On learning particle distributions in the 1D implicit Monte Carlo simulations of radiation transport

Abstract

Monte Carlo based thermal radiative transfer (TRT) codes provide a flexible framework for large-scale high-energy-density simulations. Compared to their deterministic counterparts, Monte Carlo methods are easier to implement in complex geometries and higher dimensions. However, the probabilistic nature of the Monte Carlo approach and the complexity of the underlying TRT equations describing nonlinear interactions between radiation and matter imply that Monte Carlo radiation transport codes involve massive amounts of particle data and have enormous memory footprints. This study is focused on building a statistical learning framework that can be employed to `compress' IMC data into a few probability density functions characterized by a relatively small number of distribution parameters. In order to learn complex distributions describing Monte Carlo data, we employ the Expectation Maximization (EM) method and finite mixture models adapted to learn particle distributions in the energy and angular domains targeting Implicit Monte Carlo (IMC) simulations in 1-d. Specifically, we couple EM iteration to the weighted hyper-Erlang finite mixture model in order to learn parameters of the photon distributions. We couple the EM iteration to the von Mises (Circular Normal) finite mixture model in order to learn angular distributions. The learning approach proposed in this study promises accurate resampling and significant memory savings at checkpointing and restarts of the IMC and other Monte Carlo radiation transport codes.