Space Mapping: The State of the Art

TLDR

The paper introduces a mathematical foundation for space mapping and positions it within classical optimization, aiming to obtain satisfactory solutions with few expensive fine‑model evaluations. Space mapping is described as an iterative surrogate‑based optimization framework that updates a fast coarse model to approximate a costly fine model, encompassing algorithms such as the original, Broyden‑based aggressive, trust‑region, neural, and implicit variants, with parameter extraction and uniqueness strategies illustrated by cheese‑cutting and wedge‑cutting examples. The review highlights numerous practical applications of space mapping across engineering design optimization.

Abstract

We review the space-mapping (SM) technique and the SM-based surrogate (modeling) concept and their applications in engineering design optimization. For the first time, we present a mathematical motivation and place SM into the context of classical optimization. The aim of SM is to achieve a satisfactory solution with a minimal number of computationally expensive "fine" model evaluations. SM procedures iteratively update and optimize surrogates based on a fast physically based "coarse" model. Proposed approaches to SM-based optimization include the original algorithm, the Broyden-based aggressive SM algorithm, various trust-region approaches, neural SM, and implicit SM. Parameter extraction is an essential SM subproblem. It is used to align the surrogate (enhanced coarse model) with the fine model. Different approaches to enhance uniqueness are suggested, including the recent gradient parameter-extraction approach. Novel physical illustrations are presented, including the cheese-cutting and wedge-cutting problems. Significant practical applications are reviewed.