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Fig. 6 The number of optimal samples with anchor nodes.

Fig. 4 The number of optimal samples with maximum velocity.

After preparation of powders using various surfactant concentrations, the optimal samples were chosen based on phase and particle size criteria.

Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition.

To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space.

The optimal samples exhibit a highly biaxial texture, as indicated by FWHM values in the range of 5 8° and 4 6° for respectively in- and out-of-plane orientations.

Optimal sample sizes are calculated from variance predictions by Ospats.

For other cases the optimal sampling designs does not exist.

Optimal sample sizes for predicting the response are also derived.

Optimal sampling is obtained by looking for the most isotropic sampling grid in momentum space.

The analysis demonstrates that this approach can be used to establish: optimal sample size; optimal sample allocation; and the societal payoff to proposed research.