Inverse design of nonlinear phononic crystal configurations based on multi-label classification learning neural networks

Phononic crystals, as artificial composite materials, have sparked significant interest due to their novel characteristics that emerge upon the introduction of nonlinearity. Among these properties, second-harmonic features exhibit potential applications in acoustic frequency conversion, non-reciprocal wave propagation, and non-destructive testing. Precisely manipulating the harmonic band structure presents a major challenge in the design of nonlinear phononic crystals. Traditional design approaches based on parameter adjustments to meet specific application requirements are inefficient and often yield suboptimal performance. Therefore, this paper develops a design methodology using Softmax logistic regression and multi-label classification learning to inversely design the material distribution of nonlinear phononic crystals by exploiting information from harmonic transmission spectra. The results demonstrate that the neural network-based inverse design method can effectively tailor nonlinear phononic crystals with desired functionalities. This work establishes a mapping relationship between the band structure and the material distribution within phononic crystals, providing valuable insights into the inverse design of metamaterials.