Sparse-grid approximations based on Lagrange polynomials are one of the staple methods for approximating functions that are high-dimensional and expensive to evaluate, e.g. in the context of PDE-based parametric design exploration. They are, however, known to have limited granularity: refining these sparse-grid approximations may require multiple additional function evaluations, potentially leading to computational inefficiency. To address this issue, we propose a selection criterion for the candidate collocation points introduced by the refinement procedure: the function is evaluated only at those points for which a suitable (and crucially zero-cost) discrepancy indicator suggests that the additional evaluation would significantly change the resulting approximation. The remaining collocation points are instead assigned values predicted by the already available sparse-grid approximation, i.e., following a bifidelity approach that reduces costs while preserving accuracy. The effectiveness of this methodology is demonstrated on several benchmark functions and on an engineering application concerning flashback phenomena in hydrogen-fueled perforated burners.

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