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

The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This review delves 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 predictive accuracy and relevance of reduced models. By integrating these methods into optimization frameworks, it is shown how they significantly mitigate the curse of dimensionality, streamline computational processes, and refine the exploration and optimization of complex functional surfaces. The survey provides a classification of method and highlights the transformative impact of these techniques in simplifying design challenges, thereby fostering more efficient and effective engineering solutions.