  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.
