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

arXiv: https://arxiv.org/abs/2405.13944 · HTML: https://mlsanity.com/paper/2405.13944/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 153 references that are in the map.
- First posted on arXiv 22 May 2024.

## Builds on (most cited first, 9 of 9)

- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Modeling and Optimization with Gaussian Processes in Reduced Eigenbases -- Extended Version](https://mlsanity.com/paper/1908.11272/) (2019)
- [A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems](https://mlsanity.com/paper/2006.07282/) (2020)
- [Parametric Model Embedding](https://mlsanity.com/paper/2204.05371/) (2022)
- [Generative VS non-Generative Models in Engineering Shape Optimization](https://mlsanity.com/paper/2402.08540/) (2024)
- [Model Reduction Framework with a New Take on Active Subspaces for Optimization Problems with Linearized Fluid-Structure Interaction Constraints](https://mlsanity.com/paper/2002.07602/) (2020)
- [Supporting Multi-point Fan Design with Dimension Reduction](https://mlsanity.com/paper/1910.09030/) (2019)
- [Generative Models for Anomaly Detection and Design-Space Dimensionality Reduction in Shape Optimization](https://mlsanity.com/paper/2308.04051/) (2023)
- [A Scoping Review on Simulation-based Design Optimization in Marine Engineering: Trends, Best Practices, and Gaps](https://mlsanity.com/paper/2404.18654/) (2024)

## Built on by (most cited first, 3 of 3)

- [Airfoil optimization using Design-by-Morphing with minimized design-space dimensionality](https://mlsanity.com/paper/2510.16020/) (2025)
- [A nonlinear extension of parametric model embedding for dimensionality reduction in parametric shape design](https://mlsanity.com/paper/2605.11759/) (2026)
- [A Riemannian View on Active Subspaces](https://mlsanity.com/paper/2607.25163/) (2026)

## Abstract (arXiv)

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.