A cache size based timestep limiter for Implicit Monte Carlo
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Implicit Monte Carlo, Algorithms, Computing↗
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Transport in Random Media With Inhomogeneous Mixing Statistics
The Levermore-Pomraning (LP) model has been investigated for use in implicit Monte Carlo (IMC) algorithms to describe thermal photon transport computations in stochastically mixed cells with material energy coupling. For purely absorbing non-emitting materials, the LP-model is known to predict the exact material averaged fluxes when the mixing statistics are Markovian. In the presence of scattering or reemmission, or if the mixing is non-Markovian, the LP-model is approximate and has greatly diminished accuracy for optically thick, highly scattering materials. Nevertheless, the model enables a robust extension of the simple atomic mix approximation to accommodate spatial correlation effects through well characterized parameters such as mean chord lengths. In this work, we construct exact analytical solutions of the LP-equations for piecewise constant spatial variation of the material chord lengths. It is not possible in general to obtain closed form solutions when the chord lengths are continuous functions of space, although we briefly examine special conditions under which this is feasible. However, by allowing an arbitrarily fine spatial segmentation of the medium it is possible to construct highly refined solutions to fit desired spatial chord length profiles. Material volume fractions that are consistent with the chord lengths are first constructed by solving the associated Chapmann-Kolmogorov equations and applied to obtain the material averaged fluxes in two settings: when the materials are purely absorbing, and when scattering is present in rod model geometry. Illustrative numerical results for the volume fractions and material averaged fluxes are obtained by implementing the algorithms in MATLAB for spatially linear and quadratic variations of the chord lengths.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
An Overview of the Implicit Monte Carlo Algorithm [Slides]
Abstract not provided.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Computational methods for structural load and resistance modeling
An automated capability for computing structural reliability considering uncertainties in both load and resistance variables is presented. The computations are carried out using an automated Advanced Mean Value iteration algorithm (AMV +) with performance functions involving load and resistance variables obtained by both explicit and implicit methods. A complete description of the procedures used is given as well as several illustrative examples, verified by Monte Carlo Analysis. In particular, the computational methods described in the paper are shown to be quite accurate and efficient for a material nonlinear structure considering material damage as a function of several primitive random variables. The results show clearly the effectiveness of the algorithms for computing the reliability of large-scale structural systems with a maximum number of resolutions.
Thacker, B. H.↗
A High-Order Low-Order Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer
In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S 2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used to compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.
97 MATHEMATICS AND COMPUTING↗
Electromagnetic and neutral-weak response functions of 4 He and 12 C
A major goal of nuclear theory is to understand the strong interaction in nuclei as it manifests itself in terms of two- and many-body forces among the nuclear constituents, the protons and neutrons, and the interactions of these constituents with external electroweak probes via one- and many-body currents. The objective of the present work is to calculate the quasielastic electroweak response functions in light nuclei within the realistic dynamical framework outlined above. These response functions determine the inclusive cross section as function of the lepton momentum and energy transfers. Their ab initio calculation is a very challenging quantum many-body problem, since it requires summation over the entire excitation spectrum of the nucleus and inclusion in the electroweak currents of one- and many-body terms. Green's functions Monte Carlo methods allow one to circumvent both difficulties by computing the response in imaginary time (the so-called Euclidean response) and hence summing implicitly over the bound and continuum states of the nucleus, and by implementing specific algorithms designed to deal with the complicated spin-isospin structure of nuclear many-body operators. Theoretical predictions for 4 He and 12 C, confirmed by experiment in the electromagnetic case, show that two-body currents generate excess transverse strength from threshold to the quasielastic to the dip region and beyond. In conclusion, these results challenge the conventional picture of quasielastic inclusive scattering as being largely dominated by single-nucleon knockout processes.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Demonstration of a new unstructured mesh IMC x-ray transport capability in LAP codes
In this document, the Advanced Simulation and Computing (ASC) Transport Project’s Jayenne team presents evidence that the Los Alamos National Laboratory (LANL) Level 2 milestone statement, Demonstrate a new unstructured mesh IMC x-ray transport capability in LAP codes, due Q4 FY20, has been satisfied with the release and integration of the Jayenne team’s Implicit Monte Carlo (IMC) solver libraries into the lumos multiphysics solver. The Jayenne project’s software includes the algorithms and features prescribed by the milestone description. The lumos software is maintained by the Lagrangian Applications Project (LAP) along with the hydrodynamics code flag and operates under the same ASC program as Jayenne. A set of demonstration problems has been specified, executed, and analyzed.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Optimization of processor allocation for domain decomposed Monte Carlo calculations
Load imbalance plagues domain decomposed Monte Carlo calculations when sources are not uniform. Parallel efficiency for domain decomposed Monte Carlo transport calculations improves through a nonuniform allocation of processors over subdomains. In this work, we optimize the allocation with runtime diagnostics collected during a calibration step, then complete the full calculation. The diagnostic-based approach is compared to implicit filtering, an optimization algorithm for bound constrained noisy optimization problems. Finally, we consider both forward and hybrid radiation transport calculations to measure performance.
97 MATHEMATICS AND COMPUTING↗
Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach
This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches.
Warner, James E.↗
Surface Triangulation for CSG in Mercury
Visualization routines for rendering complicated geometries are very useful for engineers and scientists who are trying to build 3D prototypes of their designs. A common way to rapidly add interesting features to a 3D model is through the use of a concept called Constructive Solid Geometry. CSG uses compositions of the boolean set operations to manipulate basic geometric primitives to form more complicated objects. The most common boolean operations employed are union, intersection, and subtraction. Most computer-aided design software packages contain some sort of ability visualize CSG. The typical workflow for the user is as follows: The user specifies the individual primitive components, the user arbitrarily combines each of these primitives with boolean operations, the software generates a CSG tree structure which normally stores these solids implicitly with their defining equation, the tree is traversed and a general algorithm is applied to render the appropriate geometry onto the screen. Algorithms for visualizing CSG have been extensively developed for over a decade. Points sampled from the implicit solids are typically used as input by variations of algorithms like marching cubes and point-cloud surface reconstruction. Here, we explain a surface triangulation method from the graphics community that is being used for surface visualization in the framework of a Monte-Carlo neutron transport code called Mercury.
97 MATHEMATICS AND COMPUTING↗
Small-Noise Analysis and Symmetrization of Implicit Monte Carlo Samplers
Implicit samplers are algorithms for producing independent, weighted samples from multivariate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two implicit samplers in the small noise regime. Our analysis suggests a symmetrization of the algorithms that leads to improved implicit sampling schemes at a relatively small additional cost. Here, computational experiments confirm the theory and show that symmetrization is effective for small noise sampling problems.
97 MATHEMATICS AND COMPUTING↗
Parameter estimation by implicit sampling
© 2015 Mathematical Sciences Publishers. Implicit sampling is a weighted sampling method that is used in data assimilation to sequentially update state estimates of a stochastic model based on noisy and incomplete data. Here we apply implicit sampling to sample the posterior probability density of parameter estimation problems. The posterior probability combines prior information about the parameter with information from a numerical model, e.g., a partial differential equation (PDE), and noisy data. The result of our computations are parameters that lead to simulations that are compatible with the data. We demonstrate the usefulness of our implicit sampling algorithm with an example from subsurface flow. For an efficient implementation, we make use of multiple grids, BFGS optimization coupled to adjoint equations, and Karhunen-Loève expansions for dimensional reduction. Several difficulties of Markov chain Monte Carlo methods, e.g., estimation of burn-in times or correlations among the samples, are avoided because the implicit samples are independent.
Morzfeld, Matthias↗
A coarse-grained model with implicit salt for RNAs: Predicting 3D structure, stability and salt effect
To bridge the gap between the sequences and 3-dimensional (3D) structures of RNAs, some computational models have been proposed for predicting RNA 3D structures. However, the existed models seldom consider the conditions departing from the room/body temperature and high salt (1M NaCl), and thus generally hardly predict the thermodynamics and salt effect. In this study, we propose a coarse-grained model with implicit salt for RNAs to predict 3D structures, stability, and salt effect. Combined with Monte Carlo simulated annealing algorithm and a coarse-grained force field, the model folds 46 tested RNAs (≤45 nt) including pseudoknots into their native-like structures from their sequences, with an overall mean RMSD of 3.5 Å and an overall minimum RMSD of 1.9 Å from the experimental structures. For 30 RNA hairpins, the present model also gives the reliable predictions for the stability and salt effect with the mean deviation ∼ 1.0 °C of melting temperatures, as compared with the extensive experimental data. In addition, the model could provide the ensemble of possible 3D structures for a short RNA at a given temperature/salt condition.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Iterative derivation of effective potentials to sample the conformational space of proteins at atomistic scale
The current capacity of computers makes it possible to perform simulations of small systems with portable, explicit-solvent potentials achieving high degree of accuracy. However, simplified models must be employed to exploit the behavior of large systems or to perform systematic scans of smaller systems. While powerful algorithms are available to facilitate the sampling of the conformational space, successful applications of such models are hindered by the availability of simple enough potentials able to satisfactorily reproduce known properties of the system. We develop an interatomic potential to account for a number of properties of proteins in a computationally economic way. The potential is defined within an all-atom, implicit solvent model by contact functions between the different atom types. The associated numerical values can be optimized by an iterative Monte Carlo scheme on any available experimental data, provided that they are expressible as thermal averages of some conformational properties. We test this model on three different proteins, for which we also perform a scan of all possible point mutations with explicit conformational sampling. The resulting models, optimized solely on a subset of native distances, not only reproduce the native conformations within a few Angstroms from the experimental ones, but show the cooperative transition between native and denatured state and correctly predict the measured free-energy changes associated with point mutations. Moreover, differently from other structure-based models, our method leaves a residual degree of frustration, which is known to be present in protein molecules.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
A radiating shock evaluated using Implicit Monte Carlo Diffusion
Implicit Monte Carlo [1] (IMC) has been shown to be very expensive when used to evaluate a radiation field in opaque media. Implicit Monte Carlo Diffusion (IMD) [2], which evaluates a spatial discretized diffusion equation using a Monte Carlo algorithm, can be used to reduce the cost of evaluating the radiation field in opaque media [2]. This work couples IMD to the hydrodynamics equations to evaluate opaque diffusive radiating shocks. The Lowrie semi-analytic diffusive radiating shock benchmark[a] is used to verify our implementation of the coupled system of equations. (authors)
97 MATHEMATICS AND COMPUTING↗
An implicit particle code with exact energy and charge conservation for electromagnetic studies of dense plasmas
A collisional particle code based on implicit energy- and charge-conserving methods is presented. A modified version of the particle-suppressed Jacobian-Free Newton-Krylov method that can enhance the solver efficiency is introduced. Mathematically, it is shown that this new approach can be viewed as a fixed-point iteration method for the particle positions. The model can exactly conserve global energy and local charge and can efficiently use time steps larger than the plasma period. In conclusion, the algorithm's ability to simulate dense plasmas accurately and efficiently is quantified by simulating the dynamic compression of a plasma slab via a magnetic piston in 1D planar geometry.
97 MATHEMATICS AND COMPUTING↗
Eigenfunction Decomposition of Reactor Perturbations and Transitions Using MCNP Monte Carlo
Monte Carlo criticality calculations for nuclear reactors have typically only been able to find the primary eigenvalue and eigenmode. With the new fission matrix capability in MCNP6, it becomes possible to solve for higher modes, which are useful in wide variety of analyses. As a test case of this new capability, two reactor models in both a base configuration and a perturbed configuration were simulated in MCNP to generate fission matrices. Tools were written to find a relatively small number of eigenpairs of the resulting matrices, whereupon it was found that the implicitly restarted Arnoldi method outperformed the previously used power iteration as an eigenvalue algorithm by a factor of 1500 for a 3600 × 3600 sparse matrix.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Data-driven linear time advance operators for the acceleration of plasma physics simulation
In this study, we demonstrate the application of data-driven linear operator construction for time advance with a goal of accelerating plasma physics simulation. We apply dynamic mode decomposition (DMD) to data produced by the nonlinear SOLPS-ITER (Scrape-off Layer Plasma Simulator - International Thermonuclear Experimental Reactor) plasma boundary code suite in order to estimate a series of linear operators and monitor their predictive accuracy via online error analysis. We find that this approach defines when these dynamics can be represented by a sequence of approximate linear operators and is essential for providing consistent projections when compared to an unconstrained application. For linear diffusion and advection–diffusion fluid test problems, we construct and apply operators within explicit and implicit time advance schemes, demonstrating that stability can be robustly guaranteed in each case. We further investigate the use of the linear time advance operators within several integration methods including forward Euler, backward Euler, and the matrix exponential. The application of this method to simulation data from SOLPS-ITER, with varying levels of Markov chain Monte Carlo numerical noise, shows that constrained DMD operators yield a capability to identify, extract, and integrate a (slow) subset of the present timescales. Example applications show that for projected speedup factors of [Formula: see text], and [Formula: see text], a mean relative error of 3%, 5%, and 8% and maximum relative error less than 20% are achievable, which appears acceptable for typical SOLPS-ITER steady-state simulations.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗