Generative inverse design of multimodal resonant structures for locally resonant metamaterials

TL;DR

This paper introduces a machine learning-based method using a conditional variational autoencoder to design multimodal resonant structures for locally resonant metamaterials, enabling efficient creation of multi-bandgap materials with predefined properties.

Contribution

It presents a novel inverse design approach for complex-shaped resonators using a conditional variational autoencoder, significantly reducing design time and improving accuracy with limited training data.

Findings

The autoencoder performs well with limited data from a few hundred modal analyses.

Generated designs closely match targeted modal characteristics.

Experimental validation confirms the accuracy of the designs and their dispersion properties.

Abstract

In the development of locally resonant metamaterials, the physical resonator design is often omitted and replaced by an idealized mass-spring system. This paper presents a novel approach for designing multimodal resonant structures, which give rise to multi-bandgap metamaterials with predefined band gaps. Our method uses a conditional variational autoencoder to identify nontrivial patterns between design variables of complex-shaped resonators and their modal effective parameters. After training, the cost of generating designs satisfying arbitrary criteria - frequency and mass of multiple modes - becomes negligible. An example of a resonator family with six geometric variables and two targeted modes is further elaborated. We find that the autoencoder performs well even when trained with a limited dataset, resulting from a few hundred numerical modal analyses. The method generates several designs that very closely approximate the desired modal characteristics. The accuracy of the best designs, proposed by the auto-encoder, is confirmed in tests of 3D-printed resonator prototypes. Further experiments demonstrate the close agreement between the measured and desired dispersion relation of a sample metamaterial beam.