Building effective models from sparse but precise data

Details Building effective models from sparse but precise data Building effective models from sparse but precise data

2009-08-05

arxiv.org/abs/0908.0659v1

Phys. Rev. B 81, 012104 (2010)

Physics

Condensed Matter

Materials Science

10 pages, 3 figures, submitted to Physical Review Letters

Scientific paper

A common approach in computational science is to use a set of of highly precise but expensive calculations to parameterize a model that allows less precise, but more rapid calculations on larger scale systems. Least-squares fitting on a model that underfits the data is generally used for this purpose. For arbitrarily precise data free from statistic noise, e.g. ab initio calculations, we argue that it is more appropriate to begin with a ensemble of models that overfit the data. Within a Bayesian framework, a most likely model can be defined that incorporates physical knowledge, provides error estimates for systems not included in the fit, and reproduces the original data exactly. We apply this approach to obtain a cluster expansion model for the Ca[Zr,Ti]O3 solid solution.

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