Optimal parallelisation strategies for flat histogram Monte Carlo sampling

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.