Numerical stability of the predictor-corrector method in Monte Carlo burnup calculations of critical reactors

Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the simplest methods, such as the beginning-of-step and middle-of-step constant flux approximations, are numerically unstable in fuel cycle calculations of critical reactors. Here we show that even the predictor-corrector methods that are implemented in established Monte Carlo burnup codes can be numerically unstable in cycle calculations of large systems. © 2013 Elsevier Ltd. All rights reserved.

Generation of SFR few-group constants using the Monte Carlo code serpent

In this study, the Serpent Monte Carlo code was used as a tool for preparation of homogenized few-group cross sections for the nodal diffusion analysis of Sodium cooled Fast Reactor (SFR) cores. Few-group constants for two reference SFR cores were generated by Serpent and then employed by nodal diffusion code DYN3D in 2D full core calculations. The DYN3D results were verified against the references full core Serpent Monte Carlo solutions. A good agreement between the reference Monte Carlo and nodal diffusion results was observed demonstrating the feasibility of using Serpent for generation of few-group constants for the deterministic SFR analysis.

A backward-simulation based Rao-Blackwellized particle smoother for conditionally linear Gaussian models

In this article, we develop a new Rao-Blackwellized Monte Carlo smoothing algorithm for conditionally linear Gaussian models. The algorithm is based on the forward-filtering backward-simulation Monte Carlo smoother concept and performs the backward simulation directly in the marginal space of the non-Gaussian state component while treating the linear part analytically. Unlike the previously proposed backward-simulation based Rao-Blackwellized smoothing approaches, it does not require sampling of the Gaussian state component and is also able to overcome certain normalization problems of two-filter smoother based approaches. The performance of the algorithm is illustrated in a simulated application. © 2012 IFAC.

Communication: energy benchmarking with quantum Monte Carlo for water nano-droplets and bulk liquid water.

We show the feasibility of using quantum Monte Carlo (QMC) to compute benchmark energies for configuration samples of thermal-equilibrium water clusters and the bulk liquid containing up to 64 molecules. Evidence that the accuracy of these benchmarks approaches that of basis-set converged coupled-cluster calculations is noted. We illustrate the usefulness of the benchmarks by using them to analyze the errors of the popular BLYP approximation of density functional theory (DFT). The results indicate the possibility of using QMC as a routine tool for analyzing DFT errors for non-covalent bonding in many types of condensed-phase molecular system.

Sequential Monte Carlo computation of the score and observed information matrix in state-space models with application to parameter estimation

Sequential Monte Carlo (SMC) methods are popular computational tools for Bayesian inference in non-linear non-Gaussian state-space models. For this class of models, we propose SMC algorithms to compute the score vector and observed information matrix recursively in time. We propose two different SMC implementations, one with computational complexity $\mathcal{O}(N)$ and the other with complexity $\mathcal{O}(N^{2})$ where $N$ is the number of importance sampling draws. Although cheaper, the performance of the $\mathcal{O}(N)$ method degrades quickly in time as it inherently relies on the SMC approximation of a sequence of probability distributions whose dimension is increasing linearly with time. In particular, even under strong \textit{mixing} assumptions, the variance of the estimates computed with the $\mathcal{O}(N)$ method increases at least quadratically in time. The $\mathcal{O}(N^{2})$ is a non-standard SMC implementation that does not suffer from this rapid degrade. We then show how both methods can be used to perform batch and recursive parameter estimation.

Control of aircraft in the terminal manoeuvring area using parallelised sequential Monte Carlo

This paper reports on the use of a parallelised Model Predictive Control, Sequential Monte Carlo algorithm for solving the problem of conflict resolution and aircraft trajectory control in air traffic management specifically around the terminal manoeuvring area of an airport. The target problem is nonlinear, highly constrained, non-convex and uses a single decision-maker with multiple aircraft. The implementation includes a spatio-temporal wind model and rolling window simulations for realistic ongoing scenarios. The method is capable of handling arriving and departing aircraft simultaneously including some with very low fuel remaining. A novel flow field is proposed to smooth the approach trajectories for arriving aircraft and all trajectories are planned in three dimensions. Massive parallelisation of the algorithm allows solution speeds to approach those required for real-time use.

Bayesian model selection for time series using Markov chain Monte Carlo

We present a stochastic simulation technique for subset selection in time series models, based on the use of indicator variables with the Gibbs sampler within a hierarchical Bayesian framework. As an example, the method is applied to the selection of subset linear AR models, in which only significant lags are included. Joint sampling of the indicators and parameters is found to speed convergence. We discuss the possibility of model mixing where the model is not well determined by the data, and the extension of the approach to include non-linear model terms.

Forward Smoothing Using Sequential Monte Carlo

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively. Essentially, it is an on-line or "forward only" implementation of a forward filtering backward smoothing SMC algorithm proposed by Doucet, Godsill and Andrieu (2000). Compared to the standard \emph{path space} SMC estimator whose asymptotic variance increases quadratically with time even under favorable mixing assumptions, the non asymptotic variance of the proposed SMC estimator only increases linearly with time. We show how this allows us to perform recursive parameter estimation using an SMC implementation of an on-line version of the Expectation-Maximization algorithm which does not suffer from the particle path degeneracy problem.