Deep learning-assisted multi-objective optimization of labyrinthine ventilated acoustic metamaterials

Labyrinthine ventilated acoustic metamaterials (LVAMs) offer great potential for applications requiring both strong sound insulation and efficient airflow, yet simultaneously optimizing these conflicting objectives remains a fundamental challenge. Unlike previous studies that directly regress the sound transmission loss (STL), this work introduces a novel deep-learning-assisted, transfer-matrix-based framework, enabling analytical STL computation for arbitrary serial combinations of unit cells. A forward predictor network (FPN) is trained to predict the four components of the transfer matrix for a single unit cell, enabling analytical computation of the STL of arbitrary serial combinations of unit cells. To enhance robustness, a peak-softening preprocessing strategy and a value-weighted loss function are introduced, yielding predictions that better align with experimentally realizable performance. The FPN is integrated with the NSGA-II algorithm to jointly optimize STL and ventilation capacity, quantified by the open area ratio, thereby obtaining Pareto-optimal designs that balance these objectives. Numerical studies demonstrate the scalability and flexibility of the proposed method across various frequency ranges and STL thresholds. Experimental validation of 3D-printed prototypes confirms close agreement between predictions, simulations, and measurements, with the proposed framework outperforming direct STL prediction, particularly near resonance frequencies. This work highlights the potential of using intermediate physical representations in deep-learning-assisted optimization of multifunctional acoustic metamaterials.