Design optimization techniques are often used at the beginning of the design process to explore the space of possible designs. In these domains illumination algorithms, such as MAP-Elites, are promising alternatives to classic optimization algorithms because they produce diverse, high-quality solutions in a single run, instead of only a single near-optimal solution. Unfortunately, these algorithms currently require a large number of function evaluations, limiting their applicability. In this article, we introduce a new illumination algorithm, Surrogate-Assisted Illumination (SAIL), that leverages surrogate modeling techniques to create a map of the design space according to user-defined features while minimizing the number of fitness evaluations. On a two-dimensional airfoil optimization problem, SAIL produces hundreds of diverse but high-performing designs with several orders of magnitude fewer evaluations than MAP-Elites or CMA-ES. We demonstrate that SAIL is also capable of producing maps of high-performing designs in realistic three-dimensional aerodynamic tasks with an accurate flow simulation. Data-efficient design exploration with SAIL can help designers understand what is possible, beyond what is optimal, by considering more than pure objective-based optimization.

Novel techniques in evolutionary optimization, simulation, and machine learning enable a broad analysis of domains like fluid dynamics, in which computation is expensive and flow behavior is complex. This paper introduces the concept of full domain analysis, defined as the ability to efficiently determine the full space of solutions in a problem domain and analyze the behavior of those solutions in an accessible and interactive manner. The goal of full domain analysis is to deepen our understanding of domains by generating many examples of flow, their diversification, optimization, and analysis. We define a formal model for full domain analysis, its current state of the art, and the requirements of its sub-components. Finally, an example is given to show what can be learned by using full domain analysis. Full domain analysis, rooted in optimization and machine learning, can be a valuable tool in understanding complex systems in computational physics and beyond.