Predicting the Dispersion Relations of One-Dimensional Phononic Crystals by Neural Networks

Abstract

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.

A survey of the iron ligand-to-metal charge transfer chemistry in water

“…This interaction gives rise to extensive associated clusters resulting in the unique surface tension of the solvent, an outstanding polarity and a high dielectric constant. [1][2][3][4][5][6] Another peculiarity of water is the tendency to orient water molecules along their axis of dipole around inorganic cations, anions or organic compounds, respectively leading to the so-called hydration shells that stabilizes the species in the liquid environment. Depending on the size of the ion or the molecule the radius of the hydration cloud and the overall number of water molecules varies drastically and an overall decrease in entropy and Gibbs free energy is achieved.…”

Vibration transmission characteristic prediction and structure inverse design of acoustic metamaterial beams based on deep learning

“…So far, some preliminary results have been obtained in the study of Bragg scattering type acoustic metamaterials. For example, Liu and Yu (2019) predicted the dispersion relations of one-dimensional (1D) phononic crystals by using the deep back propagation neural networks and radial basis function neural networks. Finol et al (2019) respectively used deep convolutional neural network (CNNs) and traditional densely connected neural networks (NNS) to predict the eigenvalue problems of phononic crystals, and concluded that the CNNs was much better than NNs (both deep and shallow).…”

Region-specified inverse design of absorption and scattering in nanoparticles by using machine learning

“…It is worth mentioning that the recent rapid advances in using machine learning for the modeling and design of nano-optic structures are undeniably rooted in increased computation capacity and availability of high-performance hardware, allowing for extensive computations at the training stage. To date, machine learning algorithms have been applied to several forward and inverse photonic problems including, modeling lossless particles [29], design of chiral metamaterials [30], design and characterization of optical elements for metasurfaces [31], inverse design [32][33][34][35][36] and response prediction [37][38][39] in one-dimensional (1D) photonic crystals, inverse design of multilayered nanostructures [40], modeling and design of electric and magnetic dipole response [41], modeling three-dimensional nanostructures [42], and dielectric metasurface design [43]. Interestingly, the machine learning-based design approach is not necessarily a blind data-driven method, and information about the physics of the problem may also be included in the model [44,45].…”