Prediction of sound absorption in TPMS-based acoustic metamaterials using convolutional neural networks and machine-learning-based feature importance analysis

Noise pollution has become a major concern recently, and acoustic metamaterials have shown great potential to mitigate it. Among different acoustic metamaterials, sheet/shell lattices based on triply periodic minimal surfaces (TPMS) are a promising class known for their sound-absorbing properties. However, studying these materials through experiments, as well as theoretical approaches (such as numerical simulations and analytical solutions), can be very complex and expensive. To solve this, we developed a deep learning model using a 1D convolutional neural network (CNN) to predict the sound absorption coefficient (SAC) of TPMS structures. We generated training and validation data through theoretical predictions based on multi-physics finite element simulations using a thermoviscous acoustic constitutive model for three TPMS topologies: Gyroid, FRD, and FKS. The input features for each topology included porosity levels (70%, 80%, 90%), cell sizes (3 mm, 5 mm, 7 mm), and thicknesses (10 mm, 15 mm, 20 mm, 30 mm) across frequencies from 200 Hz to 6400 Hz (with 200 Hz intervals). After preparing the data, we built and trained the CNN model, which includes convolution, flatten, and feed-forward layers. The performance of the proposed model was compared with other machine learning models, like the random forest algorithm and XGBoost, where the CNN provided better prediction accuracy. The predicted SAC values matched well with cross-validation results and experimental values, with less than 5% error. We also performed machine learning-based feature importance analysis using permutation to determine how each input feature (frequency, cell size, porosity, and thickness) affects the SAC. The analysis revealed that frequency is the dominant factor influencing sound absorption across Gyroid, FRD, and FKS topologies, followed by sample thickness and cell size, while porosity showed minimal impact within the considered range of 70–90%. These findings were further validated by energy dissipation data from the simulations at resonance frequencies. The outcomes of this study provide researchers with an efficient framework to accurately predict and optimize sound absorption performance in cellular structures, offering a significant reduction in computational time and cost relative to conventional approaches.