Neural Network-Based Inverse Design of Nonlinear Phononic Crystals

Phononic crystals are artificial periodic structural composites. With the introduction of nonlinearity, nonlinear phononic crystals(NPCs) have shown some novel properties beyond their linear counterparts and thus attracted significant interest recently. Among these novel properties, the second harmonic characteristics have potential applications in the fields of acoustic frequency conversion, non-reciprocal propagation, and nondestructive testing. Therefore, how to accurately manipulate the second harmonic band structure is a main challenge for the design of NPCs. Traditional design methods are based on parametric analysis and continuous trials, leading to low design efficiency and poor performance. Here, we construct the convolutional neural networks(CNNs) and the generalized regression neural networks(GRNNs) to inversely design the physical and geometric parameters of NPCs using the information of harmonic transmission curves. The results show that the inverse design method based on neural networks is effective in designing the NPCs. In addition, the CNNs have better prediction accuracy while the GRNNs have a shorter training time. These methods also can be applied to the design of higher-order harmonic band structures. This work confirms the feasibility of neural networks for designing the NPCs efficiently according to target harmonic band structures and provides a useful reference for inverse design of metamaterials.