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.