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Abstract Deep generative models have demonstrated effectiveness in learning compact and expressive design representations that significantly improve geometric design optimization. However, these models do not consider the uncertainty introduced by manufacturing or fabrication. The past work that quantifies such uncertainty often makes simplifying assumptions on geometric variations, while the “real-world,” “free-form” uncertainty and its impact on design performance are difficult to quantify due to the high dimensionality. To address this issue, we propose a generative adversarial network-based design under uncertainty framework (GAN-DUF), which contains a deep generative model that simultaneously learns a compact representation of nominal (ideal) designs and the conditional distribution of fabricated designs given any nominal design. This opens up new possibilities of (1) building a universal uncertainty quantification model compatible with both shape and topological designs, (2) modeling free-form geometric uncertainties without the need to make any assumptions on the distribution of geometric variability, and (3) allowing fast prediction of uncertainties for new nominal designs. We can combine the proposed deep generative model with robust design optimization or reliability-based design optimization for design under uncertainty. We demonstrated the framework on two real-world engineering design examples and showed its capability of finding the solution that possesses better performance after fabrication.
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This content will become publicly available on March 1, 2026
An uncertainty-aware deep learning framework-based robust design optimization of metamaterial units
Mechanical metamaterials represent an innovative class of artificial structures, distinguished by their extraordinary mechanical characteristics, which are beyond the scope of traditional natural materials. The use of deep generative models has become increasingly popular in the design of metamaterial units. The effectiveness of using deep generative models lies in their capacity to compress complex input data into a simplified, lower-dimensional latent space, while also enabling the creation of novel optimal designs through sampling within this space. However, the design process does not take into account the effect of model uncertainty due to data sparsity or the effect of input data uncertainty due to inherent randomness in the data. This might lead to the generation of undesirable structures with high sensitivity to the uncertainties in the system. To address this issue, a novel uncertainty-aware deep learning framework-based robust design approach is proposed for the design of metamaterial units with optimal target properties. The proposed approach utilizes the probabilistic nature of the deep learning framework and quantifies both aleatoric and epistemic uncertainties associated with surrogate-based design optimization. We demonstrate that the proposed design approach is capable of designing high-performance metamaterial units with high reliability. To showcase the effectiveness of the proposed design approach, a single-objective design optimization problem and a multi-objective design optimization problem are presented. The optimal robust designs obtained are validated by comparing them to the designs obtained from the topology optimization method as well as the designs obtained from a deterministic deep learning framework-based design optimization where none of the uncertainties in the system are explicitly considered.
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- Award ID(s):
- 2142290
- PAR ID:
- 10639928
- Publisher / Repository:
- Springer Nature
- Date Published:
- Journal Name:
- Structural and Multidisciplinary Optimization
- Volume:
- 68
- Issue:
- 3
- ISSN:
- 1615-147X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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