On sensitivities regarding shape and topology optimization as derivatives on Wasserstein spaces
Optimization and Control
2025-09-08 v2
Abstract
In this paper, we apply the framework of optimal transport to the formulation of optimal design problems. By considering the Wasserstein space as a set of design variables, we associate each probability measure with a shape configuration of a material in some ways. In particular, we focus on connections between differentials on the Wasserstein space and sensitivities in the standard setting of shape and topology optimization in order to regard the optimization procedure of those problems as gradient flows on the Wasserstein space.
Keywords
Cite
@article{arxiv.2411.12234,
title = {On sensitivities regarding shape and topology optimization as derivatives on Wasserstein spaces},
author = {Fumiya Okazaki and Takayuki Yamada},
journal= {arXiv preprint arXiv:2411.12234},
year = {2025}
}
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16 pages