Inverse design of membrane-type acoustic metamaterials based on physics-informed neural networks

Abstract

Inverse design of membrane-type acoustic metamaterials (MAMs) for low-frequency sound insulation is challenged by costly sample acquisition, limited interpretability of purely data-driven models, non-unique solutions, and unstable training. This study proposes a small-sample physics-informed neural network (PINN) framework for performance-oriented inverse design of MAMs. A frequency-domain theoretical model is solved in MATLAB by assembling mass, stiffness, damping, and coupling matrices, and the database is constructed from theoretical solutions. Five key geometric/material parameters are sampled to generate datasets of 5,000, 15,000, and 30,000 samples. Three acoustic indicators are extracted from sound transmission loss (STL) curves: maximum STL, average STL within 150-650 Hz, and the frequency corresponding to maximum STL. A forward surrogate network learns the mapping from structural parameters to acoustic indicators. The frozen forward surrogate, differentiable physical operator, and discrete-parameter constraints are embedded into the inverse network to predict structural parameters from target acoustic performance. To improve optimization stability, dynamic gradient-statistics balancing (DGSB) and neural tangent kernel (NTK)-based adaptive weighting are introduced. The DGSB and NTK strategy achieves the most stable convergence and best overall validation performance. Across database sizes, R2 values range from 0.9498 to 0.9685, with RMSE, MAE, NRMSE, and NMAE used for error evaluation. Finite element simulations and impedance-tube experiments verify the inverse-design results. The predicted structures meet the prescribed acoustic indicators, and the simulated and experimental STL curves show consistent trends. This method provides an efficient and physically interpretable approach for rapid inverse design of low-frequency sound-insulating acoustic metamaterials.