Inverse design of nano-sized FGM phononic crystals with anticipated band gaps using probabilistic generation based deep-learning network

Current research on the inverse design of phononic crystals, which aim to retrieve optimal structures according to given band gaps, is limited to controlling elastic waves at the macro-scale. This work extends the concept to nano-scale and implements this concept with phononic nanobeam made up of functionally graded materials by applying the nonlocal strain gradient theory and the probabilistic tandem network (PTN), which is responsible for detecting size effects and unveiling implicit relationships between band gaps and nanostructures. An analytical model that has not been published before is proposed based on the plane wave expansion method to predict band structures within size, thickness and porosity effects, enabling quick preparation for composing a dataset to train the network. Acting as an auto-encoder-like framework, the component of PTN in the reverse path allows to effectively encode required band gaps into a latent space, while the network in the forward path serves as a surrogate model to map the candidates from the latent space to band gaps. Numerical results not only show the influences of size effects on band gaps but also verify the accuracy, diversity, and generalization ability to meet different requirements of the inverse design. The proposed PTN can fulfill the on-demand design by generating multiple phononic nanobeams possessing same man-made band gaps. Undoubtedly, the framework proposed in the present work makes it a promising approach to provide flexible and diversified solutions, paving the way to discovering innovative phononic crystals at nano-scale. •A nonclassic model is developed to predict band gaps with size and thickness effects.•The inverse design is realized for FGM PnCs at the nanoscale by DL-based framework.•Diversified feasible designs regarding same requirement of band gaps are obtained.•Accurate FGM nano-PnCs are produced corresponding to band gaps tailored on-demand.