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

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.