The essence of space mapping: less is more

Abstract

Suitable physics-based surrogates can facilitate effective engineering design optimizations with high-fidelity or “fine-model” simulation accuracy and “coarse-model” simulation speed. So-called space mapping exploits the engineer’s traditional “quasi-global” intuition. It specifically implements the iterative enhancement of suitable physics-based surrogates derived from simple mappings of coarse models (the “less”) to realize highly accurate surrogates of corresponding fine models (the “more”). Importantly, space mapping offers a quantitative explanation for the engineer’s mysterious “feel” for a problem. This talk recalls how the concept came into being, as well as how it differs from other surrogate-based approaches that found favor at much the same time. The essential difference (oversimplified here for the sake of discussion) is that space mapping arises out of an understanding of the “feel” that an experienced engineer has for a complex engineering design problem, while the generic surrogate-based approach arises from the “feel” that a mathematician has for a generic optimization problem. Confusion sets in when words like surrogate, model, and simulation are used arbitrarily and interchangeably to mean almost any representation of anything. One thing is for sure: surrogates, models, and simulations imply underlying knowledge, nowadays typically the physics embodied in a simulator. How this knowledge is actually manipulated—from the “inside” or from the “outside”—depends on whether the designer is oriented towards engineering or mathematics (or perhaps both).