
We introduce a variational Monte Carlo framework that combines neural-network quantum states with the Lorentz integral transform technique to compute the dynamical properties of self-bound quantum many-body systems in continuous Hilbert spaces. While broadly applicable to various quantum systems, including atoms and molecules, in this initial application we focus on the photoabsorption cross section of light nuclei, where benchmarks against numerically exact techniques are available. Our accurate theoretical predictions are complemented by robust uncertainty quantification, enabling meaningful comparisons with experiments. Here, we demonstrate that a relatively simple nuclear Hamiltonian—based on a leading-order pionless EFT expansion and known to accurately reproduce ground-state energies of nuclei with 𝐴 ≤ 40—also provides a reliable description of the photoabsorption cross section.
Ab initio calculations↗
Application of the Probabilistic Dynamic Synthesis Method to the Analysis of a Realistic Structure
The Probabilistic Dynamic Synthesis method is a new technique for obtaining the statistics of a desired response engineering quantity for a structure with non-deterministic parameters. The method uses measured data from modal testing of the structure as the input random variables, rather than more "primitive" quantities like geometry or material variation. This modal information is much more comprehensive and easily measured than the "primitive" information. The probabilistic analysis is carried out using either response surface reliability methods or Monte Carlo simulation. A previous work verified the feasibility of the PDS method on a simple seven degree-of-freedom spring-mass system. In this paper, extensive issues involved with applying the method to a realistic three-substructure system are examined, and free and forced response analyses are performed. The results from using the method are promising, especially when the lack of alternatives for obtaining quantitative output for probabilistic structures is considered.
Brown, Andrew M.↗
Multilevel Monte Carlo Predictions of First Passage Times in Three-Dimensional Discrete Fracture Networks: A Graph-Based Approach
In this paper, we present a method combining multilevel Monte Carlo (MLMC) and a graph-based primary subnetwork identification algorithm to provide estimates of the mean and variance of the distribution of first passage times in fracture media at significantly lower computational cost than standard Monte Carlo (MC) methods. Simulations of solute transport are performed using a discrete fracture network (DFN), and instead of using various grid resolutions for levels in the MLMC, which is standard practice in MLMC, we identify a hierarchy of subnetworks in the DFN based on the shortest topological paths through the network using a graph-based method. While the mean of these ensembles is of critical importance, the variance is also essential in fractured media where uncertainty is an overarching theme, and understanding variability across an ensemble is a requirement for safety assessments. The method provides good estimates of the mean and variance at two orders of magnitude lower computational cost than MC.
54 ENVIRONMENTAL SCIENCES↗
Computational modeling of charge hopping dynamics along a disordered one-dimensional wire with energy gradients in quantum environments
This computational study investigates the effects of energy gradients on charge hopping dynamics along a one-dimensional chain of discrete sites coupled to quantum bath, which is modeled at the level of Pauli master equation (PME). This study also assesses the performance of different approximations for the hopping rates. Three different methods for solving the PME, a fourth order Runge–Kutta method, numerical diagonalization of the rate matrix followed by analytic propagation, and kinetic Monte Carlo simulation method, are tested and confirmed to produce virtually identical values of time dependent mean square displacement, diffusion constant, and mobility. Five different rate expressions, exact numerical evaluation of Fermi’s Golden Rule (FGR) rate, stationary phase interpolation (SPI) approximation, semiclassical approximation, classical Marcus rate, and Miller–Abrahams rate, are tested to help understand the effects of approximations in representing quantum environments in the presence of energy gradients. The results based on direct numerical evaluation of FGR rate exhibit transition from diffusive to non-diffusive behavior with the increase in the gradient and show that the charge transport in the quantum bath is more sensitive to the magnitude of the gradient and the disorder than in the classical bath. Among all the four approximations for the hopping rates, the SPI approximation is confirmed to work best overall. A comparison of two different methods to calculate the mobility identifies drift motion of the population distribution as the major source of non-diffusive behavior and provides more reliable information on the contribution of quantum bath.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Comparison of Generation of Higher-Order Neutron Scattering Cross Sections
The generation of high-order neutron scattering cross sections consistent with high-fidelity simulations remains an area of active research. Popular options include generating cross sections from continuous energy Monte Carlo calculations or generating cross sections from a deterministic neutron transport calculation with high-fidelity tabulated cross sections. Both options present challenges. Monte Carlo simulations can naturally process continuous energy cross section data and allow for the general description of anisotropic neutron scattering given a scattering law. However, Monte Carlo simulations are inherently related to particle weighting and it has been suggested that this may be unacceptable for generating high-order neutron scattering cross sections. Deterministic neutron transport calculations can easily calculate high-order moments of the flux to appropriately calculate higher-order neutron scattering cross sections but are generally limited by discretization of space, energy, and angle. In this work, the trade-offs between generation of high-order neutron scattering cross sections via Monte Carlo and deterministic neutron transport methods are investigated. The methods implemented in the Monte Carlo computer program Serpent and the deterministic fast reactor neutron cross section generator MC2-3 are compared. Cross sections resulting from these methods are used in Rattlesnake, a deterministic neutron transport code developed by Idaho National Laboratory (INL), and results are compared to a reference continuous energy Monte Carlo calculation. Whereas previous work investigating the effects of anisotropic neutron scattering has focused on light water reactor (LWR) simulations, this work focuses on high-order neutron scattering cross sections as they relate to fast reactor simulations. To investigate the consequences of the Serpent and MC2-3 methodologies, a test problem is developed. The test problem is a one-dimensional geometry with fast reactor materials designed to demonstrate deep penetration and exacerbate the effects of high-order neutron scattering. Based on the results of the deep penetration test problem, it is concluded that P3 neutron scattering cross sections are sufficient to describe anisotropic scattering in fast reactor materials. Any neutron scattering of order higher than P3 offers negligible change in the eigenvalue of the test problem. Additionally, it is determined that the methodology as implemented in Serpent is applicable for generating high-order neutron scattering cross sections through at least P3 in fast reactor materials.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Unconventional magnetic field response of the hyperhoneycomb Kitaev magnet β − Li 2 IrO 3
Not Available
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Lagged average forecasting, some operational considerations
The Lagged Average Forecast (LAF) method differs from the Monte Carlo Forecast (MCF) method in the definition of the ensemble of initial states which are used to generate the ensemble of forecasts. The LAF initial states are the current analysis and the forecasts made from previous analyses verifying the current time. Thus the LAF ensemble is composed of forecasts which are made by a regular operational system of numerical weather prediction and the LAF method is therefore operationally attractive. The application of the authors' previous ideas and results to an operational model requires the resolution of what might be called the degrees of freedom problem, i.e., how to obtain a homogeneous sample large enough to calculate stable statistics. It is suggested that this problem may be solved by carefully modeling the required statistics in terms of a small set of parameters and then estimating only these few parameters from the data. It is noted that there may be considerable information in each initial ensemble relating to the predictability of each particular case, and that this information may be incorporated in the model of the statistics.
Hoffman, R. N.↗
Gradient-informed Hamiltonian Monte Carlo for multicomponent CALPHAD model optimization and uncertainty quantification
CALPHAD model parameter optimization is inherently challenging due to non-smooth objective functions, high-dimensional parameter spaces, and the need for uncertainty quantification (UQ). Traditional weighted nonlinear least squares approaches are computationally efficient but local, whereas black-box global optimizers and ensemble Markov Chain Monte Carlo (MCMC) methods provide broader exploration at substantial computational cost. The objective of this work is to combine the global exploration capability of gradient-informed Hamiltonian Monte Carlo – specifically the No-U-Turn Sampler (NUTS) – with local deterministic refinement using BFGS to efficiently optimize multicomponent CALPHAD models with minimal manual intervention. Analytic gradients are computed via the Jansson derivative framework. The methodology is demonstrated on the Cr—Fe binary system and extended to the Cr—Fe—Ni ternary system with 32 degrees of freedom. For Cr—Fe, NUTS achieves comparable or superior optimality relative to ensemble MCMC while requiring over an order-of-magnitude fewer likelihood evaluations. Parameter uncertainties are quantified through NUTS sampling and propagated to thermodynamic observables using local expansion, demonstrating a novel modular approach that combines binary and ternary parameter subsets without requiring global relaxation. These results establish gradient-informed exploration as a scalable strategy for multicomponent CALPHAD optimization and provide a practical route towards efficient higher-order database development with quantified uncertainty.
36 MATERIALS SCIENCE↗