Advanced Variance Reduction Methods for Monte Carlo Particle Transport: A Comprehensive Review

Abstract

The Monte Carlo (MC) method is the reference approach for particle transport simulation in complex three-dimensional geometries and continuous-energy problems, where it avoids the phase-space discretization required by deterministic methods; yet its 1/N convergence rate renders brute-force computation infeasible for deep-penetration shielding and full-core fixed-source problems. Variance reduction (VR) methods address this bottleneck by modifying particle sampling or transport while preserving estimator unbiasedness, concentrating computational resources on high-contribution phase-space regions. This review systematically surveys VR methods for Monte Carlo particle transport, organized into three categories: classical techniques, advanced local variance reduction (LVR), and advanced global variance reduction (GVR). Using Zero-Variance Theory as the unifying framework, the review elucidates that all VR methods are fundamentally distinct approximations to the optimal importance function. A multi-dimensional classification system is proposed that traces the evolution from manual, heuristic parameter tuning to automated generation, from single-technique application to multi-solver collaborative integration, and from empirical rules to mathematically rigorous efficiency optimization. Key future directions include the rigorization of global efficiency theory, machine-learning-assisted importance function construction, and multi-solver collaborative adaptive frameworks. The field is progressing toward a hierarchical complementarity of local and global VR, jointly advancing VR methodology from academic research to engineering practice.