Theoretical justification of space-mapping-based modeling utilizing a database and on-demand parameter extraction

We present a theoretical justification of a recently introduced surrogate modeling methodology based on space mapping that relies on an available data base and on-demand parameter extraction. Fine model data, the so-called base set, is assumed available in the region of interest. To evaluate the surrogate, we perform parameter extraction with weighting coefficients dependent on the distance between the point of interest and base points.

We provide theoretical results showing that the new methodology can assure any accuracy that is required (provided the base set is dense enough), which is not the case for our benchmark space mapping modeling methodology. Illustrative examples emphasizing differences between modeling methodologies are provided.