CH-WGAN: Uncertainty-Aware Generative Design of 3D Aperiodic Architected Cellular Materials via Signed Distance Fields

Abstract Architected cellular metamaterials have shifted from periodic lattices to aperiodic arrangements to broaden achievable properties (e.g., anisotropy), but the resulting geometric uncertainty hinders validation, optimization, and manufacturing. We introduce an uncertainty-aware generative design framework that synthesizes diverse, high-fidelity 3D aperiodic architected cellular materials (AACM) while explicitly modeling uncertainty. Our Conditional Hierarchical Wasserstein GAN (CH-WGAN) hypothesizes dependencies between periodic (nominal) and aperiodic (variant) unit cells. A Parameter Generator maps nominal control parameters and an aperiodicity code, together with latent noise, into a convex mixture of analytically defined signed distance functions (SDFs). Mixture coefficients, scales, and learned periodicity distributions directly encode geometric uncertainty. A periodicalization module adaptively warps the 3D grid according to these distributions to capture spatially varying periodicity. The critic employs a Wasserstein gradient-penalty (GP) loss for realism and an InfoGAN-style Q-head with latent-regression and entropy/KL objectives to promote invertibility and multi-modal coverage. Trained on paired nominal–variant SDF data, CH-WGAN disentangles intrinsic geometry from uncertainty in periodicity, enabling multiple plausible variants for a given periodic parent. Quantitative statistics and marching-cubes visualizations show that generated variants match real aperiodicity distributions and maintain structural fidelity, while offering interpretable control over uncertainty factors. Compared with traditional probabilistic models and purely data-driven baselines, our approach reduces assumptions, improves sample quality/diversity, and enhances interpretability. The framework provides a robust, generalizable tool for uncertainty-aware exploration of AACM design spaces.