On demand design of two-dimensional phononic crystal bandgap based on machine learning and multi-objective topology optimization

To address the issue of human resource wastage and the lack of direction in phononic crystal design, this study adopts the network structures of variational autoencoder, multi-layer perceptron, and twin neural network, to achieve high-precision forward and inverse predictions for two-dimensional phononic crystals. Five-fold cross-validation was conducted on the dataset, and the resulting accuracy demonstrated the strong generalization capability and robustness of the model structures of the multi-layer perceptron and twin neural network. Specifically, 90% of the accuracy values in forward predictions are equal to or greater than 0.98, while 98% of the accuracy values in inverse predictions are no less than 0.95. From a practical design standpoint, by incorporating a loss function into the twin neural network while considering both lightweight and bandgap performance, we can achieve high-precision, on-demand design with multiple objectives. The approach and methodology presented in this study offer significant insights for the rapid and accurate development of composite or structured materials.