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In an era where scientific experiments can be very costly, multi-fidelityemulators provide a useful tool for cost-efficient predictive scientificcomputing. For scientific applications, the experimenter is often limited by atight computational budget, and thus wishes to (i) maximize predictive power ofthe multi-fidelity emulator via a careful design of experiments, and (ii)ensure this model achieves a desired error tolerance with some notion ofconfidence. Existing design methods, however, do not jointly tackle objectives(i) and (ii). We propose a novel stacking design approach that addresses bothgoals. A multi-level reproducing kernel Hilbert space (RKHS) interpolator isfirst introduced to build the emulator, under which our stacking designprovides a sequential approach for designing multi-fidelity runs such that adesired prediction error of $\epsilon > 0$ is met under regularity assumptions.We then prove a novel cost complexity theorem that, under this multi-levelinterpolator, establishes a bound on the computation cost (for training datasimulation) needed to achieve a prediction bound of $\epsilon$. This resultprovides novel insights on conditions under which the proposed multi-fidelityapproach improves upon a conventional RKHS interpolator which relies on asingle fidelity level. Finally, we demonstrate the effectiveness of stackingdesigns in a suite of simulation experiments and an application to finiteelement analysis.

Stacking designs: designing multi-fidelity computer experiments with target predictive accuracy