A data-driven framework for band-structure optimization and valley-topological control in phononic crystals

Band-structure characteristics in phononic crystals are highly sensitive to structural variations and strong multi-parameter coupling, necessitating dense sampling to effectively explore the design space. However, exhaustive searches are computationally prohibitive when using traditional simulations. To address this challenge, a Multilayer Perceptron (MLP) based surrogate model was developed and integrated with particle swarm optimization for efficient optimization of the valley-related branch separation. Its performance was benchmarked against convolutional neural network and support vector machine models. Additionally, unit-cell rotation was introduced as a key degree of freedom, allowing data-driven optimization and topological regulation to be incorporated into a unified design framework. The results demonstrated that the MLP model outperformed the comparative models in both prediction accuracy and convergence behavior, achieving a mean squared error of 6.54 × 10−5. Simultaneously, the trained MLP achieved a per-configuration speedup of approximately 8 × 104 times compared to finite element method simulations. The optimized valley-related branch separation had a width of 16 229 Hz, with lower and upper frequency bounds of 7349 and 23 578 Hz, respectively, along the Γ–K–M–Γ path. Further analysis revealed that rotational modulation induces band-structure reconstruction, generating valley-dependent edge states with controllable topological phase transitions and enabling robust propagation of interface states within the constructed heterostructure, even under complex structural perturbations. Overall, this work achieved an effective integration of data-driven design and physical mechanism regulation, providing a unified and scalable framework for the topological optimization of phononic crystal structures.