On-Demand Inverse Design of Phononic Metamaterials via Deep Learning

Metamaterials are engineered structures whose exceptional macroscopic properties stem primarily from the geometric arrangement of their subwavelength unit cells. Among the various classes of metamaterials, phononic metamaterials are specifically designed to manipulate the propagation of elastic and acoustic waves by inducing frequency band gaps, regions where waves cannot propagate. Unlike mechanical metamaterials that rely on static properties, phononic metamaterials exploit dynamic, wavelength-scale periodicity to achieve wave control. The inverse design of phononic metamaterials, which aims to generate unit cell configurations that yield user-specified bandgap characteristics, remains a fundamentally challenging problem. This is due to the nonlinear, high-dimensional, and non-unique nature of the structure-to-response mapping. Conventional optimization methods often encounter significant limitations, including high computational cost, limited solution diversity, and poor scalability. To address these challenges, this thesis develops and evaluates three deep learning-based frameworks for the inverse design of two-dimensional phononic metamaterials. The first is a tandem neural network model, augmented with Bayesian optimization, which couples forward and inverse networks to enhance design consistency. The second is a conditional variational autoencoder, which learns a structured latent space and enables the generation of multiple valid solutions for a given set of target properties. The third is a denoising diffusion probabilistic model, which gradually transforms random noise into binary topological structures aligned with specified bandgap features. Crucially, all models are trained and validated using large-scale datasets generated through high-fidelity finite element simulations. These datasets consist of thousands of binary unit cell geometries and their corresponding band structures, computed under Bloch-periodic boundary conditions. For each design, the dispersion relation is calculated along high-symmetry paths in the Brillouin zone to extract relevant metrics such as bandgap width and mid-frequency. The finite element method serves as the foundation for generating physically accurate data, ensuring that the training process is grounded in reliable simulations. Beyond model development, this work provides a comprehensive methodological contribution to the field of inverse metamaterial design. In particular, the diffusion-based framework demonstrates superior generative diversity and fidelity, effectively capturing the inherent one-to-many relationship between geometry and wave behavior. Collectively, the proposed approaches establish a scalable, data-driven foundation for the automated, efficient, and physically consistent design of functional phononic metamaterials.