Optimal parallelisation strategies for flat histogram Monte Carlo sampling

Abstract

Flat histogram methods, such as Wang--Landau sampling, provide a means for high-throughput calculation of phase diagrams of atomistic/lattice model systems. Many parallelisation schemes with varying degrees of complexity have been proposed to accelerate such sampling simulations. In this study, several widely used schemes are benchmarked -- both in isolation and in combination -- to establish best practice. The schemes studied include energy domain decomposition with both static sizing of energy sub-domains, as well as a dynamic sub-domain sizing scheme which we propose. We also assess the benefits both of replica exchange and of including multiple random walkers per sub-domain, to determine which factors have the largest impact on parallel efficiency. Additionally, the influence of energy sub-domain overlap regions is discussed. As illustrative test cases, we implement and apply the aforementioned strategies to a lattice-based model describing the internal energy of a substitutional alloy, studying the AlTiCrMo refractory high-entropy superalloy as well as the binary CuZn system, both of which crystallographically order into a B2 (CsCl) structure with decreasing temperature. We find that -- while all of the proposed strategies confer a non-negligible speedup -- parallelisation across energy domains which are non-uniform in size offers the most appreciable performance improvements. This work offers concrete recommendations for which parallelisation strategies should be prioritised to optimally accelerate flat-histogram Monte Carlo simulations.