Interacting particle Monte Carlo methods for Neutron Transport

Interacting particle systems

In the mathematical literature, there has been growing interest over the last 20-30 years in the notion of simulation variance reduction through algorithms that interact with concurrent simulations, known as interacting particle systems.

A key quantity of interest when analysing the criticality of nuclear reactors is the so-called constant keff, which describes the effective multiplication factor of neutrons across a fissile system. Current Monte Carlo methods are typically highly accurate for computing keff, but challenges remain in accurately understanding the associated errors, and also accurately estimating flux responses, for example on the edge of re- actors. Interacting particle methodology is a natural approach to these challenges and whilst this method underpins many known algorithms, they are not systematically studied in the nuclear setting.

Genetic algorithms

The basic idea behind interacting particle algorithms is to initiate a series of Monte Carlo simulations and, at key stages of each simulation, to use selection critera to remove the “poorly performing” simulations and independently replicate the “better performing” simulations. This creates dependencies between simulations which are reminiscent of certain mathematical models of genetic evolution.

In the nuclear setting, it is generally well understood how the variance of ‘single particle’ estimates behave over generations of fission events. The main technical challenge is adaptation of this understanding to the setting of interacting particles and how this plays out in terms of variance reduction.