Cluster expansions in multicomponent systems: precise expansions from noisy databases
A. Díaz-Ortiz, H. Dosch, R. Drautz.
Journal of Physics: Condensed Matter, 19, 406206,1-19, (2007)
We have performed a systematic analysis of the numerical errors contained in the databases used in cluster expansions of multicomponent alloys. Our results underscore the importance of numerical noise in the determination of the effective cluster interactions and in the expansion determination. The relevance of the size of and information contained in the input database is highlighted. It is shown that cross- validatory approaches by themselves can produce unphysical expansions characterized by non- negligible, long- ranged coefficients. A selection criterion that combines both forecasting ability and a physical limiting behavior for the expansion is proposed. Expansions performed under this criterion exhibit the remarkable property of noise filtering. A discussion of the impact of this unforeseen characteristic of the cluster expansion method on the modeling of multicomponent alloy systems is presented
Keyword(s): Special quasirandom structures; cross-validation; regression-models; alloys; selection