Inverse design and spatial optimization of SFAM via deep learning

Pipeline noise is characterized by low-frequency and broadband characteristics, for which space-folded acoustic metamaterials (SFAM) have been proposed as a solution. However, the SFAM design suffers from low efficiency, high errors, and high space occupation. To address these limitations, we proposed a tandem long short-term memory (LSTM)–Transformer autoencoder-like network model for SFAM inverse design. An accurate mapping between structural dimensions and acoustic performance was established using the positional encoding and attention mechanism unique to the Transformer model. More data-implicit features were extracted from the target curves, utilizing the long-term dependencies of the LSTM model. The accurate inverse design of SFAM was realized by concatenating the LSTM model with the pre-trained Transformer model. Through comparison with traditional deep learning networks, such as convolutional neural network (CNN) and multilayer perceptron (MLP), the influence of the model internal structure on the design results was revealed. The experimental results show that the Transformer and LSTM model tandem strategy integrates the advantages, resulting in highly consistent design results with the target curve. Based on multi-objective optimization, the design results were optimized to consider the effects of peak frequency, peak quantity, sound isolation bandwidth, and space occupancy. The two optimized SFAMs not only meet acoustic insulation requirements but also reduce spatial occupancy by 16.81 % and 19.39 %, respectively, providing an efficient and feasible solution for designing acoustic metamaterials under space-constrained conditions.