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The cost is then minimized by means of a suitable optimization algorithm, thus defining an optimal sampling strategy.

The C function can be optimized with respect to n, h, and L to yield an optimal sampling schedule.

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

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

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.

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.

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.

Step 2: 10,000 × samples of d and E are generated around the optimal sample by random function.