Distributionally robust shape and topology optimization: overview and deployment for geometric uncertainties
Abstract
This article contributes to the development of shape optimization formulations that take into account the presence of uncertainty in the parameters of the underlying physical model. More precisely, it aims to apply the idea of distributional robustness in the context of the minimization of a cost function evaluating the performance of the shape of a mechanical structure. This concern is motivated by the fact that in practice, the law of the uncertain parameters itself is often unknown, making unefficient the usual practice of minimizing the expectation of the cost under a necessarily approximate law. One then wises to minimize the worst-case expected value of the cost over probability laws that are "close" to a nominal law, reconstructed from a few observed samples, which is the only available information. This idea is relatively recent in convex analysis and operations research, where the problems at stake typically enjoy a rich mathematical structure. It was adapted to the setting of optimal design in a series of recent works, where tractable versions of distributionally robust optimal design problems were proposed, leveraging recent findings in robust optimization and optimal transport. The first part of this article reviews these contributions. Its second part is devoted to a new development, about the adaptation of this framework to the treatment of geometric uncertainties: the optimized shape itself is subject to uncertain perturbations, instead of a set of independent parameters, which requires a suitable reformulation of the problem. Two numerical examples are discussed to assess the main features of the proposed methods.
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BibTeX
@misc{dapogny2026distributionally,
title = {{Distributionally robust shape and topology optimization: overview and deployment for geometric uncertainties}},
author = {Charles Dapogny and Franck Iutzeler and Julien Prando and Boris Thibert},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05740258v1},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Distributionally robust shape and topology optimization: overview and deployment for geometric uncertainties
AU - Charles Dapogny
AU - Franck Iutzeler
AU - Julien Prando
AU - Boris Thibert
PY - 2026
DA - 2026/09/07
PB - HAL
UR - https://hal.science/hal-05740258v1
AB - This article contributes to the development of shape optimization formulations that take into account the presence of uncertainty in the parameters of the underlying physical model. More precisely, it aims to apply the idea of distributional robustness in the context of the minimization of a cost function evaluating the performance of the shape of a mechanical structure. This concern is motivated by the fact that in practice, the law of the uncertain parameters itself is often unknown, making unefficient the usual practice of minimizing the expectation of the cost under a necessarily approximate law. One then wises to minimize the worst-case expected value of the cost over probability laws that are "close" to a nominal law, reconstructed from a few observed samples, which is the only available information. This idea is relatively recent in convex analysis and operations research, where the problems at stake typically enjoy a rich mathematical structure. It was adapted to the setting of optimal design in a series of recent works, where tractable versions of distributionally robust optimal design problems were proposed, leveraging recent findings in robust optimization and optimal transport. The first part of this article reviews these contributions. Its second part is devoted to a new development, about the adaptation of this framework to the treatment of geometric uncertainties: the optimized shape itself is subject to uncertain perturbations, instead of a set of independent parameters, which requires a suitable reformulation of the problem. Two numerical examples are discussed to assess the main features of the proposed methods.
ER -