🤖 AI Summary
This work proposes a novel diffusion Monte Carlo (DMC) implementation, termed DMCD, which replaces the conventional breadth-first traversal and particle ensemble simulation with a depth-first traversal strategy leveraging a stack-based structure. By introducing, for the first time, a stack-oriented approach from particle transport into the DMC framework, DMCD provides a unified treatment of both eigenvalue and linear equation problems. The method naturally accommodates population control and offspring weighting, and effectively addresses the challenge of initializing new walkers upon stack depletion through mechanisms including splitting, Russian roulette, and importance sampling. Experimental results demonstrate that DMCD substantially reduces memory consumption and enhances utilization of memory hierarchies and coprocessors, highlighting its potential as a viable alternative to traditional DMC implementations.
📝 Abstract
Diffusion Monte Carlo (DMC) and Monte Carlo for particle transport with importance sampling both involve simulations of weighted walkers that undergo birth and death processes (splitting and Russian Roulette). The established implementations of these methods are quite different: Particle simulation Monte Carlo employs a stack to handle the splitting history whereas in traditional DMC one follows a swarm of walkers. The particle simulation Monte Carlo approach involves a depth first traversal of the visited configurations whereas the traditional DMC approach may be seen as a breadth first traversal. In the present work the implementation of a depth first, stack based approach to DMC is described and a complete code is presented. The depth first approach, called DMCD here, can be more memory efficient than the breadth first approach, both for total memory and for use of a memory hierarchy and of co-processors. The implementation appears very natural for population control and for descendant weighting and it unifies algorithmic treatment of the eigenvalue problem (DMC) with the linear equation problem (particle transport). A concern with DMCD that is not present in the breadth first approach, and that is successfully addressed here, is the need to maintain a pool of starters for use when a new walker is required and the stack is empty. The DMCD approach appears to have the potential to become the preferred implementation for many DMC applications.