GAN-DUF: Hierarchical Deep Generative Models for Design Under Free-Form Geometric Uncertainty
This work addresses uncertainty quantification in engineering design optimization, which is incremental as it extends deep generative models to handle free-form geometric variations without simplifying assumptions.
The paper tackles the problem of quantifying free-form geometric uncertainty in design optimization, which is difficult due to high dimensionality, by proposing GAN-DUF, a hierarchical deep generative model that learns compact representations of nominal designs and conditional distributions of fabricated designs, and demonstrates its capability to find solutions with better post-fabrication performance in two real-world engineering examples.
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. 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 performances after fabrication.