# Modeling and Optimization with Gaussian Processes in Reduced Eigenbases -- Extended Version

arXiv: https://arxiv.org/abs/1908.11272 · HTML: https://mlsanity.com/paper/1908.11272/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2019.

## Built on by (most cited first, 8 of 8)

- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Comparison of High-Dimensional Bayesian Optimization Algorithms on BBOB](https://mlsanity.com/paper/2303.00890/) (2023)
- [Revisiting Bayesian Optimization in the light of the COCO benchmark](https://mlsanity.com/paper/2103.16649/) (2021)
- [A Survey on Design-space Dimensionality Reduction Methods for Shape Optimization](https://mlsanity.com/paper/2405.13944/) (2024)
- [Variational Bayesian surrogate modelling with application to robust design optimisation](https://mlsanity.com/paper/2404.14857/) (2024)
- [Uncertainty-Aware Data-Based Method for Fast and Reliable Shape Optimization](https://mlsanity.com/paper/2601.21956/) (2026)
- [Multi-view Bayesian optimisation in an input-output reduced space for engineering design](https://mlsanity.com/paper/2501.01552/) (2025)
- [A nonlinear extension of parametric model embedding for dimensionality reduction in parametric shape design](https://mlsanity.com/paper/2605.11759/) (2026)

## Abstract (arXiv)

Parametric shape optimization aims at minimizing an objective function f(x) where x are CAD parameters. This task is difficult when f is the output of an expensive-to-evaluate numerical simulator and the number of CAD parameters is large. Most often, the set of all considered CAD shapes resides in a manifold of lower effective dimension in which it is preferable to build the surrogate model and perform the optimization. In this work, we uncover the manifold through a high-dimensional shape mapping and build a new coordinate system made of eigenshapes. The surrogate model is learned in the space of eigenshapes: a regularized likelihood maximization provides the most relevant dimensions for the output. The final surrogate model is detailed (anisotropic) with respect to the most sensitive eigenshapes and rough (isotropic) in the remaining dimensions. Last, the optimization is carried out with a focus on the critical dimensions, the remaining ones being coarsely optimized through a random embedding and the manifold being accounted for through a replication strategy. At low budgets, the methodology leads to a more accurate model and a faster optimization than the classical approach of directly working with the CAD parameters.