An Uncertainty-aware Deep Learning Framework-based Robust Design Optimization of Metamaterial Units

TL;DR

A novel uncertainty-aware deep learning framework-based robust design approach is proposed for the design of metamaterial units with optimal target properties and it is demonstrated that the proposed design approach is capable of designing high-performance metamaterial units with high reliability.

Abstract

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.

Figures (13)

• Figure 1: An uncertainty-aware deep learning framework is employed to characterize 3D metamaterial units and their mechanical properties, incorporating uncertainty in the analysis. This model is composed of two primary elements: a DGM that extracts low-dimensional features and a PDNN that forecasts properties. The outputs of the PDNN, encompassing both mean values and standard deviations, offer a probabilistic interpretation of the mechanical behaviors.
• Figure 2: Performing robust design optimization on the trained latent feature space. The optimization seeks to reduce the aggregate impact of the predicted mean and corresponding uncertainty across various property values.
• Figure 3: Examples of metamaterial units in three data sources.
• Figure 4: Generation process of the dataset and histograms of the elastic modulus and Poisson's ratio across all three data sources.
• Figure 5: Distribution of negative and positive Poisson's ratio samples in the dataset.