# Parametric Model Embedding

arXiv: https://arxiv.org/abs/2204.05371 · HTML: https://mlsanity.com/paper/2204.05371/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2022.

## Built on by (most cited first, 5 of 5)

- [A Survey on Design-space Dimensionality Reduction Methods for Shape Optimization](https://mlsanity.com/paper/2405.13944/) (2024)
- [XVoxel-Based Parametric Design Optimization of Feature Models](https://mlsanity.com/paper/2303.15316/) (2023)
- [Generative Models for Anomaly Detection and Design-Space Dimensionality Reduction in Shape Optimization](https://mlsanity.com/paper/2308.04051/) (2023)
- [PCA-Based Interpretable Knowledge Representation and Analysis of Geometric Design Parameters](https://mlsanity.com/paper/2603.17535/) (2026)
- [A nonlinear extension of parametric model embedding for dimensionality reduction in parametric shape design](https://mlsanity.com/paper/2605.11759/) (2026)

## Abstract (arXiv)

Methodologies for reducing the design-space dimensionality in shape optimization have been recently developed based on unsupervised machine learning methods. These methods provide reduced dimensionality representations of the design space, capable of maintaining a certain degree of the original design variability. Nevertheless, they usually do not allow to use directly the original parameterization method, representing a limitation to their widespread application in the industrial field, where the design parameters often pertain to well-established parametric models, e.g. CAD (computer-aided design) models. This work presents how to embed the parametric-model original parameters in a reduced-dimensionality representation of the design space. The method, which takes advantage from the definition of a newly-introduced generalized feature space, is demonstrated, as a proof of concept, for the reparameterization of 2D Bezier curves and 3D free-form deformation design spaces and the consequent solution of simulation-driven design optimization problems of a subsonic airfoil and a naval destroyer in calm water, respectively.