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Deep generative models have demonstrated effectiveness in learning compactand expressive design representations that significantly improve geometricdesign optimization. However, these models do not consider the uncertaintyintroduced by manufacturing or fabrication. Past work that quantifies suchuncertainty often makes simplifying assumptions on geometric variations, whilethe "real-world", "free-form" uncertainty and its impact on design performanceare difficult to quantify due to the high dimensionality. To address thisissue, we propose a Generative Adversarial Network-based Design underUncertainty Framework (GAN-DUF), which contains a deep generative model thatsimultaneously learns a compact representation of nominal (ideal) designs andthe conditional distribution of fabricated designs given any nominal design.This opens up new possibilities of 1)~building a universal uncertaintyquantification model compatible with both shape and topological designs,2)~modeling free-form geometric uncertainties without the need to make anyassumptions on the distribution of geometric variability, and 3)~allowing fastprediction of uncertainties for new nominal designs. We can combine theproposed deep generative model with robust design optimization orreliability-based design optimization for design under uncertainty. Wedemonstrated the framework on two real-world engineering design examples andshowed its capability of finding the solution that possesses betterperformances after fabrication.

GAN-DUF: Hierarchical Deep Generative Models for Design Under Free-Form Geometric Uncertainty