Data-driven inverse design of aperiodic metastructures for tailored vibration isolation using evolutionary active learning

Traditional metamaterials often struggle to adaptively manage broadband random disturbances and specific frequency resonances for complex equipment under time-varying conditions due to their fixed bandgaps. To address this, we propose a physically embedded evolutionary active learning framework for the inverse customization and intelligent reconfiguration of non-periodic flexible metastructures using small-sample data. Specifically, a hierarchical decoupling strategy—training a Deep Neural Network (DNN) solely for local constitutive mappings and coupling it with physical transfer matrices—is proposed to fundamentally overcome the “curse of dimensionality” inherent in global designs. Furthermore, an active learning-driven closed-loop feedback mechanism is integrated with the Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm. Ablation studies confirm that, by dynamically updating the surrogate model through targeted physical validations, this closed-loop strategy achieves superior convergence efficiency and computational efficiency compared to traditional optimization approaches. Results indicate a coefficient of determination ( R ²) exceeding 0.98 on the validation set, with relative errors kept within 2.0%. The framework demonstrates a hierarchical “global customization-individual reconfiguration” capability. In the passive customization phase, the Pareto front autonomously provides a broad coverage of aperiodic designs to meet diverse isolation requirements. Subsequently, active reconfiguration was validated on two typical configurations selected from the Pareto front. For Configuration 1, current control significantly expanded the tunable ranges: attenuation constants to [0.39, 1.49], starting frequencies to [14.98, 41.90] Hz, and effective bandwidths to [21.74, 68.29] Hz. For Configuration 2, stiffness reconfiguration maintained high attenuation levels [0.51, 1.41] while enabling flexible adjustment of starting frequencies [14.03, 38.57] Hz and bandwidths [16.89, 47.98] Hz. Finally, wave mechanics and experiments confirm that this data-driven approach provides a comprehensive solution for intelligent vibration isolation in complex engineering.