Comparison of global variance reduction techniques for Monte Carlo radiation transport simulations of ITER

2011 ◽  
Vol 86 (9-11) ◽  
pp. 2698-2700 ◽  
Author(s):  
Andrew Davis ◽  
Andrew Turner
Keyword(s):  
Monte Carlo ◽  
Variance Reduction ◽  
Radiation Transport ◽  
Variance Reduction Techniques ◽  
Reduction Techniques ◽  
Global Variance Reduction

scholarly journals Variance-Reduction Methods for Monte Carlo Simulation of Radiation Transport

2021 ◽  
Vol 9 ◽  
Author(s):  
Salvador García-Pareja ◽  
Antonio M. Lallena ◽  
Francesc Salvat
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Variance Reduction ◽  
Radiation Transport ◽  
Scattering Method ◽  
Variance Reduction Techniques ◽  
Simulation Efficiency ◽  
Reduction Techniques ◽  
Exponential Transform ◽  
Reduction Methods

After a brief description of the essentials of Monte Carlo simulation methods and the definition of simulation efficiency, the rationale for variance-reduction techniques is presented. Popular variance-reduction techniques applicable to Monte Carlo simulations of radiation transport are described and motivated. The focus is on those techniques that can be used with any transport code, irrespective of the strategies used to track charged particles; they operate by manipulating either the number and weights of the transported particles or the mean free paths of the various interaction mechanisms. The considered techniques are 1) splitting and Russian roulette, with the ant colony method as builder of importance maps, 2) exponential transform and interaction-forcing biasing, 3) Woodcock or delta-scattering method, 4) interaction forcing, and 5) proper use of symmetries and combinations of different techniques. Illustrative results from analog simulations (without recourse to variance-reduction) and from variance-reduced simulations of various transport problems are presented.

scholarly journals Some variance reduction methods for numerical stochastic homogenization

2016 ◽  
Vol 374 (2066) ◽  
pp. 20150168 ◽  
Author(s):  
X. Blanc ◽  
C. Le Bris ◽  
F. Legoll
Keyword(s):  
Monte Carlo ◽  
Variance Reduction ◽  
Stochastic Homogenization ◽  
Numerical Homogenization ◽  
Variance Reduction Techniques ◽  
Reduction Techniques ◽  
Effective Coefficients ◽  
Engineering Sciences ◽  
Reduction Methods ◽  
The Cost

We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here.

scholarly journals On the Robust Estimation of Small Failure Probabilities for Strong Nonlinear Models

2019 ◽  
Vol 5 (4) ◽  
Author(s):  
Matthias Faes ◽  
Jonathan Sadeghi ◽  
Matteo Broggi ◽  
Marco de Angelis ◽  
Edoardo Patelli ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Structural Reliability ◽  
Variance Reduction ◽  
Surrogate Models ◽  
Accurate Estimation ◽  
Simulation Tools ◽  
Strongly Nonlinear ◽  
Variance Reduction Techniques ◽  
Reduction Techniques ◽  
Failure Probabilities

Abstract Structural reliability methods are nowadays a cornerstone for the design of robustly performing structures, thanks to advancements in modeling and simulation tools. Monte Carlo-based simulation tools have been shown to provide the necessary accuracy and flexibility. While standard Monte Carlo estimation of the probability of failure is not hindered in its applicability by approximations or limiting assumptions, it becomes computationally unfeasible when small failure probability needs to be estimated, especially when the underlying numerical model evaluation is time consuming. In this case, variance reduction techniques are commonly employed, allowing for the estimation of small failure probabilities with a reduced number of samples and model calls. As a competing approach to variance reduction techniques, surrogate models can be used to substitute the computationally expensive model and performance function with an easy to evaluate numerical function calibrated through a supervised learning procedure. Both these tools provide accurate results for structural application. However, particular care should be taken into account when the reliability problems deal with high-dimensional or strongly nonlinear structural performances since the accuracy of the estimate is largely dependent on choices made during the surrogate modeling process. In this work, we compare the performance of the most recent state-of-the-art advance Monte Carlo techniques and surrogate models when applied to strongly nonlinear performance functions. This will provide the analysts with an insight to the issues that could arise in these challenging problems and help to decide with confidence on which tool to select in order to achieve accurate estimation of the failure probabilities within feasible times with their available computational capabilities.

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