Proof that Combining the Forced-collision and DXTRAN Monte Carlo Variance-reduction Techniques is Fair

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.

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Voxel based Monte Carlo calculations of nuclear medicine images and applied variance reduction techniques

Lecture Notes in Computer Science - Information Processing in Medical Imaging ◽

10.1007/bfb0033739 ◽

2005 ◽

pp. 23-33 ◽

Cited By ~ 25

Author(s):

George Zubal ◽

Chuck Harrell

Keyword(s):

Monte Carlo ◽

Nuclear Medicine ◽

Variance Reduction ◽

Variance Reduction Techniques ◽

Monte Carlo Calculations ◽

Reduction Techniques

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Variance-Reduction Methods for Monte Carlo Simulation of Radiation Transport

Frontiers in Physics ◽

10.3389/fphy.2021.718873 ◽

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.

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