Inverse design of isotropic auxetic metamaterials via a data-driven strategy

Abstract

Efficiently and precisely designed isotropic auxetic metamaterials present significant challenges due to the inherent uncertainties in their geometric configurations. This study introduces an innovative data-driven structural design strategy that enables accurate prediction of the mechanical properties and inverse design for isotropic auxetic metamaterials. Notably, Kolmogorov–Arnold networks (KANs) are utilized, replacing fixed activation functions with learnable functions, to successfully establish a precise mapping between design parameters and mechanical responses for classical missing rib auxetic metamaterials. The predicted mean square error (MSE) for the stress dataset is as low as 0.81%, only one-fourth of that achieved by multilayer perceptron (MLP) models of equivalent width, while computational efficiency surpasses finite element methods by more than 10³ times. Building on this mapping, Model III, optimized using a genetic algorithm, achieves an average MSE of just 0.05%, significantly outperforming the original structure (Model I) and a randomly perturbed structure (Model II) with an average MSE of 2.28% and 1.79%, respectively. Experimental validation and finite element analysis further confirm the accuracy of these results, demonstrating the successful realization of isotropic mechanical response designs. This study presented a data-driven inverse design method as a powerful and efficient tool for the precise design of auxetic metamaterials with isotropic mechanical responses. It holds particular promise for applications in flexible wearable devices and tissue engineering, providing a robust foundation for future innovations in these fields.