School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, China.
Sci Rep. 2019 Oct 25;9(1):15322. doi: 10.1038/s41598-019-51662-3.
In this paper, deep back propagation neural networks (DBP-NNs) and radial basis function neural networks (RBF-NNs) are employed to predict the dispersion relations (DRs) of one-dimensional (1D) phononic crystals (PCs). The data sets generated by transfer matrix method (TMM) are used to train the NNs and detect their prediction accuracy. In our work, filling fractions, mass density ratios and shear modulus ratios of PCs are considered as the input values of NNs. The results show that both the DBP-NNs and the RBF-NNs exhibit good performances in predicting the DRs of PCs. For one-parameter prediction, the RBF-NNs have shorter training time and remarkable prediction accuracy, for two- and three-parameter prediction, the DBP-NNs have more stable performance. The present work confirms the feasibility of predicting the DRs of PCs by NNs, and provides a useful reference for the application of NNs in the design of PCs and metamaterials.
本文采用深度反向传播神经网络（DBP-NNs）和径向基函数神经网络（RBF-NNs）来预测一维（1D）声子晶体（PCs）的频散关系（DRs）。利用传递矩阵法（TMM）生成的数据集对神经网络进行训练，并检测其预测精度。在我们的工作中，PCs 的填充率、质量密度比和剪切弹性模量比被视为神经网络的输入值。结果表明，DBP-NNs 和 RBF-NNs 都能很好地预测 PC 的 DRs。对于单参数预测，RBF-NNs 具有较短的训练时间和显著的预测精度，对于双参数和三参数预测，DBP-NNs 具有更稳定的性能。本工作证实了神经网络预测 PC 的 DRs 的可行性，并为神经网络在 PC 和超材料设计中的应用提供了有益的参考。
