Efficient sampling in materials simulation - Exploring the parameter space of grain boundaries

In the framework of materials design there is the demand for extensive databases of specific materials properties. In this work we suggest an improved strategy for creating future databases, especially for extrinsic properties that depend on several material parameters. As an example we choose the energy of grain boundaries as a function of their geometric degrees of freedom. The construction of existing databases of grain boundary energies in face-centred and body centred cubic metals relied on the a-priori knowledge of the location of important cusps and maxima in the five-dimensional energy landscape, and on an as-densely- as-possible sampling strategy. We introduce two methods to improve the current state of the art. The location and number of the energy minima along which the hierarchical sampling takes place is predicted from existing data points without any a-priori knowledge, using a predictor function. Furthermore we show that it is more efficient to use a sequential sampling in a \design of experiment" scheme, rather than sampling all observations homogeneously in one batch. This sequential design exhibits a smaller error than the simultaneous one, and thus can provide the same accuracy with fewer data points. The new strategy should be particularly beneficial in the exploration of grain boundary energies in new alloys and/or non-cubic structures.