Abstract Phononic crystals achieve precise acoustic wave manipulation by utilizing engineered band gaps properties arising from periodic structures or local resonance effects to enable. Traditional finite element methods struggle to simultaneously optimize band gaps accuracy, width, and structural robustness. Besides, existing machine learning approaches, despite advancing forward prediction capabilities, remain are constrained by the non-uniqueness issue in band-structure mapping during inverse design. This study presents a physics-informed deep learning framework integrating adaptive composite loss functions and dual-branch feature extraction to address the challenge of forward prediction and inverse design in pentamode metamaterials. A convolutional neural network with a hybrid loss function comprising smoothness regularization, peak alignment penalty, and dynamic boundary constraints was constructed for forward modeling, which enhanced the reconstruction fidelity of key phonon band gaps features, and achieved a mean prediction accuracy of 99.1%. For inverse design, a dual-branch Transformer was developed, which combined convolutional extraction of global band gaps parameters with attention-based encoding of local dispersion topology. This architecture effectively mitigated the non-uniqueness in spectral-to-structure mapping, achieving a validation accuracy of 98.2%. Six inversedesigned structures exhibited precise alignment with target band gaps in the specified frequency ranges. This framework accelerates the design of bidirectional phononic crystal, and is particularly expected to be used in multi-frequency and broadband acoustic control applications.
Wang et al. (Tue,) studied this question.