# Parameter-free shape optimization: various shape updates for engineering applications

arXiv: https://arxiv.org/abs/2302.12100 · HTML: https://mlsanity.com/paper/2302.12100/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2023.

## Built on by (most cited first, 1 of 1)

- [Adjoint-based shape optimization of a ship hull using a Conditional Variational Autoencoder (CVAE) assisted propulsion surrogate model](https://mlsanity.com/paper/2602.14907/) (2026)

## Abstract (arXiv)

In the last decade, parameter-free approaches to shape optimization problems have matured to a state where they provide a versatile tool for complex engineering applications. However, sensitivity distributions obtained from shape derivatives in this context cannot be directly used as a shape update in gradient-based optimization strategies. Instead, an auxiliary problem has to be solved to obtain a gradient from the sensitivity. While several choices for these auxiliary problems were investigated mathematically, the complexity of the concepts behind their derivation has often prevented their application in engineering. This work aims at an explanation of several approaches to compute shape updates from an engineering perspective. We introduce the corresponding auxiliary problems in a formal way and compare the choices by means of numerical examples. To this end, a test case and exemplary applications from computational fluid dynamics are considered.