On sensitivities regarding shape and topology optimization as derivatives on Wasserstein spaces

2024/11/19 by Fumiya Okazaki, Okazaki, Fumiya, Takayuki YAMADA +1
Computer Science · #Digital Image Processing Techniques #FOS: Mathematics #Optimization and Control (math.OC) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2411.12234

openalex publication_date 2024/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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