Full-Spectrum Inverse Design of Compact Ring-Curve Fractal-Maze Acoustic Metamaterials via an LSTM–PPS-Net Tandem Framework

Low-frequency sound insulation remains a major challenge for conventional passive materials, as improved attenuation is usually achieved at the expense of increased thickness and mass. In this work, a smooth fixed third-order ring-curve fractal-maze acoustic metamaterial is proposed for compact low-frequency sound insulation, and a physics-guided long short-term memory–physics prediction surrogate network (LSTM–PPS-Net) tandem framework is developed for its full-spectrum inverse design. Different from conventional Hilbert-type, right-angled, or sharply folded labyrinthine structures, the proposed topology uses recursively arranged curved channels to extend the effective acoustic propagation path and enhance phase accumulation within a limited space. Based on this mechanism, four physically meaningful parameters, namely slit width d, characteristic radius R3, wall thickness tw, and inter-column spacing lE, are selected to construct a low-dimensional design space. A COMSOL–MATLAB automated finite-element method (FEM) workflow is established to generate 1000 valid transmission-loss (TL) spectra over 100–1700 Hz with a 5 Hz interval. For forward prediction, PPS-Net is developed by integrating geometry encoding, frequency-conditioned spectral decoding, and peak-weighted learning. The proposed PPS-Net achieves the best prediction accuracy among the tested models, with a mean absolute error (MAE) of 0.75 dB, a root mean square error (RMSE) of 1.88 dB, and a coefficient of determination (R2) of 0.96, outperforming multi-layer perceptron (MLP), convolutional neural network (CNN) and Transformer models under the same dataset and training protocol. For inverse design, the LSTM encoder extracts frequency-ordered spectral features from the target TL curve, while the frozen PPS-Net decoder provides differentiable acoustic-response feedback, thereby addressing the non-unique mapping from acoustic response to structural parameters. Furthermore, a compactness-oriented optimization strategy is introduced to balance spectral consistency, peak alignment, bandwidth preservation, and occupied-area reduction. In two representative cases, the optimized designs reduce the occupied area by approximately 21% in both representative cases, while maintaining the target attenuation characteristics after FEM verification. These results demonstrate that the proposed framework provides an efficient and physically interpretable route for the full-spectrum inverse design and compact optimization of low-frequency acoustic metamaterials.