A surrogate-assisted generative framework for on-demand inverse design of phononic metamaterials

This work presents a surrogate-assisted generative framework for on-demand inverse design of two-dimensional phononic metamaterials with prescribed lower and upper band-edge frequencies. A C 4v -symmetric binary representation with 136 independent variables is adopted, and 100,000 valid unit-cell designs are evaluated using Bloch-Floquet finite element analysis. A multilayer perceptron is trained as a forward surrogate to predict the lower and upper band edges, achieving mean absolute errors of 1.271 and 1.215 kHz and coefficients of determination of 0.9700 and 0.9675 on the held-out test set. A conditional generative adversarial network then generates candidate topologies, followed by geometric filtering, surrogate-based ranking, diversity-aware selection, and final Bloch-FEM verification. Over 100 held-out test targets, the framework achieves a 97% FEM-valid target rate and an 89% success rate within a 5% band-edge tolerance, with mean absolute errors of 2.189 and 1.969 kHz. Budget-controlled ablation identifies surrogate screening as the dominant contributor to target accuracy. By restricting FEM verification to 10 of 100 generated candidates, the framework reduces the online FEM budget by 90% and yields an estimated 9.89× wall-clock speedup relative to verifying all candidates by FEM. These results demonstrate an effective balance between generative exploration, rapid surrogate screening, and direct numerical verification.