Improved diffusion Monte Carlo
For practitioners of Monte Carlo simulation, this work improves the feasibility of DMC for rare event problems where standard methods fail due to variance explosion.
The authors propose a modification to diffusion Monte Carlo (DMC) based on RESTART and DPR rare event simulation algorithms, achieving lower variance per workload and enabling DMC in regimes where standard DMC's variance explodes exponentially. Numerical demonstrations on a Lennard-Jones cluster transition and a high-frequency data assimilation problem show effectiveness.
We propose a modification, based on the RESTART (repetitive simulation trials after reaching thresholds) and DPR (dynamics probability redistribution) rare event simulation algorithms, of the standard diffusion Monte Carlo (DMC) algorithm. The new algorithm has a lower variance per workload, regardless of the regime considered. In particular, it makes it feasible to use DMC in situations where the "naïve" generalisation of the standard algorithm would be impractical, due to an exponential explosion of its variance. We numerically demonstrate the effectiveness of the new algorithm on a standard rare event simulation problem (probability of an unlikely transition in a Lennard-Jones cluster), as well as a high-frequency data assimilation problem.