  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.
