A Survey on Design-space Dimensionality Reduction Methods for Shape Optimization

TL;DR

This survey reviews various dimensionality reduction techniques for shape optimization, highlighting their role in simplifying high-dimensional design spaces and improving computational efficiency in engineering design.

Contribution

It provides a comprehensive classification and analysis of traditional, nonlinear, and physics-informed dimensionality reduction methods for shape optimization.

Findings

Physics-informed methods enhance physical relevance of reduced spaces

Dimensionality reduction mitigates curse of dimensionality in optimization

Streamlines computational processes in complex surface design

Abstract

The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This survey paper offers a scoping review, i.e., a literature mapping synthesis borrowed from clinical medicine, delving into the field of design-space dimensionality reduction techniques tailored for shape optimization, bridging traditional methods and cutting-edge technologies. Dissecting the spectrum of these techniques, from classical linear approaches like principal component analysis to more nuanced nonlinear methods such as autoencoders, the discussion extends to innovative physics-informed methods that integrate physical data into the dimensionality reduction process, enhancing the physical relevance and effectiveness of reduced design spaces. By integrating these methods into optimization frameworks, it is shown how they significantly mitigate the curse of dimensionality, streamline computational processes, and refine the design exploration and optimization of complex functional surfaces. The survey provides a classification of methods and highlights the transformative impact of these techniques in simplifying design challenges, thereby fostering more efficient and effective engineering solutions.