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 the choice of size of energy sub-domain overlap regions is discussed. As an illustrative test case, we implement and apply the aforementioned strategies to a lattice-based model describing the internal energies of the AlTiCrMo refractory high-entropy superalloy, which is understood to 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.