Teaming Finite Element Analysis and Deep Learning to Advance Inverse Design of Metamaterial With Adaptive Pressure Response in Footwear Design

Abstract

Abstract. Metamaterials (MMs) offer a promising solution for footwear design by enabling spatially tunable mechanical responses associated with comfort-related considerations. However, the current application of MMs in footwear manufacturing remains relatively limited. Furthermore, effective optimization of MM structures under comfort-related mechanical considerations remains a largely unexplored space. This study explores a framework that teams finite element analysis (FEA) and deep learning (DL) to optimize MM-based shoe sole designs by using the individual plantar pressure distribution data. Specifically, the FEA is deployed to analyze the mechanical response of the sole, and it establishes links among pressure, deformation, and geometry, while a DL model is developed to map plantar pressure to MM lattice geometry. In our proposed method, a multimodal convolutional neural network (CNN) model is designed and trained to predict the optimized lattice-rod radii in MM based on multimodal input, including the pressure image, rod coordinates, and deformation data. The DL-optimized MM structures are subsequently validated through FEA simulations. With this proposed approach, this study conducted a case study relevant to potential footwear applications under a deformation-based surrogate objective. The results show that the proposed method achieves significant improvement in deformation–pressure alignment compared with a benchmark design. In summary, the proposed FEA–DL framework enables direct generation of optimized MM designs from user-specific plantar pressure and a surrogate design objective. This synergistic approach offers a promising pathway to achieve a customizable, efficient, high-performance, resource-conserving inverse design.